% File: bmcm9203.tex
\documentstyle[twocolumn,bmcmtr,citead]{article}

\newcommand{\dd}[2]{\frac{d \; #1}{d #2}}

\newcommand{\rpl}{replicator}
\newcommand{\intr}{interactor}
\newcommand{\lng}{longevity}
\newcommand{\arpl}{A-rep\-licator}
\newcommand{\arpls}{A-rep\-licators}
\newcommand{\lrpl}{L-rep\-licator}
\newcommand{\lrpls}{L-rep\-licators}
\newcommand{\alng}{A-longev\-ity}
\newcommand{\llng}{L-longev\-ity}
\newcommand{\agene}{A-gene}
\newcommand{\lgene}{L-gene}
\newcommand{\agenes}{A-genes}
\newcommand{\lgenes}{L-genes}

\begin{document}

\trnum{9203}
\date{May 1992}
\title{Essays on Darwinism \\3: Genic and Organismic Selection}
\maketitle

\begin{abstract}
The notion that {\em genes\/} play a uniquely distinguished
\role\ in biological evolution has been championed by Richard
Dawkins \cciteD{Dawkins:SelfishGene,Dawkins:NewSelfishGene}.
Furthermore, Dawkins has argued that this idea can be generalised
in a way which makes it applicable to any properly Darwinian
evolutionary process, at least if that process gives rise to a
growth in adaptive complexity
\cciteAD{Dawkins:UniversalDarwinism}.  It is evident, therefore,
that if Dawkins' analysis is correct, it has profound
implications for any attempt to realise a growth of adaptive
complexity in {\em artificial systems\/} by Darwinian means.

This essay is concerned with a detailed evaluation and critique
of Dawkins' claims, and, to a lesser extent, of the related
analysis carried out by David L.~Hull
(\ociteD{Hull:IndividualityAndSelection,Hull:UnitsOfEvolution}).
It provides a reformulation which, it is claimed,
captures the core of valid insights which these workers have
achieved while, at the same time, avoiding certain confusions
and misconceptions which might otherwise be read into their views.

The essay draws on concepts introduced in two previous essays
(McMullin
\ociteD{McMullin:DarwinianOntology,McMullin:Organismic}); the
three essays are therefore best read in conjunction with each
other.

\end{abstract}

\pagenumbering{roman}
\tableofcontents

\pagenumbering{arabic}
%\draft

\section{Introduction}

In this essay I review the debate between so-called ``genic'' and
``organismic'' selection. The {\em problem\/} being addressed
here is what I have previously \cciteAD{McMullin:Organismic}
called {\em Darwin's Problem\/} (or \pr{d}): it is the problem of
the phylogenetic growth of adaptive complexity (in at least some
organismic lineages). Further, the {\em solution\/} presented in
that previous essay is still accepted here in its essential
respects---i.e.\ that this growth arose primarily, if not
exclusively, by a process of unjustified variation and natural
selection.  The {\em only\/} point at issue here is which
biological entities can or should be considered as the Darwinian
{\em actors\/} (D-actors---see
\ociteAD{McMullin:DarwinianOntology}; this terminology is briefly
reviewed in the next section) in this process.  In the
analysis of \cciteAD{McMullin:Organismic} the D-actors were taken
to be organisms (hence {\em organismic\/} Darwinism).  In this
essay I want to consider whether there are any ``rival''
candidates for this \role, and, if so, whether we can establish
any preferences among them.

I will be concentrating almost exclusively on the contributions
of David L.~Hull and Richard Dawkins to the analysis of this
issue. I should therefore make absolutely clear, at the outset,
my admiration and respect for these two men and their work. It is
only because of this respect that, even as a relative outsider to
the fields in question, I venture to offer criticism of
aspects of their views, and some limited suggestions for
improvement and clarification.  But certainly, if I have
succeeded in making any worthwhile contribution at all, it is
only because I have been able to build on the insights which Hull
and Dawkins had already carved out.

\section{Terminology}

This section provides a short summary of terminology introduced
in \cciteAD{McMullin:DarwinianOntology}; please consult that
essay for more detailed discussions.

Very briefly, {\em actors\/} are individuals which reproduce,
with some degree of heritability. A Similarity-lineage or {\em
S-lineage\/} is a lineage of actors which includes, at each
generation, {\em only\/} those offspring which are ``similar'' to
their parent(s) in some specified way.  Distinct, heritable,
``similarities'' (similarity-classes or {\em S-classes\/}) thus
distinguish distinct S-lineages.  In the general case, any given
actor may be a member of many distinct S-lineages.  In certain
circumstances an S-lineage may grow consistently until limited by
resource availability; and, in so doing, may exclude or eliminate
one or more other S-lineages.  This is S-lineage {\em selection}.
{\em S-value\/} is a parameter of an S-lineage such that
differences in S-value are predictive of the rate and ultimate
outcome of selection.

The birth of an actor with some heritable characteristic not
possessed by any of its parents is called {\em S-creation}.
S-creation initiates new S-lineages. If S-creation is
unjustified (not informed by anticipatory models of S-value) the
actors are called Darwinian- or {\em D-actors}. A lineage of
D-actors, incorporating multiple distinct S-lineages, whose
evolution can be usefully described in terms of selection events
between those S-lineages, is called a {\em D-lineage}.
A system of D-actors, forming D-lineage(s), is called a {\em
D-system.}

\section{Replicating Confusion}

\label{repl}

There has been considerable ambiguity, if not confusion, in the
literature of evolutionary biology regarding specific technical
usage of the terms {\em replication\/} and {\em replicator}. I
hope to clear up some of this ambiguity in the course of my
detailed discussion of genic and organismic selection; but before
proceeding with that, I should like to illustrate these problems
of interpretation in a general way.

As far as I am aware, the abstract, technical, idea of a {\em
replicator\/} was first introduced by Dawkins
\cciteD{Dawkins:SelfishGene,Dawkins:ReplicatorSelection}.  Hull
subsequently elaborated the idea (Hull
\ociteD{Hull:IndividualityAndSelection,Hull:UnitsOfEvolution}),
and Dawkins has since extended his own analysis somewhat further
\cciteAD{Dawkins:ExtendedPhenotype}. I shall generally be relying
on these sources in the discussion which follows.

I shall argue that ``replicator'' has been used to refer to at
least two distinct kinds of entity, corresponding roughly to my
\mbox{(D-)actors} and \mbox{(S-)lineages}; and that the distinction
between these two kinds of entities (which I consider crucial)
has not been satisfactorily recognised or respected.

Where necessary in the following, I shall explicitly distinguish
the two possible meanings of ``replicator'' as {\em \arpl,} for
actor-replicator, and {\em \lrpl,} for lineage-replicator.

The ambiguity of usage can be conveniently illustrated by
considering the concept of replicator {\em longevity}, introduced
by Dawkins. In {\em The Selfish Gene\/}, Dawkins first defines
longevity as relating to the lifetime of an individual
replicator, i.e.\ an \arpl:
\begin{quote}
  Certain molecules [supposed primordial replicators], once
  formed, would be less likely than others to break up again.
  These types would become relatively numerous in the soup, not
  only as a direct logical consequence of their `longevity', but
  also because they would have a long time available for making
  copies of themselves.  Replicators of high longevity would
  therefore tend to become more numerous and, other things being
  equal, there would have been an `evolutionary trend' towards
  greater longevity in the population of molecules.
  \iciteAD[p.~18]{Dawkins:SelfishGene}
\end{quote}

He goes on to argue that there would be an overall trend toward
the evolution of ``varieties'' (classes or lineages?) of
replicator with high ``longevity/fecundity/copying-fidelity''
\cciteAD[p.~19]{Dawkins:SelfishGene}.\footnote{Note
  carefully that Dawkins' ``fecundity'' here refers to \arpls; it
  should not be confused with my {\em S-fecundity\/} which properly
  refers only to S-lineages, or \lrpls.}

Henceforth, I shall call this first form of longevity {\em
\alng,} for actor-longevity.

Somewhat later in the same source, Dawkins specifies that
``Copying fidelity is another way of saying
longevity-in-the-form-of-copies {\em and I shall abbreviate this
simply to longevity\/}'' \cciteAD[p.~30, emphasis
added]{Dawkins:SelfishGene}.  Now {\em this\/} version of longevity
evidently refers to a replicator viewed as a lineage
(``in-the-form-of-copies''), or \lrpl. Henceforth, I shall call
this {\em \llng,} for lineage-longevity.

So far, any confusion is latent: as long as we remember that
Dawkins is using ``longevity'' in two quite different ways, and
judge his meaning from the context, it should not cause too much
trouble.  In particular, we might reasonably suppose that the
slogan ``longevity/fecundity/fidelity'' will always refer to
\arpls, not to \lrpls---i.e.\ the ``longevity'' in question will
be \alng\ rather than \llng. I say this for two distinct reasons.
Firstly, \alng\ is the sense of longevity with which Dawkins
first introduced the slogan. But secondly, and more
significantly, Dawkins claims that \llng\ is effectively
synonymous with copying {\em fidelity\/} (a dubious equation in
any case, but let it stand). It follows that, if the longevity in
the slogan were interpreted as \llng, the slogan would become
synonymous with ``fidelity/fecundity/fidelity''---which is at
least redundant and confusing, if not actually incoherent.

Unfortunately, however, Dawkins did indeed subsequently use the
slogan in precisely this confusing way:
\newpage
\begin{quote}
  The qualities of a good replicator may be summed up in a slogan
  reminiscent of the French Revolution: Longevity, Fecundity,
  Fidelity [Dawkins
  \ociteD{Dawkins:SelfishGene,Dawkins:ValueJudgements}]. Genes
  are capable of prodigious feats of fecundity and fidelity.
  {\em In the form of copies of itself, a single gene may persist
  for a hundred million individual lifetimes.}

  \nopagebreak
  \begin{quote}
  Dawkins\\
  \cciteD[p.~68, emphasis added]{Dawkins:ReplicatorSelection}
  \end{quote}
\end{quote}

So we have the slogan, which I have just argued {\em must\/}
imply \arpl, followed immediately by an elaboration that
obviously implies \lrpl. Given Dawkins' own confusion here, it is
hardly surprising that Hull then compounded the error further:
\begin{quote}
  According to Dawkins
  [\ociteAD[p.~68]{Dawkins:ReplicatorSelection}],
  the qualities of a good replicator may be summed up in a slogan
  reminiscent of the French Revolution: Longevity, Fecundity,
  Fidelity.  As striking as this slogan is, it can easily be
  misunderstood.  The fidelity which Dawkins is talking about is
  copying-fidelity, and the relevant longevity is
  longevity-in-the-form-of-copies [\ociteAD[p.~19,
  p.~30]{Dawkins:SelfishGene}].
  \iciteAD[p.~31]{Hull:UnitsOfEvolution}
\end{quote}

Hull's last citation here refers to the two locations in {\em The
Selfish Gene\/} (1976 edition), which I have already identified
above, where ``longevity'' was defined---but he omits to mention that
these are two different, {\em and incompatible,} definitions!

Hull is surely correct that Dawkins' slogan may be easily
``misunderstood''---for, on my view, both he (and Dawkins
himself) have suffered from just such misunderstanding. The
interpretation Hull gives here is not the ``correct'' one---i.e.\
that which accompanied the original formulation of the slogan in
\cciteAD[p.~19]{Dawkins:SelfishGene}, and which referred to
\arpls---but the confusing and redundant one which refers to
\lrpls\ (Dawkins \ociteD[p.~30]{Dawkins:SelfishGene};
\ociteD[p.~68]{Dawkins:ReplicatorSelection}).

Hull also uses Dawkins' slogan ``longevity, fecundity and
fidelity'' in another paper
\citeAD[p.~317]{Hull:IndividualityAndSelection}, but, on this
occasion, citing only \cciteAD{Dawkins:ReplicatorSelection} as
the source. Again, Hull goes on to specify that the ``relevant
longevity concerns the retention of structure through descent''
(i.e.\ \llng).  Again, he does not comment on the fact that
(according to Dawkins) this version of longevity is synonymous
with (Dawkins' version of) fidelity, and is therefore redundant
and confusing as a separate criterion for judging replicators, of
{\em either\/} kind.

The problem is further compounded by
\citeAD[p.~84]{Dawkins:ExtendedPhenotype} where he quotes, at
length, from \cciteAD{Hull:IndividualityAndSelection}, and
specifically endorses Hull's interpretation of longevity in this
context---thus reinforcing the confusion he himself originated in
\cciteAD{Dawkins:ReplicatorSelection}.

I should point out that, although Hull may have been led astray by
Dawkins on the use of the term {\em longevity}, as such, he also quite
independently originated a related confusion himself.  Recall
that the underlying problem is not really concerned with
longevity as such, but with the distinction between \arpl\ and
\lrpl. So consider this passage:
\begin{quote}

  Certain entities (replicators) pass on their structure largely
  intact from generation to generation.  These entities either
  interact with their environments in such a way as to bias {\em
  their\/} distribution in later generations or else produce more
  inclusive entities that do.

  \nopagebreak
  \begin{quote}
  Hull\\
  \cciteD[p.~315,emphasis added]{Hull:IndividualityAndSelection}
  \end{quote}
\end{quote}

Clearly, Hull means \arpl\ here. Indeed, Hull emphasises this
interpretation---that a replicator is an individual, which may
form a component of a lineage, but is not itself a lineage in
general---in several distinct passages. But in the passage quoted
above he refers to these entities biasing ``their'' distribution
in later distributions. Now an \lrpl\ might properly be said to
have a ``distribution'' (i.e.\ a size); but an \arpl, as such
cannot have a ``distribution'' in any coherent sense---most
especially not in a ``later generation''.

As it happens, Dawkins typically (but by no means exclusively)
adopts the opposite usage---replicator in the sense of \lrpl\
rather than \arpl. But, on the other hand, Dawkins also
alternates between the two usages with bewildering speed.  Thus,
we have the following two comments (quoted from consecutive
paragraphs):
\begin{quote}
  A {\it germ line replicator\/} (which may be active or passive)
  is a replicator that is potentially the ancestor of an
  indefinitely long line of descendant replicators\ldots\newline
  [{\em Evidently this refers to \arpls}.]

  \pagebreak
  \ldots\ But whether it succeeds in practice or not, any germ
  line replicator is {\em potentially immortal}. It `aspires' to
  immortality but in practice is in danger of failing.\newline
  [{\em Yet now we must be talking about \lrpls.}]
  \iciteAD[p.~83]{Dawkins:ExtendedPhenotype}
\end{quote}

This confusion between \arpl\ and \lrpl\ is counter\-pointed
(presumably with unconscious irony) by Dawkins' approving remark,
that {\em Hull\/}
\cciteD{Hull:IndividualityAndSelection,Hull:UnitsOfEvolution}
is ``particularly clear about the logical status of
the lineage, and about its distinction from the replicator and the
interactor'' \cciteAD[p.~100]{Dawkins:ExtendedPhenotype}.

% [This next bit is just *too* obscure...]
%
% Dawkins is certainly aware of the possibility of some kind of
% confusion, for he has explicitly referred to such a danger:
% \begin{quote}
%
%   This does not mean, of course, that genes or other replicators
%   literally face the cutting edge of natural selection.  It is
%   their phenotypic effects that are the proximal subjects of
%   selection. I have been sorry to learn that the phrase
%   `replicator selection' can be misunderstood along those lines.
%   One could, perhaps, avoid this confusion by referring to
%   replicator survival rather than replicator selection.
%
%   \iciteAD[p.~47]{Dawkins:ReplicatorsAndVehicles}
% \end{quote}
%
% Viewed out of context, Dawkins seems to be saying here that he
% has been previously been in the habit of using the phrase
% `replicator selection' rather than `replicator survival'; but in
% fact, `replicator survival' is precisely the term which Dawkins
% had already {\em adopted\/} just one page earlier!

In conclusion: the objective of this section has been simply to
establish that, though Dawkins and Hull make considerable use of
the term {\em replicator,} their usage is quite generally
ambiguous as between \arpl\ and \lrpl, and calls for very careful
interpretation.  The recognition of this fact is an essential
prerequisite for the analysis of their theories and arguments in
following sections.

\section{Two Questions}

I suggest that the following two substantive questions in
evolutionary biology have been wrongly confounded, and that the
terminological confusion discussed in the previous section has
contributed significantly to this. The first question may be put
as follows:
\begin{description}

\item 1: {\em Is the unit of selection an actor or an
\mbox{(S-)lineage?}}

\end{description}

This is an issue, specifically raised by Dawkins, which I believe
to be of central importance to any abstract analysis or
understanding of Darwinism. I have already considered this
question at some length
\cciteAD[Section~11]{McMullin:DarwinianOntology}. I
accepted Dawkins' particular formulation of this question (``The
central theoretical problem of teleonomy will be that of the
nature of the entity for whose benefit adaptations may be said to
exist''---\ociteAD[p.~81]{Dawkins:ExtendedPhenotype}). I will not
repeat that discussion, but simply note my conclusion (which I
take to be identical with Dawkins' conclusion, though expressed
in different terminology): that {\em only\/} S-lineages can be
said to be units of selection in this substantive sense.

I consider this to be a very important insight into the Darwinian
process.  It is a substantial clarification compared to earlier
views of Darwinian theory which presumed that actors were the
units of selection. Indeed, a primary objective in building up
the abstract formalism of the D-system was precisely to allow
this insight of Dawkins' to be expressed in the clearest possible
terms. While Dawkins himself credits Fisher, Hamilton,
G.C.~Williams and others, with the original inspiration
\cciteAD[p.~ix]{Dawkins:NewSelfishGene}, I may say that
my own debt here is entirely to Dawkins.

To precisely the extent that we interpret the term ``gene'' as
capturing, in the biological world, the abstract notion of {\em
continuity through generations\/} represented by an S-lineage,
then it is true to say that ``genes'' are the units of selection in
the biological world.  I claim that this was the interpretation
Dawkins properly had in mind when he formulated the doctrine of
the {\em The Selfish Gene\/}; that, indeed, it is identical with
my doctrine of the ``selfish S-lineage''
\cciteAD[Section~11]{McMullin:DarwinianOntology}.

The second question at issue is quite different:
\begin{description}

\item 2: {\em Is there a uniquely distinguished ``level'' of
organisation (biological or otherwise) which characterises
entities that can qualify as D-actors?}

\end{description}

I suggest that this is the question which Hull set out to answer.
As we shall see, Hull's answer seems a little ambivalent; it
might be paraphrased as ``{\em probably\/} not''; I shall attempt
to clarify this answer somewhat, but will essentially agree with
it.

It is not clear whether Dawkins, on the other hand, ever
consciously recognised this second question---not, at least, as a {\em
separate\/} question.  However he does {\em seem\/} to
suggest an answer (implicitly or otherwise)---namely that {\em
genes\/} are uniquely distinguished as the only biological
entities which should properly be said to be D-actors.  I shall
argue that such a claim is quite mistaken (but also that it is
questionable whether Dawkins really intended to make it).

Specifically, to the extent that we interpret ``gene'' as a
material part of an organism (a fragment of DNA, say), then I
shall accept that such genes {\em might\/} be usefully considered
as D-actors (in ``suitable'' circumstances); but I reject
absolutely the idea that they are {\em uniquely\/} qualified for
this \role.  I suggest that there are always alternative
candidate D-actors (particularly, but not exclusively,
organisms); alternatives which will be {\em equivalent\/} in the
precise sense of yielding a selection dynamics which is either
identical, or differs only by a bijective transformation of the
state variables. Preferences among these different candidates
therefore arise {\em only\/} from pragmatic considerations
relating to the particular circumstances in which the theory of
(natural) selection is being applied.

It is, of course, no accident that the term ``gene'' turns up in
two quite different senses in these two questions.  For Dawkins,
genes are the prototypical examples of replicators---and his
conflation of both \mbox{(D-)actor} and S-lineage into the single term
``replicator'' is more or less mirrored in his usage of the term
``gene'' (though with some extra complications as will be
discussed later). Again, we should try to distinguish between (at
least) actor-genes or \agenes, and lineage-genes or \lgenes.  The
former may (or may not) play the \role\ of D-actors, and,
correspondingly, the latter may (or may not) play the \role\ of
S-lineages. Dawkins first argues, correctly in my view, that only
S-lineages can qualify as units of selection.  He then equates
this with a claim that only ``genes'' (or ``replicators'') can
qualify as units of selection; I can accept this also, if it is
read in the sense of ``only \lgenes\ {\em (as opposed to
\agenes)\/}'' or ``only \lrpls\ {\em (as opposed to \arpls)\/}''.
But Dawkins then seems to go on to parlay this into a claim that
only ``genes''---now specifically meaning \agenes---can qualify
as {\em \mbox{(D-)actors}}.  I believe this to be definitely in
error. The confusion is deep seated and subtle; but identifying
and resolving it is the key objective of this essay.

To repeat: my intention here is to consider (and ultimately
rebut) the idea that a certain level of biological
organisation---the ``genes'' or the ``DNA'' or the ``genetic
material''---uniquely fills the \role\ of D-actor (in the
solution of Darwin's Problem specifically). I refer to this
flawed idea as {\em genic\/} selectionism---as opposed to the
{\em organismic\/} selectionism discussed in
\cciteAD{McMullin:Organismic}.  My position will be the pluralist
one that genic and organismic selection, properly viewed, are not
competitors or rivals, but merely alternative, formally
interchangeable, descriptions of the same underlying biological
reality; that, indeed, there may exist an indefinite number of
other, similarly equivalent, descriptions; but that, {\em
whichever\/} of these viewpoints may be adopted, there will be a
crucial distinction between D-actors and S-lineages, with only
the latter being properly regarded as units of selection, or
entities for whose benefit (Darwinian) adaptations may be said to
exist.  This latter question, of D-actor versus S-lineage as the
unit of selection, thus cuts at right angles to the question of
gene versus organism as D-actors; confounding these two questions
leads only to confusion and error.

\newpage
\section{Candidate D-actors}

\label{candidates}

\subsection{Formal Equivalence}

\label{equivalence}

I should now like to clarify my claim that there exists a variety of
biological entities which are more or less equivalent candidates
to play the \role\ of D-actor in the Darwinian solution to
\pr{d}---including, amongst others, genes and organisms.

Let me consider the question abstractly at first.  Suppose that
we have identified a D-system---i.e.\ we have identified a class
of entities which qualify as D-actors, exhibiting a selective
dynamics.  Let us further suppose that these D-actors are such
that they are in one-to-one correspondence with some other class
of entities, and that it is possible to identify the S-class(es) of
the D-actors (which is to say, ultimately, identify the S-values
of the corresponding S-lineages) by inspection of these other
entities. If this is the case then, clearly, we can, if we wish,
regard the latter entities as the D-actors (defining
S-procreation for these entities in the obvious manner), and our
dynamic model of the system (and its predictions, particularly in
terms of selective displacements) will remain completely
unchanged---the same number of S-lineages will be identified,
with the same S-sizes, undergoing the same selection dynamics.

We can also envisage more general cases.  The relationship
between the different entities need not be a simple one to one
mapping.  In principle, it can be arbitrarily complicated, just
as long as it is bijective---which is to say that, given a
description of the population structure in terms of one kind of
entity, the structure in terms of the other is uniquely
determined---for in this case the two descriptions are formally
interchangeable.  Of course, with more complex transformations,
the dynamics in one state space or the other may no longer be
recognisably ``selective''; this suggests one minimal criterion
for possibly preferring one representation over another---namely
that we would prefer a representation in which the operation of
selection is most clearly visible.\footnote{This is closely
  analogous to the search for a ``normal'' form of a state
  description, in which the state variables are maximally
  decoupled.  See, for example, the so-called {\em
  quasi-species\/} of \citeAD{Eigen:Hypercycle} for a
  particular illustrative example of this process actually
  applied to a D-system; but compare also my comments in
  \cciteAD[Section~6.5]{McMullin:DarwinianOntology}.}

Let us consider the specific case of organisms and genes (and/or
genomes). I accept here, as my starting point, the arguments of
a previous essay \cciteAD{McMullin:Organismic} for believing that
organisms can and do form S-lineages which can selectively
displace each other in suitable circumstances---i.e.\ that
organisms, {\em at least,} can be validly regarded as D-actors in the
solution of \pr{d}.

I shall initially restrict attention to cases where the organism
S-lineages are disjoint (either because reproduction is asexual,
or reproduction is sexual but the S-lineages under consideration
are reproductively isolated---i.e.\ belong to different species).
Consider the genomes of the organisms.  To keep matters simple, I
suppose that we are dealing only with unicellular organisms, so
that, by ``genome'' I mean a definite material component of the
organism (being essentially some collection of DNA and/or RNA
molecules). Clearly, there is now a one to one correspondence
between organisms and genomes.

Let us accept, furthermore, that the organism characteristics
which distinguish S-class are related to the genomes such that
the S-class of an organism can be determined (in principle at
least) by examination of its genome.  This assumption is made
plausible by the modern theory of inheritance which stipulates,
in effect, that only those organism characteristics which are
{\em correlated\/} with some genome characteristics can be heritable
(and, of course, only characteristics which are at least
potentially heritable, can subserve S-classification).

Note carefully that I do not comment here (one way or the other)
on whether there is any unique or universal mapping from genomes
to organisms; merely that such a mapping may be established
``locally'' (in space and time)---i.e.\ for specified organism
lineages over some specified period of time (which is
sufficiently long for certain selection events of interest to
work through). I do not even claim that some such local mapping
is always possible---merely that it may be sometimes possible
(and that these are, ultimately, the relevant cases to the
solution of \pr{d}).

If all this is granted then it follows that, in such cases, we
can regard the genomes as D-actors, and the resulting S-lineages
will have precisely the same S-sizes, and precisely the same
selection dynamics, as the original organism S-lineages.  There
is no sense in which either kind of entity may be said to be
inherently or formally preferable for the \role\ of
D-actor---though there may well be {\em pragmatic\/} reasons for
focusing on one rather than the other in any particular case.

It may be remarked that, although this argument has been phrased
in terms of whole genomes, it may well be that, in particular
cases, the relevant S-classifications can be achieved just by
consideration of characteristics of one or more {\em fragments\/}
(contiguous or otherwise) of the genome. For example, the
significant difference between two genomes might well consist in
a single nucleotide substitution, at a particular, identifiable,
locus along a particular chromosome.  We could then perfectly
sensibly regard the nucleotides occupying this particular locus
in each genome as D-actors, forming competing S-lineages etc.

And, of course, it need not stop there: the relevant difference
between two nucleotides can, in general, be established just by
looking at the the attached base (i.e.\ whether Cytosine,
Adenine, Guanine or, in the DNA case, Thymine).  Or, there again,
Cytosine and Thymine (say) could, in theory, be resolved by the
presence of an NH$_2$~group in place of an O~atom respectively:
we could then regard these, suitably located, O~atoms and
NH$_2$~groups as perfectly good D-actors.

This kind of argument would not be significantly altered if a
number of distinct loci in the genome had to be taken into
account in order to achieve S-classification. The {\em sets\/} of
``occupants'' of these specified loci in each genome (whether
polynucleotides, single nucleotides, bases, etc.)
could then be treated as D-actors, provided they are sufficient,
in the particular case of interest, to distinguish (S-classify)
the selectively significant S-lineages.

Consider next the case of multicellular organisms, but still with
disjoint S-lineages (i.e.\ where the organism S-lineages of
interest are reproductively isolated from each other).  This
permutation may be of limited biological significance, but it is
a convenient conceptual stepping stone.

Matters are now slightly more complicated in that there is no
single ``genome'' (in the sense of an identifiable material part
of the organism).  Typically, there are DNA molecules in each
cell, and new cells may be manufactured on an on-going basis
throughout the lifetime of the organism.  Let us call the
DNA molecules in a single cell a {\em c-genome}. Now, let us
call the set of {\em all\/} c-genomes ``belonging'' to a
single organism (over its complete life-time) an {\em
o-genome}.\footnote{An o-genome can be formally
  thought of as a lineage of sorts, with c-genomes as its
  members---but {\em not\/} an S-lineage, as such.}
By this definitional contrivance, we can again assert that there
is a one-to-one relationship between organisms and their
\mbox{(o-)genomes}.

It then follows, just as in the unicellular case, that we can
regard the \mbox{(o-)genomes} as D-actors, and the resulting
o-genome S-lineages will have precisely the same S-sizes, and
precisely the same selection dynamics, as the original (organism)
S-lineages.  Again, there is no sense in which either kind of
entity may be said to be inherently preferable for the \role\ of
D-actor.

It may even be possible to treat the c-genomes as the D-actors in
this case. Granted, the various c-genomes of a single organism
may differ in various respects (this underlies the process of
cellular differentiation); but they also exhibit various strong
similarities---most notably, a very high similarity, if not
complete identity, of base sequence. Let us suppose, for the sake
of the argument, that the S-class of an organism can be reliably
inferred (in principle at least) by examination of {\em any\/} of
its c-genomes (i.e.\ the relevant organism characteristics are
correlated with c-genome characteristics which are identical for
all cells of the given organisms). Suppose further that the
number of c-genomes per organism (of given S-classification) is
approximately constant; then counting c-genomes (instead of
o-genomes) would give a reasonably accurate, scaled, S-size of
the organism S-lineage. Such scaling of the state variables by
constant multiples is, of course, a bijective transformation, so
regarding the c-genomes as the D-actors would indeed yield yet
another formally equivalent, interchangeable, dynamic description
of the selection process. I mention this possibility for
completeness, but it is very difficult to envisage a situation in
which it would have any particular merit---that is, a case in
which there would be any practical advantage in attempting to
count c-genomes rather than o-genomes (or
organisms).\footnote{Regarding c-genomes as D-actors in this
  sense (formally equivalent to organism D-actors) should not be
  confused with selective theories of embryological development,
  in which the c-genomes of a {\em single\/} organism are
  S-classified in a way reflecting cellular differentiation. This
  may well be an important embryological mechanism, but is not
  relevant to the present discussion.}

It should be clear that, although this argument has been made in
terms of DNA molecules, it can apply, {\it mutatis mutandis}, to
many other kinds of entity, provided the following two
general conditions are satisfied:
\begin{itemize}

\item The entities must support S-class\-if\-ication(s) equivalent to
the original organism S-class\-if\-ication(s); in effect, they must
exhibit characteristics which allow the S-class(es) of the
corresponding organism D-actor to be reliably inferred.

\item The entities must bear a fixed numerical relationship to
the corresponding organisms; that is, the S-sizes of entity
S-lineages must be related by constant scale factors (possibly
depending on S-class) to the S-sizes of the original organism
S-lineages.

\end{itemize}

Thus, anything from biochemical reaction paths, through gross
morphological features, through extra-somatic artefacts (shells,
webs, etc.), through behavioural patterns, through social
structures, {\em might\/} conceivably be regarded as valid D-actors
in suitable cases.

Significant further complications arise when we consider the
possibility of {\em sexual\/} reproduction---in the sense of
meiosis or recombination of the chromosomes.

Again, for conceptual simplicity, I shall first consider a
somewhat contrived case, of relatively little biological
importance---namely, organisms (multicellular or otherwise) with a
strictly {\em haploid\/} genotype (each c-genome consists of a
set of unique chromosomes, rather than of homologous chromosome
{\em pairs}, or even higher multiples).  This qualification of the
structure of the genome was not relevant in the previous
cases, but becomes important when we consider sexual
reproduction.

I assume that recombination occurs between homologous parental
chromosomes to yield modified chromosomes which are then passed
to offspring.  I further assume that this can be satisfactorily
modelled by reproduction and (Mendelian) segregation of distinct
particulate ``genes'' (with varying degrees of linkage between
them, depending on chromosomal organisation).  A ``gene'' here
should be thought of as an \agene\ in the sense introduced
previously; it physically corresponds to some characteristic
(usually base sequence) of an identifiable, ``short'', fragment
of some chromosome in the genome.  In the case of
multicellular organisms, we may technically distinguish c-genes
from o-genes (and, indeed, c-chromosomes from o-chromosomes) in
precisely the same way as for c-genomes and o-genomes.

The difference which arises in this case, at the organism level,
is that selectively significant characteristics may be
transmitted to offspring more or less independently of each
other.  This means that coherent, organism, S-lineages may now
{\em intersect\/} to a greater or lesser extent---a single
organism may be a member of many selectively distinguished
S-lineages. We must now enquire as to the dynamic relationships
between these S-lineages, and, in particular, whether any will
compete in such a way as to result in selection.  That is, we
consider whether selection can or will occur within a single
interbreeding population (which I call {\em phyletic\/}
selection, following
\ociteAD{Eldredge:PunctuatedEquilibria}).

The general answer is that these dynamic relationships may be
very complicated, and will {\em not\/} generally realise any
simple form of selection.  However, we can distinguish some
special cases where phyletic selection, as such, may arise.

We focus initially on organism characteristics which are
correlated solely with alternative genes at a single
Mendelian ``locus''---i.e.\ such that any single organism will
display exactly one of these characteristics.\footnote{The
  interpretation of what qualifies as a single, Mendelian,
  ``locus'' is somewhat obscure; I shall simply stipulate
  that genetic fragments which are ``short'' enough to have a
  ``small'' probability of being disturbed by recombination are
  at least one plausible case.}

By definition, organism S-lineages anchored on such
characteristics {\em will\/} still be disjoint (with a haploid
chromosome any single organism must have one gene or the other at
the relevant locus, and must therefore be uniquely a member of one
S-lineage or the other).  If the characteristics are selectively
distinct (i.e.\ the corresponding S-lineages have significantly
different S-value) then selection will occur.

By exactly the same argument as was applied in the previous cases
we can now conclude that such a selection dynamics, if it arise
at all, can be equally well described by regarding the
(allelomorphic) \mbox{(o-)genes} as D-actors, instead of the whole
organisms.  In fact, so far, this case is essentially identical
to the earlier case which allowed that, even with reproductively
isolated organism lineages, more or less short genetic fragments
(or, generally, sets of such fragments) could serve as D-actors
in suitable circumstances (namely if they sufficed to make the
relevant S-classifications).  The only difference under sexual
reproduction is that, due to the possibility of recombination,
only characteristics (S-lineages) correlated uniquely with a
single locus can generally display this clear selection dynamics.
But the point remains that, if such characteristics exist,
precisely the same dynamic description will result whether the
D-actors are considered to be the genes, the genomes, the
organisms, or any of the other possibilities previously
identified---for these distinct entities still exhibit one-to-one
correspondences, and the relevant S-classifications can still (by
hypothesis) by carried out by examining any of them.

This situation does not change at all if we suppose that there
exist other selectively significant organism characteristics,
which are correlated with other independently segregating genetic
loci (i.e.\ there is no {\em linkage\/} between the loci), {\em
and\/} if we can assume that the contributions of the
characteristics correlated with these different loci to overall
S-value of the corresponding S-lineages, are {\em additive\/}
(i.e.\ there are no so-called {\em epistatic\/} interactions).
If I understand it correctly, this is another way of formally
stating that, in such circumstances, the dynamics of the
S-lineages relating to different loci interact {\em linearly\/}
(if at all) and therefore can be {\em decoupled} from each other.
Should this happen to be the case, we can think of the system as
consisting of a set of effectively independent D-systems, with
the S-lineage dynamics in any one having no effects on any other.
This is (arguably) made most clear by thinking of each genetic
locus as defining an independent D-system in itself; that is, if
we regard the genes as D-actors (instead of genomes or
organisms), then we do not have to deal with the ``complicated''
idea of intersecting S-lineages.

This is (finally) a positive argument in favour of regarding
genes as ``uniquely'' qualified candidate D-actors.  However, I
consider it to be rather weak. In the first place, even in this
case, it is still perfectly possible to regard genomes or
organisms as S-lineages---the only disadvantage is that one must
more or less consciously recognise that, in that case, each
D-actor may be simultaneously a member of an indefinitely large
number of different, intersecting, S-lineages.  But, in any case,
the scenario is extremely contrived, and its biological
significance is very doubtful.  It ``works'' only on an assumption
of linear interactions between loci in the S-lineage dynamics,
and this, in turn, seems to rely on the absence of both linkage
and epistasis---whereas, in practice, linkage and/or epistasis
seem to be almost invariably present.

This is not to say that phyletic evolution cannot occur in the
face of linkage and/or epistasis, but merely that regarding genes
as D-actors need not offer any particular simplification in this
case. If there are non-linear interactions of this sort then the
``complication'' of intersections between different S-lineages
defined at the genome or organism levels must be mirrored by
formally equivalent couplings between the dynamics of (admittedly
disjoint) S-lineages defined at the gene level.

So, on this view, genes have no decisive merits as D-actors; but,
equally, neither have they any special disadvantages.  However,
even this is not the case for the {\em shifting balance\/} model
of (phyletic) evolution, due to Sewall Wright. This model was
originally formulated in the 1920's
\cciteAD{Provine:SewallWright}, but Wright has continued to
develop and elaborate the theory since---see
\cciteAD{Wright:ShiftingBalanceTheory} for a recent review. In
this model,\footnote{I introduce the shifting balance model here
  because this is the point in the argument where it
  first becomes logically applicable and relevant; however, the model
  is, of course, normally formulated in the more general case of
  {\em diploid\/} organisms.}
significant events of phyletic selection can relate
to S-classes which are distinguished at more than a single
(Mendelian) genetic locus. To whatever extent this process does
occur in practice, single (Mendelian) genes would not even be
{\em candidate\/} D-actors---for they would not allow the
necessary S-classification to be carried out. Genomes and
organisms, on the other hand, may continue as more or less
satisfactory candidate D-actors.

Let me now turn to the final case, perhaps the case of most
practical interest---phyletic selection in a sexual species with
a {\em diploid\/} (or, more generally, polyploid) genome.

At this point we lose the simple numerical relationship between
the S-sizes of organism (or genome) S-lineages, and S-sizes of
putative gene lineages---for each organism carries two (or more)
genes, which are possibly selectively distinct, at each locus.
Now, not even organism S-lineages grounded on a single genetic
locus can be disjoint---a heterozygote harbours both heritable
characteristics (though they may not both be fully ``expressed'')
and must therefore be included in both S-lineages. The conditions for
selection occurring even relative to a single locus become quite
complex to establish---though it {\em can\/} be done, at least in
some special cases, as analysed in detail in
\cciteAD{McMullin:Organismic}.  This revolved around establishing
that competition could occur---in the sense that changes in
S-size of the two S-lineages were constrained to be {\em
opposite\/} (though generally unequal).

If we now consider the alternative of treating single genes as
the D-actors we discover quite a different situation.  Any single
gene will, of course, be strictly in one S-lineage or the other,
and not both---whether it occurs in a homozygote or otherwise.
Thus, the {\em gene\/} S-lineages, established by (allelomorphic)
genes, will (still) be disjoint.  In the case of a fixed population
size, we have the original simple competitive situation that any
change in the size of one S-lineage must be matched by an equal
and opposite change in the size of the other. We regain (more or
less) a simple model of selective dynamics between disjoint
S-lineages.

So: in the case of phyletic selection in a {\em diploid\/}
species, the choice of genes as D-actors potentially has a
definite advantage, relative to a choice of genomes or whole
organisms.  Such a choice involves a substantive {\em
transformation\/} of state variables---a transformation which
yields a state description in which the operation of selection
may be significantly easier to recognise.  A transformation of
state variables arises precisely because, for the first time, our
alternative candidate D-actors are no longer in a simple
numerical relationship with the original D-actors (organisms).
So, this is a case where genes do seem to have a definite claim
to be preferred as D-actors.

I must repeat: although genes may be ``preferred'', it is still
perfectly {\em possible\/} to treat the organisms or genomes
etc.\ as D-actors.  The latter would still yield a state
description which can be transformed into a description in terms
of genes, and {\it vice versa}. I assume here that the
mating pattern is known (for example, randomised---yielding a
Hardy-Weinberg relationship between heterozygote and homozygote
distributions), for otherwise the transformation between a gene
D-actor model and a genome (or organism) D-actor model would be
indeterminate.  This is not, however, an additional or {\it ad
hoc\/} assumption; the S-values of the gene S-lineages obviously
depend on how the genes are shuffled into organisms---the
relative proportions of hetero- and homozygotes etc.---so the
mating pattern is implicated in the formulation of the dynamical
equations anyway, regardless of which entities are to be
notionally described as the D-actors.

In any case, at best we have now identified a somewhat stronger
reason for regarding genes as D-actors---that it yields a
simpler, more clearly selective, state description in certain
circumstances. But although this is a stronger reason than could
be proposed in the case of a haploid genome, I still do not
regard it as being at all compelling. The state descriptions in terms of
the other candidate D-actors are still formally equivalent
(merely slightly more opaque).  Furthermore, the {\em defects\/}
of the gene level view, already identified for the haploid case,
still apply with (at least) equal force: that is, given
non-linear interactions between the dynamics relative to distinct
loci, the supposed simplification of the gene level
description will be greatly compromised; and if Wright's shifting
balance process is significant then a gene level description will
positively obscure the operation of selection relative to a
description in terms of genomes or organisms.

I have now fairly exhaustively reviewed the significance of the
choice of D-actor (primarily as between organism, genome, and
gene) and concluded that, in all cases which I have considered,
there is no crucial {\em formal\/} effect on the resulting system
description or model.  In fact, the only case where there is a
substantive formal distinction at all is for phyletic selection
among diploid (or polyploid) organisms; and that can be
considered as a more or less simple, bijective, transformation of
state variables which may (or may not) simplify the form of the
dynamic equations somewhat.  In conclusion: none of this provides
any grounds for claiming that any of the candidate D-actors which
have been considered have any special or unique claim on that
\role.

\subsection{A Pragmatic Distinction}
\label{pragma}

I should now like to consider an essentially {\em pragmatic\/} or
methodological argument for preferring one candidate D-actor over
another. This has already been implicitly referred to above, in
the context of the effect of breeding pattern on the relationship
between gene and genome (or organism) descriptions for diploid
organisms: it is the apparent conflict between S-classification
on the one hand, and measuring or estimating S-value on the
other.

S-classification relies on identifying {\em heritable\/}
distinctions between D-actors. It is generally difficult to
establish whether, or to what extent, gross characteristics of
whole organisms are heritable. Similarly, an organism may have
significant heritable characteristics which are virtually
undetectable at the organism level. The latter is especially the
case with dominance in diploid (or polyploid) organisms; if
dominance is complete, the heterozygotic organism {\em appears\/}
indistinguishable from the dominant homozygote, at least in terms
of gross morphology and behaviour etc.  In general, if we are
restricted to examining gross characteristics of an organism,
then controlled breeding experiments will be necessary to
reliably achieve S-classification.

By contrast, heritable characteristics can be identified with
great confidence (if not great ease) by examining genes and/or
genomes. Thus, if our greatest concern or difficulty in any
particular application of selection theory is with actually
carrying out S-classification, we may be inclined to consistently
regard genes and/or genomes etc.\ as the D-actors.

Conversely, measuring or estimating S-value for an S-lineage
depends on an understanding of the relationship between the
particular heritable characteristic(s) (which distinguish the
S-lineage) and S-fecundity and/or S-mortality.  In general this
is very difficult if not impossible to recognise from
consideration only of the genes and/or genomes.  In fact, it is
typically only at the level of the whole organism (or, in the
case of a parasite or symbiote, perhaps at the level of some {\em
other\/} organism, or for a social organism, at the level of a
colony) that it becomes possible to make reliable assessments of
relative S-value. Thus, if our greatest concern is with measuring
or comparing S-value then we may well be inclined to consistently
regard whole organisms (or perhaps organism artefacts etc.) as
the D-actors of interest.

Of course, in practice, {\em both\/} aspects mentioned here must
always be considered, so the supposed conflict is somewhat
illusory. A class of entities is a class of D-actors only if the
entities satisfy {\em both\/} the heritability requirement (so
that coherent S-lineages are established at all) {\em and\/} the
requirement for significant differences in S-value (so that, under
competitive conditions, a quasi-deterministic, selective,
dynamics will result).   Which is to say that, while there may be
pragmatic reasons for emphasising either genes or organisms (or
various other entities) as D-actors, there is no genuine
conflict, no possibility of considering either kind of entity to
the exclusion of the other.  This is the real force of the formal
equivalence which has been established in the previous section.

\subsection{On Genetic Absolutism}
\label{absolutism}
\begin{quote}

  We have often heard it said that genes contain the
  ``information'' that specifies a living being.  This is wrong
  for two basic reasons.  First, because it confuses the
  phenomenon of heredity with the mechanism of replication of
  certain cell components (DNA), whose structure has great
  transgenerational stability.  And second, because when we say
  that DNA contains what is necessary to specify a living being,
  we divest these components (part of the autopoietic network) of
  their interrelation with the rest of the network.  It is the
  network of interactions in its entirety that constitutes and
  specifies the characteristics of a particular cell, and not one
  of its components.  That modifications in those components
  called genes dramatically affect the structure is very certain.
  The error lies in confusing essential participation with unique
  responsibility.
  \iciteAD[p.~69]{Maturana:TreeOfKnowledge}
\end{quote}

I will present a somewhat different kind of argument for genic
selectionism in this section. It is related to the issues already
considered, but might best be called aesthetic, or perhaps
metaphysical.  In any case, I shall claim that it is fatally
flawed. I introduce it, not because of any merit it has in its
own right, but because it provides a necessary contrast for a
final, and much more subtle, argument, which is to be presented
in the following section.

We ask, roughly, whether any of the rival entities considered
here are {\em minimal, sufficient\/} candidates. By ``sufficient''
I mean that these entities are sufficient in themselves (given
extra-organismic ``environmental'' constraints) to identify the
selective dynamics of the system. Sufficiency demands both that
S-classification can be carried out (including prediction of
S-values), and that the S-sizes of the resulting S-lineages can
be established (which is to say that the D-actors in each
S-lineage can be unambiguously counted), purely by reference to
the designated D-actors.  By ``minimal'' I mean something like
smallest physical size and/or organisation---``simplest''.

So far, in discussing the relationship between organisms and
their parts (particularly genes and genomes) I have been
concerned solely with {\em correlation}.  I have stipulated that
all heritable organism characteristics are correlated with some
genetic characteristics---which is to say that, at least
``locally'' (relative to specified organism lineages, localised
in space and time), there exists a mapping between
genomes and organisms, and thus between genomes and S-value.
This was, of course, a necessary assumption to allow genomes as
even {\em candidate\/} D-actors.

Now consider the possibility of a much stronger stipulation.
Correlation implies some underlying {\em causal\/} structure. Let
us suppose that this structure is entirely {\em from\/} genomes
{\em to\/} organisms---i.e.\ that organism characteristics (or,
at least, all heritable ``regularities'' thereof) are caused
exclusively by (regularities of) genome characteristics.

Causation is, of course, a notoriously problematic concept, and I
do not wish to lay much weight on it.  For my purposes, since I
am ultimately going to reject the argument anyway, I will rely on
a completely informal notion of causation. Specifically, I
stipulate that, if the ``causal'' relationship outlined above
holds, a minimal implication is that there {\em is\/} a unique and
universal mapping from genomes to organisms (and thus to S-value).
Genomes must have intrinsic or {\em absolute\/} effects in the
terrestrial world (including, {\it inter alia}, ``causing'' whole
organisms to come about).  This is what I call {\em genetic
absolutism\/} (for terminology, compare Bateson's ``absolute
genetic unit''---see \ociteAD[p.~82]{Bateson:HumanPolitics}).

Genetic absolutism is closely related to, but should be very
clearly distinguished from, genetic {\em determinism\/} (see,
for example, \ociteAD[Chapter~2]{Dawkins:ExtendedPhenotype}).  Genetic
absolutism does not require that the effects of genomes (much
less individual genes) be deterministic, only that they exhibit
``regularities''; these regularities can be purely statistical.
That is, genetic absolutism is perfectly consistent with a
stochastic or probabilistic {\em in-\/}determinism.  Furthermore,
genetic absolutism in no way implies that the effects of genomes
are independent of the {\em general\/} (extra-organismic)
environmental context; indeed, it is obvious that genomes could
not have interesting effects except in a more or less amenable
environment.  So, again, genetic absolutism is compatible with an
arbitrary degree of environmental plasticity or contingency.  The
{\em only\/} significant claim of genetic absolutism is that the
{\em organisms\/} (associated with the genomes under discussion)
can be completely factored out (they are {\em not\/} part of the
``environment''). Which is to reiterate that S-value can be
reliably inferred purely from characteristics of the genome in
association with the (extra-organismic) environment.  Genetic
determinism would imply genetic absolutism, but not {\it vice
versa}.

I have expressed genetic absolutism in terms of a relationship
between a complete genome and an associated organism.  As such it
is compatible with decomposition of a genome into genes which, in
turn, individually have absolute effects---though the effects of
each gene may be qualified to an arbitrary extent by interaction
with every other gene in the genome.  However, the possibility of
such systematic decomposition into smaller absolute units
(so-called {\em Genetic Atomism\/}---see for example
\ociteAD[p.~271]{Dawkins:NewSelfishGene}) is not {\em necessary\/} to
the argument I will present; I will therefore ignore it, thus
restricting myself to the strongest form of the argument.

Genetic absolutism has, no doubt, a long pedigree.  It was
perhaps implicit in the formulation of the very term {\em gene\/}
for {\em genetic determinent}. It seems that, with the
rediscovery of Mendelian inheritance, there came about an idea or
assumption that genes were some kind of biological ``atom''
analogous to chemical atoms; that, in the same way as the
characteristics of chemical compounds were implicit in
characteristics of the different elementary atoms, the
characteristics of biological ``compounds'' (organisms) were
implicit in characteristics of elementary biological ``atoms'' or
genes ({\em whatever\/} genes might ultimately prove to consist
in).\footnote{As noted in
  \cciteAD[Section~3.2]{McMullin:Organismic}, this absolute and
  atomistic concept of gene was {\em not\/} proposed by Mendel
  himself.}
In these terms, genetic absolutism evidently has roots in a
generally reductionist philosophy; but again should not be
confused with reductionism {\em per se}. It should be clear in
the discussion which follows that genetic absolutism {\it per
se\/} can be false without compromising a {\em general\/}
biological reductionism. In any case, I am not qualified to
review the detailed development or ramifications of genetic
absolutism---and such detail is not necessary to my purposes. It
is enough to recognise that genetic absolutism is, at least, a
{\em coherent\/} theory of biological organisation, and to then
ask where that leads us.

The question at hand is: what implication, if any, would genetic
absolutism have for choosing between genomes and organisms as
D-actors?

To develop an answer, note first that, if such a reliable and
universal mapping existed between genomes and organisms, then we
could {\em theoretically\/} dispense entirely with everything
other than genomes in our analysis or description of the
evolution of organisms (including the growth of adaptive
complexity)---for everything else can be ``calculated'' back in
at any time. Thus, genomes, in themselves, would be {\em
sufficient\/} candidates, and, furthermore, would be uniquely
distinguished as the {\em minimal\/} entities for which this
holds. Therefore they would indeed deserve to be preferentially
regarded as the ``true'' D-actors in the biological world.

The fundamental problem with all this is, of course, that, if our
modern theories of the processes of molecular biology are to be
believed at all, then genetic absolutism is simply false.  In
fact, I do not know of any contemporary biologist who explicitly,
and unambiguously, espouses such a view (although Dawkins, among
others, can sometimes {\em seem\/} to be doing so---a point I
shall return to in due course).

Now it is true that there are some limited aspects of the
genotype/phenotype mapping which seem to be more or less
universal (at least on Earth)---notably the ``genetic code''
relating DNA/m-RNA base sequence to the amino acid sequence of
protein.  But even this is not completely universal (e.g.\
\ociteAD[p.~26]{Dyson:OriginsOfLife}), and is not
in any sense intrinsic or absolute---the coding seems to be
have a significant degree of arbitrariness, a result of
historical evolutionary contingency.  It is now effectively
fixed---self-reinforcing as it were---but there seems to be no
reasonable sense in which a DNA based genetic material requires,
imposes, or causes, this one particular coding to be used.
Indeed, \citeAD[Chapter~27]{Hofstadter:Metamagical}
has provided an extended analysis of the essentially
arbitrary nature of this coding.

In any case, universality of coding between DNA/m-RNA and protein
is a very far cry indeed from universality (and uniqueness) of
the {\em complete\/} mapping from DNA to phenotype (and thus to
S-value).

% [This next paragraph is very weak and best omitted...]
%
% Taken at face value, genetic absolutism predicts that a ``naked
% genome'' should be capable of ``causing'' the spontaneous formation
% of a complete organism, {\it in vitro}.  We would allow, of
% course, a suitable culture of biochemical building
% blocks---nucleotides, amino acids etc.; but we would rigorously
% exclude anything which is supposed to be causally produced by the
% DNA---m-RNA, t-RNA, ribosomes etc.\footnote{Viruses provide a
%   case which would require special discussion in this context.
%   However, that would take me too far afield, and would not
%   affect the basic propositions being made here.  I do not suppose
%   that anyone would argue that viruses provide a satisfactory
%   {\em general\/} model for biological evolution.}
%
% I do not know of any attempt to actually carry out such an
% experiment; but it is quite clear that it would fail. That is,
% such a naked gene absolutely could not spontaneously bootstrap
% itself even to the point of being able to synthesize m-RNA, much
% less a complete organism.

We may conclude that genetic absolutism, though it is coherent,
and perhaps even initially plausible, has been decisively
refuted; it follows that the claim that genomes provide a
minimally sufficient (and thus preferred) candidate D-actor must
be rejected.

Finally, I may say that the underlying goal of identifying
a minimally sufficient D-actor can actually survive this
criticism---but only just.  While it is true that genomes, on
their own, are not sufficient to predict phenotypes (and thus
S-values) it does not {\em necessarily\/} follow that whole
organisms are the only other choice.  That is, we can envisage
that, corresponding to any conventional organism, there may be
some kind of minimal biochemical machinery which is, admittedly,
more than a naked genome, but less than a complete organism,
which {\em would\/} be capable of developing into the complete
organism {\it in vitro}.  We can imagine this all right; but it
has by no means been demonstrated, and there is no particular
reason to suppose that the required decomposition of organisms,
even if it is possible at all, would be systematic (in the way
that the genotype/phenotype decomposition is systematic).
In any case, it seems to me extremely doubtful that any useful
insight could be gained into evolutionary biology by directing
attention at these hypothetical quasi-organisms as preferred
D-actors, in place of conventional organisms.

\subsection{On Genetic Relativism}

\label{relativism}

I now turn to a much modified version of the argument of the
previous section, which seeks to recover the preference for genomes
over organisms among candidate D-actors, {\em despite\/} the fact that
genomes do {\em not\/} have absolute phenotypic expressions or
interpretations.

The argument goes like this. Even though genomes do not have an
absolute mapping to organisms, the mapping of any new (mutated)
genome is well defined {\em relative\/} to the mapping of the
parental genome.  So, given any starting point---some initial
organism(s)---the subsequent evolution of the system {\em can\/}
be tracked purely in terms of genomes.  This is not because the
genomes have absolute phenotypic effects; rather, each mutational
step from the founder organisms is characterised by a
well-defined phenotypic effect {\em relative\/} to the phenotypic
effects of the immediate ancestor; knowing the original effects,
accumulation of these relative effects yields a mapping for an
arbitrary descendant genome.  This is, in effect, an explicit
formulation of my earlier claim that a well defined
genotype/phenotype mapping can be established as long as we are
willing to accept some localisation in space and time.  In
effect, we say something like ``within this species'', or
``within this genus'', certain genotypes cause certain,
consistent, phenotypic effects.

Another way of looking at this is to say that, although genomes
in themselves do not permit the prediction of phenotypes (and
thus S-value), a genome {\em augmented\/} with some extra
information does allow such prediction; and this extra
information is, in a sense, also ``genomic''---it is an ancestry,
identifying the particular sequence of genomic {\em changes\/}
between the given genome and the founder stock (for which the
phenotypic expression is presumed known).

This kind of argument is precisely what licenses the use of
genomes as D-actors at all; and we may, indeed, say that, in any
context where this is done, the genomes (suitably augmented, as
described) {\em are\/} minimally sufficient D-actors, and should
be (mildly) preferred for that reason.

I actually accept this as far as it goes; but I want to emphasise
its limitations, and the ease with which this argument can lead
into error.

Firstly, this approach clearly does {\em not\/} squeeze organisms
out of the evolutionary story: since the phenotypic effects of
the genomes are only defined relatively, they must ultimately be
referred back to some founder stock of {\em organisms}.  There is
no question of being able to tell a complete
evolutionary story {\em entirely\/} without reference to organisms.

Secondly, the approach becomes more and more cumbersome, as
genomes become further removed from the founder organisms
(relative to which their phenotypic expressions can be ultimately
evaluated).  As long as we restrict attention to a species or
genus there may be some hope of a fairly uniform mapping from
genomes to phenotypes; but if we wish to think about the broad
sweep of biological evolution, then the mapping from genomes to
phenotypes is likely to have altered drastically, and the process
of establishing a mapping by tracing back to some remote ancestor
whose mapping is assumed known seems, at best, counter
intuitive.\footnote{The situation is, formally, much more complex
  that I detail here. For example, it is a commonplace assumption
  that evolutionary descent is theoretically reversible (e.g.\
  \ociteAD[p.~3]{Dawkins:ExtendedPhenotype}), although such
  reversal is of vanishingly small probability over any
  significant number of steps (this is known as ``Dollo's
  Law''---\ociteAD[p.~94]{Dawkins:BlindWatchmaker}); but this
  ignores the essential relativity involved in genotypic
  expression.  Specifically, a ``reverse mutation'' (which
  restores a prior genomic configuration) cannot be {\em
  guaranteed\/} to restore a prior phenotypic expression. It
  seems to me that such a guarantee would, in general, be
  possible {\em only\/} under conditions of genetic absolutism.
  However, such complications serve only to further strengthen my
  claim that evaluating the phenotypic expression of a given
  genome by reference to some arbitrarily remote ancestor is
  conceptually misguided, and virtually impossible to carry
  through in practice.}

Let us recall what our D-actors now are, in effect.  They are
genomes, {\em augmented with whatever information is necessary to
infer their phenotypic effects\/} (always, of course, as
functions of whatever extra-organismic environmental factors are
relevant). We stipulate that this information which is being
tagged on the genomes {\em can\/} always take the form of a
record of genomic changes relative to some ancestor
organism---plus a specification of the mapping for the ancestor
organism (this is the force of our assumption that S-creation
{\em necessarily\/} involves correlated genomic modification). We
recognise however that, in simple cases, this ``extra''
information may be essentially identical for all the genomes
under consideration---for example, if they are all only one
mutational step away from the founder organism(s). In such cases,
we can lapse into thinking of the genomes themselves as being the
D-actors---but only temporarily; as further mutations occur,
particularly if they accumulate in particular
\mbox{(D-)lineages,} we may have to augment and diversify this
``extra'' information that is associated with each genome.

It is admitted that genomes, augmented in this way, have become
(by definition) minimally sufficient D-actors, and preferred
candidates for that reason.  But we must surely ask whether there
is any more concise representation for this extra information
which is conceptually tagged on to the genomes---particularly if we
are concerned with long term evolutionary change.  That is,
rather than having to trace back through the relative effects of
particular genomic modifications, to some potentially remote
ancestor, could we short circuit this process by, as it were,
accumulating the changes as we go along?  In effect, instead of
tagging on a record of genomic descent, can we tag on a record of
the ``current genotype/phenotype mapping''?

Once the process is viewed in this light, the answer is hopefully
fairly clear.  There is already an entity which concisely
accumulates precisely the information we require; conveniently,
it is already securely attached to each genome---it is, of course,
the organism itself (or the phenotype, if you prefer)!

We are now back essentially at the same conclusion as at the end
of the previous section.  There is, conceptually, such a thing as
a minimally sufficient D-actor; it is certainly something more
than just a genome; it is either less than, or equal to, the complete
organism; in fact, it is very close to a {\em definition\/} of what we
mean by the ``organism'', and the attempt to systematically
distinguish it, in practice, from a complete organism offers no
benefits (that I can perceive).

The conclusion from all of this is that, if we seriously wish to
pursue a minimally sufficient D-actor, in the solution of \pr{d},
then organisms are the only candidates which are even
approximately satisfactory.  We can use genomes (or even genes
etc.) as D-actors in strictly circumscribed circumstances.
However, the severe limitations of these other candidates must be
carefully remembered; otherwise, one will slip almost inevitably
into a position which is hardly distinguishable from the fallacy
of genetic absolutism.

\section{Hull: Replicators and Interactors}

\label{hull}

I now turn to a detailed comparison between the analysis
presented in previous sections, and the work of David L.~Hull.
Hull is a philosopher, who has explicitly taken on the problem of
revealing the ontological or metaphysical foundations upon which
(biological) Darwinism is built. In what follows, I shall rely on
the two papers (Hull
\ociteD{Hull:IndividualityAndSelection,Hull:UnitsOfEvolution}) in
which he has presented his ideas at some length.

Hull's analysis is explicitly related to, and draws upon, earlier work
by Dawkins.  Dawkins, in turn, has integrated some of Hull's ideas back
into his own framework.  Thus, their two approaches are strongly
interconnected.  Nonetheless, there are fundamental differences between
them, and I therefore consider them separately, even at the risk
of some repetition.

To anticipate somewhat, I shall first summarise the
interpretation I propose of Hull's work.  I shall then attempt to
validate this interpretation in detail (for it is by no means
obvious).

I take Hull to be concerned {\em exclusively\/} with the question
of which kinds of biological entities can be validly regarded as
D-actors (especially, but perhaps not exclusively, in the
solution of \pr{d}), and which (if any) should be preferred; he
is {\em not\/} concerned with the (important) distinction between
the abstract \roles\ played by D-actors and S-lineages. However,
somewhat unfortunately (though consistently with other related
literature), he identifies his discussion as part of the debate
over ``units of selection''.  As I have already argued, it may be
preferable to restrict this particular term (following Dawkins)
to entities for whose benefit Darwinian adaptations may be said
to exist; as such, the debate over the ``units of selection''
should then be best regarded as concerned with the relative
merits of S-lineages over D-actors (regardless of which
biological entities are mooted for realising these \roles)---a
question which Hull does not touch upon at all.

In considering the question of which biological entities can or
should be regarded as D-actors, I interpret Hull as follows:
\begin{itemize}

\item He accepts that \mbox{(A-)genes} and organisms (at least)
can be formally equivalent alternative candidates.

\item He recognises that a pragmatic choice between these
candidates may be made, in particular
cases, by emphasising S-class inheritance ({\em formation\/} of
coherent S-lineages) relative to S-value differences ({\em
selection\/} between S-lineages), or {\it vice versa}.

\item He accepts that the former emphasis would yield a
preference for regarding genes (or other entities close to that
``level'' of biological organisation) as D-actors, and the latter
would suggest a preference for regarding organisms (etc.) as
D-actors.

\item But he stresses that, in any case, neither pragmatic
emphasis will serve, on its own, to support the understanding or
analysis of selection processes, for both S-class inheritance and
S-value differences are essential to such processes.

\item Thus, neither genes nor organisms (nor, implicitly, other
related candidates) have a unique claim to be preferentially
regarded as the ``true'' biological D-actors.

\end{itemize}

Thus far (on this interpretation) Hull is making essentially the
same points as I have argued for in
section~\ref{candidates} above---which is to say that, thus far, we are
in complete agreement.  We disagree only when Hull attempts to go
slightly further, and suggests that the \role\ played by genes
may be especially distinguished from that of organisms, in having
a certain ``causal'' priority; and that, further, this may give a
basis for regarding genes as uniquely preferred D-actors. I shall
argue that this idea should be interpreted as a version of the
claim, based on genetic relativism, for genes (or, better,
genomes) being minimally sufficient D-actors; and, as already
discussed, I consider {\em this\/} idea to be, at best,
misleading.  I should stress however, that Hull introduces this
idea only tentatively, and as a minor qualification of his main
claims; the scope of my agreement with him is much greater than
that of any disagreement.

It now remains to justify these interpretations of Hull's
position.

Hull describes his central idea as being to distinguish between
two functions which he says are necessary for (Darwinian)
evolution: {\em replication\/} and {\em interaction}. Hull
considers this distinction to be of critical importance; he goes
as far as to say that ``A pervasive ambiguity in the literature
on levels of selection can be eliminated by consistently
distinguishing between replication and interaction''
\cciteAD[pp.~33--4]{Hull:UnitsOfEvolution}.

I shall argue that Hull's ``replication'' denotes essentially the
preservation of S-class in S-descent---the necessary condition
for the formation of coherent S-lineages; and his ``interaction''
denotes whatever gives rise to significant differences in S-value
between distinct S-lineages---a necessary condition for
selection between S-lineages (competition is, of course, also
required).

However, as well as distinguishing between these {\em
functions\/} as such, Hull goes on to distinguish between {\em
entities\/} capable of discharging these functions---{\em
replicators\/} and {\em interactors\/} respectively.  I think
this is a dangerous, if not actually erroneous, step.  By taking
this step Hull certainly implies, and sometimes comes close to
explicitly stating, that the two functions can be sensibly
thought of as being {\em independently\/} discharged by distinct
biological entities---which is to say that there exist biological
replicators which are not also biological interactors and {\it
vice versa}.

Now Hull actually uses this as a sort of straw man---he wants to
argue, in effect, that the {\em functions\/} of replication and
interaction must go together to support selection.  That is, only
replicator/interactors can serve as D-actors.  I agree with the
conclusion of course---``replicator/interactor'' could be read
almost as a {\em definition\/} of my concept of D-actor. But I
find the preliminary idea---that the functions of replication
and interaction {\em might\/} be separated into independent
entities---to be a potentially misleading fiction.  To repeat:
in my view, an S-classification capable of identifying a
selection process can only be fully defined by reference {\em
both\/} to the fact of its being heritable, {\em and\/} that
the consequent S-lineages of the different S-classes have well
defined (and significantly different) S-values (in specified
environmental circumstances).

Before examining Hull's analysis proper, I want to establish that
he genuinely is talking about candidate D-actors, and not about a
contrast between D-actors and S-lineages.  As detailed in
section~\ref{repl}, these is some potential confusion about this
issue---particularly from Dawkins, and Hull does take the term
``replicator'' from Dawkins after all. Hull's intended position
can be seen (fairly) unambiguously in the following passage:
\begin{quote}
  In order to perform the functions they do, both replicators and
  interactors must be discrete individuals which come into existence and
  cease to exist.  In this process they produce lineages which
  change indefinitely through time.
  \iciteAD[p.~41]{Hull:UnitsOfEvolution}
\end{quote}

So: both replicators and interactors are ``individuals'' with
finite lifetimes.  I suggest that this must be interpreted, in my
terms, as meaning that they are candidates for the \role\ of
D-actor.  In fact, the point Hull ultimately intends to make is
that, not only are they candidates for this \role, but they are
strictly {\em complementary\/} candidates---any putative D-actor
must exhibit both kinds of function.

Hull adds that, {\it qua\/} \mbox{(D-)actors,} both replicators and
interactors form lineages. It should be carefully noted that Hull
does not distinguish here between lineages in general, and S-lineages in
particular (but see also his reference to ``spatiotemporal
sequences of replicates'', discussed below); to put it another
way, he does not distinguish between descent in general and
S-descent in particular.  Hull would presumably consider {\em
all\/} offspring of any given replicator or interactor as members
of the parent's lineage(s). I, on the other hand, consider that
there are crucial distinctions to be made. S-lineages are the
entities which compete with, and may selectively displace, each
other, and they can do this precisely because they do {\em not\/}
``change through time'', in some well specified and relevant
sense.  If we must speak of something changing or evolving
through time at all, then {\em D-lineages\/}
are arguably the best candidates. In any case, this is
a digression here: the point of immediate interest is that
Hull intends both replicators and interactors as candidate
\mbox{(D-)actors,} and not as lineages (of any sort).

Let me now consider Hull's notion of replication and replicators
in more detail.  Hull bases his discussion on Dawkins' original
ideas, but elaborates as follows:
\begin{quote}

  \ldots\ what really matters in selection processes is, as
  Dawkins points out, {\em retention of structure through
  descent\/} \ldots\ Two atoms of gold can be structurally
  identical to each other without one being a replicate of the
  other, or both being replicates of some other atom.  Descent is
  missing.  Conversely, a complex organic molecule can be broken
  down into smaller molecules by rupturing its quarternary bonds,
  and these molecules broken into even smaller molecules, etc.,
  but the resulting molecules would not form replicates because
  retention of structure is missing.

  For selection to take place, spatiotemporal sequences of
  replicates are necessary.  Similar entities alone won't do;
  neither will spatiotemporal sequences of entities alone.
  \iciteAD[pp.~31--32]{Hull:UnitsOfEvolution}
\end{quote}

Hull's point here is that, in thinking about selection processes,
we must clearly distinguish between relationships of similarity
and of descent.  The two {\em need\/} not go together (Hull gives
examples where each could be present without the other), but they
might---and of course, the latter is the crucially interesting
case because a selective dynamics then becomes possible. This is the
case for which Hull reserves the term {\em replication}, and
entities satisfying this condition will be called {\em
replicators}.

What exactly qualifies as ``structure''?  Hull is not explicit,
but I take him to mean any objectively measurable characteristic
(or array of such characteristics) of an entity; thus, Hullean
replication is a relationship of descent distinguished by the
fact that parent and offspring entities are also similar, in that
they share certain (presumably, {\em specified\/}) measurable
characteristics.  This is essentially the inheritance condition
whereby S-descent was defined, so Hullean replication can be
taken as synonymous with S-descent. Hullean replicators will (at
least) satisfy this inheritance condition for D-actors, and his
``spatiotemporal sequences of replicates'' are, precisely, my
coherent S-lineages.

Hull raises a question here as to whether replication merely
involves {\em similarity\/} of structure, or whether strict {\em
identity\/} is required (``required'' in the sense of being able
to support a selective dynamics).  As quoted above, Hull himself
has only stipulated that similarity is required, but he
immediately goes on to say:
\begin{quote}

  Dawkins' exposition is couched, however, not in terms of {\em
  similarity\/} of structure, but in terms of {\em identity\/} of
  structure.  {\em Although nothing much rides on the decision, I
  find requiring structural identity too strong.}  For example,
  physicists consider two atoms to be atoms of the same element
  even if they are not structurally identical.  Isotopes are
  allowed.  Similarly, biochemists consider cytosome $c$ to be a
  single protein even though extensive variation in its
  composition is common.  Such examples could be multiplied
  indefinitely.

  \nopagebreak
  \begin{quote}
  Hull\\
  \cciteD[p.~32, emphasis added]{Hull:UnitsOfEvolution}
  \end{quote}
\end{quote}

I agree entirely with Hull's conclusion here---i.e.\ that we
should require only ``similarity''---but I should like to be a
little more formal.  By ``similarity'' I mean firstly that
we restrict attention to some specified set of characteristics
rather than requiring similarity of ``all'' characteristics.
Secondly we require ``similarity'' of these specified
characteristics, in the following sense: a partition is defined
over the set of all discriminable values for each characteristic;
two entities are said to be ``similar'' with respect to a
characteristic iff their respective values for the characteristic
fall into the same class (as defined by the partition).  By
choosing the set of characteristics, and the partitions on their
ranges, we can make this criterion of similarity as loose or as
tight as we wish in any particular case.  The point is that an
entity (or class of entities) is only a replicator {\em with
respect to\/} some such specific definition of ``similarity''.
There can be no such thing as a replicator ``as such'' (of and in
itself).  If we can validly call a real entity a replicator at all, it
will be true only under some particular representation(s) of
it.\footnote{This definition of ``similarity'' is essentially
  equivalent to the notion of ``S-classification'', and the
  condition stated here for regarding an entity as a Hullean replicator is
  equivalent to the definition of S-descent as a case of descent
  preserving a particular S-class
  \cciteAD[Section~5]{McMullin:DarwinianOntology}.}

I think that all this is fairly clear, and I conjecture that Hull
would endorse it.  However, I spell it out at some length because
I want to disagree strongly with Hull's associated assertion that
``nothing much rides on the decision'' (between requiring
similarity or identity of structure, as a criterion of
``replication''). On my interpretation (and I can see no other
feasible one) ``identity'' of structure must imply identity of
{\em all\/} objectively measurable characteristics (possibly
subject to some ``tolerance'' on each characteristic---defining
such a tolerance satisfactorily would be very problematic, but I
will happily allow the possibility since it does not affect the
argument at all).  Now such a requirement would be infeasibly
strong.  The ``objectively measurable'' characteristics of any
real (as opposed to formal) entity are never (known to be) even
finitely enumerable---never mind actually (known to be)
enumerated. So ``identity'' of ``structure'' between two real
entities is not something we could ever positively establish
(though its absence may well be demonstrable). Indeed, strict
identity may not, in fact, be possible in the real universe at
all---though that must evidently remain a metaphysical question.

To put it in a more tangible way: if we restricted the
interpretation of ``replication'' to require strict identity of
structure in this sense, then {\em none\/} of the candidate
biological entities which Hull (or Dawkins, for that matter)
wishes to discuss would qualify!  As Hull himself notes, two
atoms of the same element can be structurally different---for
example, if they are of different isotopes.  But nothing in the
modern theory of DNA based heredity ensures that isotopic
properties of the parental DNA molecules are preserved in the offspring,
and, as a matter of empirical fact, such properties are {\em
not\/} so preserved.\footnote{\samepage The example is not capricious:
  precisely this kind of substitution has been used in certain
  experimental investigations of the nature of the DNA molecules
  in living organisms---see, for example,
  \citeAD[pp.~112--113]{Hardy:LivingStream}.}
On a criterion of strict ``identity'' we should have to conclude
than not even fragments of DNA (embedded in biological
organisms)---which are the very paradigmatic cases for both Hull
and Dawkins---qualify as ``replicators''.

Seen in this light, Hull's assertion that ``nothing much rides on
the decision'' cannot be sustained, and was, for me at least,
deeply confusing.  Furthermore (and {\it pace\/} Hull) I cannot
accept that Dawkins {\em has\/} required strict identity as a
criterion for ``replication'' (not, at least, in the sense of
``identity'' which I have described---and again, I have been
unable to identify a plausible alternative), though I can
possibly see how such an impression might arise.  I shall return
to Dawkins' views in the next section; for now I merely note
that, insofar as Dawkins proposes any special criterion for
``replication'', this is not so much about any notion of a
``degree'' of similarity between parent and offspring, but rather
about the {\em mechanism\/} whereby such similarity as may exist
is achieved. This is a quite separate issue.

I now turn to Hull's notions of interaction and interactors.
Consider first the following points:
\begin{quote}

  Replication by itself is sufficient for evolution of sorts, but not
  evolution through natural selection.  In addition, certain entities
  must interact causally with their environments in such a way as to
  bias their [{\it sic\/}] distribution in later generations.
  \iciteAD[p.~317]{Hull:IndividualityAndSelection}

  \bigskip
  If an entity is to function as a replicator, it must have a structure
  and be able to pass this structure on to successive generations of
  replicators.  As a replicator it need interact with its environment
  only to the extent necessary to replicate itself.
  \iciteAD[p.~318]{Hull:IndividualityAndSelection}
\end{quote}

The point Hull is making is that, given the way he has defined
replication, it only guarantees that spatiotemporal sequences of
entities (S-lineages) will form, where the entities are
``similar'' only according to an essentially arbitrary criterion;
it says nothing, and can say nothing, about the dynamic
behaviours (and interactions) of these sequences---whether they
will expand, contract, stabilise, oscillate, etc.  Indeed, there
is no guarantee (even in a fixed environment) they they will show
any dynamic regularities at all, because, so far, we have no
constraint or axiom linking the ``structure'' which is preserved
in replication with the ``behaviour'' of the replicators and/or
the sequences of replicators.  To put it another way, it is a
truism that the characteristics of an entity (which is to say,
its ``structure'' in general) in some sense define its possible
behaviours in its world; but there is no guarantee that the
characteristics which are relevant to its behaviours (in the
natural environments it finds itself in) are the {\em same\/}
characteristics as are preserved in replication; and if they are
not the same---if the ``behavioural'' structure is not in some
degree related to the ``replication'' structure---then the
sequences of replicators, though similar in some more or less
abstruse technical sense, will not be related in relevant
behavioural respects, and will not exhibit any regular
dynamics.

So: if we want entities which will form \mbox{(S-)lineages}
exhibiting some kind of dynamic regularities (including, of
course, {\em selection\/}) then, certainly, they must be
replicators, but {\em replication on its own is (still) not
enough}.  It matters {\em what\/} is being replicated, which is
to say which, of the potentially infinite number of objectively
measurable characteristics of any entity, are being preserved,
and how well.  This, of course, is the stage in my own
formulation where I introduce the ideas of S-fecundity and
S-mortality (then leading on to S-value) of an S-lineage, and stipulate
that these should be ``reasonably'' determinate functions of the
S-class (and the environment---the latter possibly including
other S-lineages, of course)---see
\cciteAD[Section~6.1]{McMullin:DarwinianOntology}.  Without this
correlation between S-class and S-value we cannot possibly have a
selective dynamics.

Hull introduces {\em interaction\/} for essentially the same
purpose:
\begin{quote}

  When Dawkins [\ociteAD{Dawkins:ReplicatorSelection}] defines
  ``replicator,'' he has replicators interacting with their
  environments in two ways---to produce copies of themselves and
  to influence their own survival and the survival of their
  copies.$^[$\footnote{Hull lapses here into the confusion between
    survival$_1$ (i.e.\ of actors) and survival$_2$ (of lineages)
    discussed in \cciteAD[Section~5.1.1]{McMullin:Organismic};
    but his intention is presumably that (Dawkinsian) replicators
    influence the S-value of their S-lineages
    (survival$_2$)---via S-mortality (mean survival$_1$) or
    otherwise\ldots}$^]$
  Just as Dawkins coined the term ``replicator'' for the entities
  that function in the first process, I
  [\ociteAD{Hull:UnitsOfEvolution}] have suggested ``interactor''
  for the entities that function in the second process \ldots\
  Thus the two sorts of entities that function in selection
  processes can be defined as follows:
  \begin{description}

  \item[\it replicator:] an entity that passes on its structure directly in
  replication.

  \item[\it interactor:] an entity that directly interacts as a
  cohesive whole with its environment in such a way that
  replication is differential.

  \end{description}
  \iciteAD[p.~318]{Hull:IndividualityAndSelection}
\end{quote}

(Note carefully the distinction Hull makes here between himself
and Dawkins.  As Hull describes it, a Dawkinsian replicator
combines the functions of {\em both\/} a Hullean replicator and a
Hullean interactor.)

Now Hull does two things at once here---he distinguishes the
{\em functions\/} of replication and interaction, and also
distinguishes {\em entities\/} which perform these functions.  I
endorse the first step; indeed, as already discussed, I have
embedded essentially the same idea in my distinction between the
preservation of S-class in \mbox{(S-)descent,} and the correlation of
S-class with S-value.  But I find Hull's second
step---distinguishing {\em entities\/} which perform the two
functions---to be unhelpful and confusing. It suggests that the
two functions are {\em logically\/} independent---which is to say
that replication need not entail interaction (which I accept),
and that interaction need not entail replication (which I
reject).

Certainly, as we have already seen, one can envisage something
which replicates but does not interact (in Hull's senses)---a
``pure'' Hullean replicator.  But it seems to me very difficult,
if not impossible, to imagine something which could interact
(still in Hull's technical sense) but
not replicate---that is, a pure Hullean interactor.  I suggest
that interaction {\em does\/} necessarily entail or presuppose
replication, and that Hullean interactors must be regarded as a
{\em subset\/} of Hullean replicators (effectively, the subset
representing Dawkinsian replicators, or my D-actors---though that
will have to be qualified later). This is
implicit in the fact that Hull's very definition of interactor
refers to ``replication''.  It is explicit in my own formulation
of S-lineage selection: we can formulate the inheritance (S-descent)
requirement without reference to S-value, but not {\it vice
versa\/}---because without inheritance there are no S-lineages,
and, without S-lineages, the concept of S-value cannot even be
formulated.

However, the important issue here is not whether Hull {\em
implies\/} the existence (or conceptual coherence) of entities
which would be interactors but not replicators, but whether he
actually attempts to explicitly {\em use\/} such entities.  It
would only be in the latter case that there would be a
substantive (as opposed to merely terminological) difference
between us.  Unfortunately, there is no straightforward answer to
this.

Certainly Hull consistently emphasises the need for
{\em both\/} replication and interaction in order to have a
selective process. Thus, we have the following:
 \begin{quote}

  With the aid of these two technical terms [replicator and
  interactor], the selection process itself can be defined:

  \begin{description}

  \item[\it selection:] a process in which the differential
  extinction$^[$\footnote{Again, we have a possible confusion between
    notions of survival$_1$ and survival$_2$; from the context I
    presume Hull must mean death of individual interactors,
    rather than ``extinction'' (in the sense of termination of an
    interactor lineage).}$^]$
  and proliferation of interactors cause the differential
  perpetuation of the replicators that produced them

  \end{description}
  \iciteAD[p.~318]{Hull:IndividualityAndSelection}
\end{quote}

Or again:
\begin{quote}

  Evolution of sorts could result from replication alone, but
  evolution through natural selection requires an interplay
  between replication and interaction. Both processes are
  necessary. Neither process by itself is sufficient.  Omitting
  reference to replication leaves out the mechanism by which
  structure is passed from one generation to the next.  Omitting
  reference to the causal mechanisms that bias the distribution
  of replicators reduces the evolutionary process to the
  ``gavotte of the chromosomes,'' to use Hamilton's
  [\ociteAD{Hamilton:EvolutionOfSex}] propitious phrase.
  \iciteAD[pp.~319--320]{Hull:IndividualityAndSelection}
\end{quote}

But even here, the underlying ambiguity of Hull's analysis
reasserts itself.  What are we make of the statement that
``Neither process by itself is sufficient'' except that both
replication and interaction {\em can\/} conceivably occur, each
without the other?  Which is to say that there could, in
principle, be such a thing as an interactor which is not a
replicator?  But then again consider the following:
\begin{quote}
  The structure of replicators is differentially perpetuated
  because of the relative success of the interactors {\em of
  which the replicators are part.}

  \nopagebreak
  \begin{quote}
  Hull\\
  \cciteD[p.~41, emphasis added]{Hull:UnitsOfEvolution}
  \end{quote}
\end{quote}

Hull all but stipulates that interactors always ``contain''
replicators, which would effectively be a recognition that
interactors must {\em be\/} replicators. The argument would go
like this: the characteristics of a ``part'' of an entity are
surely characteristics of the entity itself; so if
characteristics of the part are preserved in descent, then
characteristics of the entity itself are also preserved in
descent, and the entity (the whole interactor) must be a (Hullean)
replicator in its own right.  The only flaws in this argument
would seem to be if Hull envisages that not all interactors have
these particular ``parts'' (in which case the original definition of
interactor seems to fail) or replication of these ``parts'' does
not necessarily correspond in any definite way with
``replication'' (procreation?) of the interactors
themselves---but in that case I cannot see how the relative
success of the interactors (in ``proliferation'' and
``extinction'') can map onto ``differential perpetuation'' of the
embedded replicators.

There {\em is\/} one case in which Hull seems to explicitly and
unambiguously refer to entities which {\em are\/} interactors but
{\em not\/} also replicators:
\begin{quote}

  In order to function as replicators, species must exhibit structural
  characteristics and be able to pass on these characteristics.  Species
  must somehow `reproduce' themselves as distinct individuals.  One of
  the major reservations which biologists have to species selection is
  that they do not see how species can make the necessary copies of
  themselves to permit selection at the level of species.  {\em But even if
  species cannot function as replicators, they still might be
  sufficiently cohesive to function as interactors} \ldots\ A
  species, once formed, is not capable of extensive change.
  Instead, species form lineages, and it is these lineages which
  evolve \ldots

  \nopagebreak
  \begin{quote}
  Hull\\
  \cciteD[p.~40, emphasis added]{Hull:UnitsOfEvolution}
  \end{quote}
\end{quote}

In the present context I am not concerned with the details of the
argument as to whether ``species selection'' is or is not a real
biological phenomenon; rather I am concerned with the structure
of the argument, and the specific way Hull employs the concepts
of replicator and interactor.  In outline, Hull recognises that a
particular kind of entity (``species'') might be absolutely
unable to qualify as a replicator because it doesn't even
procreate (`reproduce'); but that, notwithstanding this, it might
act as an interactor. Unfortunately, after allowing that the
entity cannot procreate, Hull immediately goes on to speak of its
being a member of a lineage (which may evolve). But without
procreation the entities cannot form lineages---which is to say
that, while the entities in question may be ``interactors'' in
some colloquial sense, they seemingly cannot be {\em Hullean\/}
interactors---and it is precisely this latter point which is at
issue.

I shall not labour this discussion any further.   My point is
firstly that I absolutely agree with Hull's distinction between
the {\em functions\/} of replication and interaction, and
secondly that, although I find his further distinction between
{\em entities\/} (replicators and interactors) to be deeply
confusing, I have been unable to establish that it represents any
substantive disagreement between us.

So far I have argued that Hull's idea of an entity which
performs functions of replication {\em and\/} interaction is
essentially equivalent to my concept of a \mbox{(D-)actor}.  Having
distinguished these functions, the substance of Hull's analysis
is then to consider how well (or badly) specific biological
entities, at different ``levels of organisation'' qualify as
performing them.  His conclusion is that the balance between
these two functions is clearly different at different levels.
Thus, genes can be seen as very directly discharging a function
of replication, but their (Hullean) interaction with the
environment (and hence the relationship between their structure
and S-value) is extremely indirect.  Conversely, organisms can be
seen as very directly interacting with their environment (their
structures are directly related to S-value) but their replication
is extremely indirect---as exemplified by the fact that, without
actually carrying out breeding experiments, it is extremely
difficult to establish whether a given organismic characteristic
is heritable (``replicated'') or not.

Hull's further claim is that a significant element of
disagreement over ``units of selection'' may be traced to a
failure to distinguish the functions of replication and
interaction, and a {\em tacit\/} emphasis on only one or the
other.  Thus, if one concentrates on the fact that D-actors {\em
must\/} replicate, one may strongly advocate the primacy of genes
(or, at least, entities at that general level) over organisms;
and conversely, if one concentrates on the fact that D-actors
{\em must\/} interact (in Hull's technical sense), then one may
strongly advocate the primacy of organisms over genes (etc.).
Hull's point is that this is a mistaken dichotomy---{\em both\/}
functions are necessary, and both must be discussed in any
adequate theory of selection.  He makes this point explicitly as
follows:
\begin{quote}

  Genes tend to be entities which pass on their structure most
  directly, while they interact with ever more global
  environments with decreasing directness.  Other, more inclusive
  entities interact directly with their environments but tend to
  pass on their structure, if at all, more and more indirectly.
  {\em Both\/} processes must be performed successfully if
  evolution by natural selection is to take place.  Reasons for
  choosing one necessary element over the over as {\em the\/}
  unit of selection are hard to come by \ldots
  \iciteAD[pp.~34--35]{Hull:UnitsOfEvolution}
\end{quote}

This can now be seen to be essentially equivalent to my own
discussion of these issues in section~\ref{candidates} above, as
originally claimed.

I should emphasise that Hull explicitly accepts that whole
organisms (and possibly even more inclusive entities) {\em can\/}
function as (Hullean) replicators (albeit with a relatively
indirect replication process).  This is significant because he
differs in this regard from Dawkins;  Dawkins argues, for various
reasons, that organisms {\em cannot\/} function as
replicators---not, at least, in his sense of that term.  I shall
consider Dawkins' arguments fully in the next section. For the
moment I merely wish to say that I agree entirely with Hull's
analysis on this point; indeed, insofar as I come up with a
preference among candidate D-actors at all, it is in favour of
organisms.

Finally we come to the point where Hull and I may diverge
somewhat. I agree totally up to the conclusion of the passage
quoted immediately above, where Hull observes that reasons for
preferring replication over interaction (or {\it vice versa\/}),
in judging candidate D-actors, are ``hard to come by''; however,
Hull does not stop at this conclusion, but continues instead to
{\em seek\/} some reason for ranking one function over the other:
\begin{quote}

  \ldots\ The best I can do is the following.  Everyone agrees that both
  genes and organisms are individuals, and that genes form
  lineages by replication. Any change in a gene is reflected
  immediately and directly in successive replicates of that gene.
  Because the sort of inheritance attributed (inappropriately)
  to Lamarck does not occur, changes in the phenotype cannot be
  transmitted directly to the genetic material to be passed on to
  future generations. Instead, the only influence which changes
  in the phenotype is which organisms succeed in reproducing
  themselves and which not [{\it sic\/}].  Genes causally produce
  other genes.  They also enter into the causal production of
  organisms.  But the only thing that organisms can do is
  influence quite indirectly the statistical distribution of
  genes in future gene pools.  In passing from the action of
  genes to the action of organisms, we proceed from definite gene
  lineages to amorphous gene pools, from causal connections to
  relative frequencies.  As persuasive as these considerations
  may (or may not) be, they depend on viewing species as classes
  rather than lineages, an interpretation which biologists are
  beginning to question in increasing numbers.
  \iciteAD[p.~35]{Hull:UnitsOfEvolution} \end{quote}

I have quoted this passage in full, because I find it extremely
difficult to interpret.

Thus: it is simply not true that ``any change in a gene
is reflected immediately and directly in successive replicates of
the gene''---the example of a change in isotopic constitution
demonstrates this much.  Similarly, it is simply not true that,
by contrast, ``the only thing than organisms can do is influence
quite indirectly the statistical distribution of genes in future
gene pools''---or at least, it is not true if Hull is making a
valid comparison with a similar claim about genes.  The point
about a gene is not that ``any'' change to it is replicated, but
that at least {\em some\/} changes to it are replicated---which
is just another way of saying that it is, indeed, a replicator.
But, under Hull's own analysis, organisms are also perfectly good
replicators, in their own right. Or to put it another way, a
change to a gene {\em is\/} a change to an organism.  Granted,
depending on the precise point in the organismic life cycle at
which such a change occurs, it may not be fully ``expressed'' (at
the organism ``level''---or higher) until one or more subsequent
generation(s) have elapsed; but Hull can hardly mean to attach
importance to this, since its ultimate significance is on the
working through of selection, and thus it has exactly the same
relationship to both genes and organisms---it determines the fate
of their respective S-lineages.

Hull seems to see some crucial difference in the ``causal''
\role\ of genes and organisms---a theme that will be taken up
again by Dawkins, as we shall see---but it is difficult to know
what he could be getting at.  He seems to say that genes have a
causal \role\ in the production of organisms, but not {\it vice
versa\/}; but, of course, he cannot really intend that (not at
least with a common sense interpretation of ``causation'') for it
would be tantamount to my genetic absolutism again, which is
embryological nonsense.  On the contrary, organisms play a very
major ``causal'' \role\ in the production of their offspring
(including the production of their offspring's genes).  If Hull's
case is to rest on ``causation'', some further clarification of
his intended usage of the concept would be required.

Despite these difficulties of interpretation, I do think that
Hull has a substantive point to make---and that the key to this
lies in his final remark, when he raises the question of whether
``species'' should be viewed as classes or lineages. In the
light of this final remark, I will attempt to reformulate
Hull's argument in a more explicit form.

Suppose species are well defined classes (in Hull's
sense of ``class'', which is to say that membership is
spatiotemporally unrestricted).  This suggests the possibility
(at least) that, for each such species, there exists a
(spatiotemporally unrestricted) mapping from genotype to
phenotype.  If this is so, then, providing organisms can be
successfully classified as to their species membership, then all
evolutionary processes can be (minimally) expressed purely in
terms of genes (or, at least, genomes), without any
explicit reference to organisms at all (since the Hullean
interaction effects, up to and including the establishment of
S-values, can be inferred from knowledge of the genotype, the
species, and the environment).  This yields a basis (within each
such species) for regarding genomes as minimally sufficient, and
therefore uniquely qualified, D-actors.

This, of course, is just the position I considered and rejected
in my own analysis.  It may well be satisfactory if it is
limited, exclusively, to phyletic evolution---but even then only
if no significant evolutionary changes in ``embryology'' are
occurring. It is flawed as a general view of biological
evolution, because, on any view of what constitutes a
``species'', we want to be able to deal with evolutionary
establishment of species; whereas, if our models are restricted to
work in terms only of genomes {\em within\/} a species (which is
precisely the hypothesis under discussion), then they are
preempted from addressing such establishment.

In anticipating this discussion previously, I said that Hull
presents this particular argument only tentatively, so that the
scope of the disagreement between our analyses is small.  I can
now say that even this may be an overstatement of our differences.
As Hull himself makes clear, the argument he presents only goes
through {\em if\/} species are viewed as classes (rather than
somewhat arbitrarily delimited organism lineages). I can
actually agree with that position---as far as it goes; but I then
go on to make a strong assertion that species should {\em not\/}
be regarded as classes, and that the argument therefore fails
(and is, in fact, pernicious and misleading). By contrast, as far
as I can see, Hull does not commit himself one way or the other
on how ``species'' should be interpreted, and thus leaves the
argument hanging.  So I should say, in conclusion, that any
lingering disagreement I have with Hull seems to be very small
indeed, and may actually be non-existent.

\section{Dawkins: Replicators and Vehicles}

Unlike Hull, Dawkins is primarily an evolutionary biologist
rather than a philosopher, and has not generally regarded himself
as being concerned with an abstract, metaphysical, or ontological
analysis of Darwinism. However, as
\citeAD[p.~30]{Hull:UnitsOfEvolution} puts it, ``Although he is likely to
be shocked, if not offended at being told so, Dawkins
[Dawkins \ociteD{Dawkins:SelfishGene,Dawkins:ReplicatorSelection}] has
made an important contribution to the metaphysics of evolution''.
Indeed, Dawkins himself has explicitly made the claim that
Darwinism (in a suitably abstract formulation) captures
principles which should be applicable to all {\em possible\/}
forms of life:
\begin{quote}
  When astronauts voyage to distant planets and look for life,
  they can expect to find creatures too strange and unearthly for
  us to imagine. But is there anything that must be true of all
  life, wherever it is found, and whatever the basis of its
  chemistry?  If forms of life exist whose chemistry is based on
  silicon rather than carbon, or ammonia rather than water, if
  creatures are discovered that boil to death at $-100$ degrees
  centigrade, if a form of life is found that is not based on
  chemistry at all but on electronic reverberating circuits, will
  there still be any general principle that is true of all life?
  Obviously I do not know but, if I had to bet, I would put my
  money on one fundamental principle. {\em This is the law that
  all life evolves by the differential survival of replicating
  entities.}
  \iciteAD[pp.~205--206, \\emphasis added]{Dawkins:SelfishGene}
\end{quote}

The reference here to ``electronic reverberating circuits''
strongly suggests that Dawkins' claim for the generality of
(abstract) Darwinian processes extends {\it mutatis mutandis\/}
to any attempt to realise ``artificial'' life inside some kind of
computational system. The general concept of the {\em
necessary\/} universality of Darwinian principles has since been
elaborated in more detail by
\citeAD{Dawkins:UniversalDarwinism}.

It is clear then that Dawkins's views are directly relevant to the
stated objectives of this essay (and, indeed, the others in this
series); unfortunately, as has been anticipated somewhat in
previous sections, these views are not at all simple or
clear-cut.  In this section I shall present my own detailed
reinterpretation and critique.

I shall first attempt to justify my claim that Dawkins' doctrine
of the ``Selfish Gene'' is {\em essentially\/} equivalent to my
argument for the ``Selfish S-lineage''.  I consider this to be
the important and valid core of Dawkins' ideas.  Secondly I
consider Dawkins' arguments for genic selectionism---for the idea
that genes (in the sense of fragments of DNA in terrestrial
organisms) are preferred candidates for the \role\ of D-actor (in
the solution of \pr{d}).  Dawkins offers two general kinds of
arguments---one applying only in the case of sexual reproduction
(with recombination of the genetic material) and the other
applying generally.  I shall claim that both of these are flawed,
though in very distinct ways.  However, I shall finally conclude
that, once the question of genic selectionism is separated from
the question of actors versus \mbox{(S-)lineages}---a separation
which Dawkins himself does not recognise or admit---then it
becomes very doubtful whether Dawkins would really wish to pursue
the arguments for genic selectionism {\em in isolation\/} at all.

I should stress at this point that Dawkins does recognise that
there are two separate questions at issue; but his particular
decomposition is, in my view, mistaken.  Consider the
following statement of his position:
\begin{quote}

  \ldots\ I shall develop a distinction between {\em replicator
  survival\/} and {\em vehicle selection}.  Anticipating the
  conclusion, there are two ways in which we can characterise
  natural selection.  Both are correct; they simply focus on
  different aspects of the same process.  Evolution results from
  the differential survival of {\em replicators}. Genes are
  replicators; organisms and groups of organisms are not
  replicators, they are vehicles in which replicators travel
  about. Vehicle selection is the process by which some vehicles
  are more successful than other vehicles in ensuring the
  survival of their replicators.  The controversy about group
  selection versus individual selection is a controversy about
  the rival claims of two suggested kinds of vehicle.  The
  controversy about gene selection versus individual (or group)
  selection has been a controversy about whether, when we talk
  about a unit of selection, we ought to mean a vehicle {\em at
  all,} or a replicator.
  \iciteAD[p.~46]{Dawkins:ReplicatorsAndVehicles}
\end{quote}

In the light of the previous discussion, I would rephrase this as
follows (throughout, ``survival'' should be read as survival$_2$,
or survival of {\em lineages\/}):
\begin{quote}

I shall develop a distinction between {\em S-lineage
survival\/} and {\em D-actor selection}.  Anticipating the
conclusion, there are two ways in which we can characterise
natural selection.  Both are correct; they simply focus on
different aspects of the same process.  Evolution results from
the differential survival of {\em S-lineages}. \lgenes\ (for
example) are S-lineages; \agenes, organisms and groups of
organisms are not S-lineages, they are (at best) D-actors which
compose S-lineages. D-actor selection is the process by which
some D-actors are more successful that other D-actors in ensuring
the survival of their S-lineages.  The controversy about group
selection versus individual selection is a controversy about the
rival claims of two suggested kinds of D-actor.  The controversy
about gene selection versus individual (or group) selection has
been a controversy about whether, when we talk about a unit of
selection, we ought to mean an D-actor {\em at all,} or an
S-lineage.

\end{quote}

Read in {\em this\/} way, there would seem to be no disagreement
between us at all.  This appearance of agreement arises because,
in the passage quoted, Dawkins comes very close to using ``vehicle'' in
my sense of ``D-actor'' and ``replicator'' (or ``gene'' for that
matter) in my sense of ``S-lineage''.  Unfortunately, such an
interpretation seems not to be consistent with the bulk of Dawkins'
writings. The difference between us is exemplified
by the fact that, according to Dawkins, biological organisms {\em
cannot\/} qualify as Dawkinsian replicators; whereas I argue that they
certainly {\em can\/} qualify as D-actors.  The task then, is to
establish precisely the scope both of our agreement and of our
disagreement.

\subsection{What {\em is\/} a Selfish Gene?}

I must now try to justify the claim that the idea of the selfish
S-lineage is (at the least) compatible with Dawkins' analysis---that
Dawkins holds, firstly, that the unit of selection must be a
lineage rather than an actor and, secondly, that the particular
and unique kind of lineage required is what I have termed an
S-lineage.

I have already argued that Dawkins uses ``replicator'' in both of
the distinct senses I have identified---\arpl\ and \lrpl. I can
now elaborate this claim in more detailed and formal terms; I
claim that:
\begin{enumerate}

\item A Dawkinsian \lrpl\ is a lineage whose members are
Dawkinsian \arpls, though he refers to both these distinct kinds of
entities simply as ``replicators''.

\item When Dawkins is discussing the identity of the unit of
selection---particularly in phrases like {\em The Selfish Gene\/} or
{\em The Selfish Replicator}---he exclusively uses ``gene'' or
``replicator'' in the sense of \lrpl.

\item Dawkins' \arpls\ are {\em essentially\/} (but not exactly)
equivalent to my D-actors.  In particular, when their offspring
are ``identical'' in Dawkins' terms, they are procreating as
D-actors (preserving S-class) in my terms, and such offspring are
S-offspring, members of S-lineage(s). These, and only these,
lineages are what Dawkins' recognises as \lrpls\, or the units of
selection.

\end{enumerate}

I shall not argue the first point: were this not the case, Dawkins'
ambiguity of usage between \arpl\ and \lrpl\ (already documented in
section~\ref{repl} above) could hardly arise.

Taking the second point, consider the following sample
quotations:
\begin{quote}

  Genes, like diamonds, are forever, but not quite in the same
  way as diamonds.  It is an individual diamond crystal that
  lasts, as an unaltered pattern of atoms.  DNA molecules don't
  have that kind of permanence.  The life of any one physical DNA
  molecule is quite short---perhaps a matter of months, certainly
  not more than one lifetime.  But a DNA molecule could
  theoretically live on in the form of {\em copies\/} of itself
  for a hundred million years.
  \iciteAD[p.~37]{Dawkins:SelfishGene}

  \bigskip
  What is the selfish gene?  It is not just one single physical
  bit of DNA \ldots\ it is {\em all replicas\/} of a particular
  bit of DNA, distributed throughout the world.
  \iciteAD[p.~95]{Dawkins:SelfishGene}

  \bigskip
  The reason a replicator is interesting to Darwinians is that it
  is potentially immortal, or at least very long-lived in the
  form of copies. A successful replicator is one that succeeds in
  lasting, {\em in the form of copies,} for a very long time
  measured in {\em generations} \ldots\
  \iciteAD[pp.~87--88, \\emphasis added]{Dawkins:ExtendedPhenotype}

  \bigskip
  I have lavished much rhetoric, or irresponsibly purple prose if
  you prefer, on expounding the view that `the unit of
  selection' \ldots\ must be a unit that is potentially immortal
  [\ociteAD[chapter~3]{Dawkins:SelfishGene}] a point which I
  learned from Williams [\ociteAD{Williams:Adaptation}].
  Briefly, the rationale is that an entity must have a low rate
  of spontaneous, endogenous change, if the selective advantage
  of its phenotypic effects over those of rival (`allelic')
  entities is to have any significant evolutionary effect.
  \iciteAD[p.~48]{Dawkins:ReplicatorsAndVehicles}
\end{quote}

I think these clearly show that Dawkins intends gene/replicator
as a lineage rather than an actor in this context, i.e.\ when he
is speaking of `the unit of selection'. It is important at this
point to reiterate a critical difference between Dawkins and
Hull. This is that Hull normally uses ``replicator'' ({\em and\/}
``interactor'', for that matter) in the sense of an actor,
whereas Dawkins uses ``replicator'' in the sense of a
lineage---at least when he is referring to the ``unit of
selection''.  Thus their two viewpoints on the unit of selection
are not merely different, but incommensurable---they are
answering different questions, using different concepts; which
makes it somewhat unfortunate, to say the least, that they both
elect to employ a single token ({\em replicator\/}) for their
different purposes.  This point must be emphasised because it has
not been recognised by Hull, and Dawkins has actively suggested
that the opposite is the case---that they are both presenting
similar answers to the same question
\cciteAD[pp.~82--83]{Dawkins:ExtendedPhenotype}.

But to return to the issue at hand: the fact that Dawkins intends
{\em gene}, or {\em replicator}, as a lineage rather than an
actor still leaves open the question of whether he means {\em
S-lineage\/} as such (and not any other kind of lineage).  This,
in turn, depends on the third claim made above, that when Dawkins
uses replicator in the sense of \arpl, he has in mind the notion
of descent with {\em similarity\/} (S-descent); that is, only
offspring which are similar, in some particular way(s), to the
parent(s) will ``count'' as offspring at all.

Consider then Dawkins' basic definitions:
\begin{quote}

  I define a {\em replicator\/} as anything in the universe of
  which copies are made.  Examples are a DNA molecule, and a
  sheet of paper that is xeroxed \ldots\

  An {\em active replicator\/} is any replicator whose nature has
  some influence over its probability of being copied. For
  example a DNA molecule, via protein synthesis, exerts
  phenotypic effects which influence whether it is copied: this
  is what natural selection is all about.  A {\em passive
  replicator\/} is a replicator whose nature has no influence
  over its probability of being copied.  A xeroxed sheet of paper
  at first sight seems to be an example, but some might argue
  that its nature {\em does\/} influence whether it is copied,
  and therefore that it is active: humans are more likely to
  xerox some sheets of paper than others, because of what is
  written on them, and these copies are, in their turn,
  relatively likely to be copied again. A section of DNA that is
  never transcribed might be a genuine example of a passive
  replicator \ldots\
  \iciteAD[p.~83]{Dawkins:ExtendedPhenotype}

  \bigskip
  No copying process is infallible.  It is no part of the
  definition of a replicator that its copies must all be perfect.
  It is fundamental to the idea of a replicator that when a
  mistake or `mutation' does occur it is passed on to future
  copies: the mutation brings into existence a new kind of
  replicator which `breeds true' until there is a further
  mutation.  When a sheet of paper is xeroxed, a blemish may
  appear on the copy which was not present on the original.  If
  the xerox copy itself is now copied [the] blemish is
  incorporated into the second copy (which may also introduce a
  new blemish of its own).  The important principle is that in a
  chain of replicators errors are cumulative.
  \iciteAD[p.~85]{Dawkins:ExtendedPhenotype}
\end{quote}

There are a number of points to be made here.

Firstly it should be clear that, throughout {\em this\/}
discussion, Dawkins is referring to \arpls\ and not \lrpls.

Secondly I should mention that, in addition to distinguishing
active and passive \arpls, Dawkins also distinguishes between
``germ-line'' and ``dead-end'' \arpls.  I take the latter
distinction to be an attempt to deal with the fact that
multicellular organisms (for example) have multiple genomes
(etc.), which complicates the numerical relationship between
genomes and (organismic) S-sizes. Related difficulties can arise
in various other contexts also---social insect colonies for
example.  I chose to deal with this kind of problem via the
distinction between c-genomes and o-genomes.  Obviously I have a
(mild) preference for my own approach; but I do not think there
is a fundamental disagreement here, and I shall not pursue this
particular issue.

Thirdly, while Dawkins is not too explicit about exactly what
``copying'' involves, it clearly includes {\em at least\/} the
notions of descent and similarity---which are essentially the
defining notions for my S-descent, and for Hull's
``replication''. Indeed, Dawkins explicitly and favourably quotes
Hull's distinction between similarity and descent (as also quoted
in section~\ref{hull} above), and the need for both to be
present \cciteAD[p.~84]{Dawkins:ExtendedPhenotype}.

Fourthly, in distinguishing active and passive \arpls\ Dawkins
introduces something essentially equivalent to Hull's distinction
between replication and interaction.  That is, {\em all\/}
Dawkinsian \arpls\ are Hullean replicators; {\em active\/}
Dawkinsian \arpls\ additionally qualify as Hullean interactors;
{\em passive\/} Dawkinsian \arpls\ qualify as Hullean
replicators but not as Hullean interactors (and are thus a
class of entity for which Hull has no explicit name).

As already discussed, Hulls' approach implies the possible
existence of interactors which are not (Hullean)
replicators---i.e.\ entities which realise (Hullean) interaction
but not (Hullean) replication.  I said that I found this implied
concept incoherent, and Hull's presentation confusing as a
result. Dawkins' approach, on the other hand, is explicitly
stated as a {\em partition\/} of the class of Dawkinsian \arpls,
and avoids any analogue of the Hullean
interactor-but-not-replicator; one does not even try to imagine
an entity which, in Dawkins' terminology, would be {\em active\/}
but not a (Dawkinsian) \arpl. I therefore prefer Dawkins'
formulation.  On the other hand, as Dawkins himself stipulates,
it is only active \arpls\ which are of interest in discussing
Darwinian evolution, so the distinction is perhaps not all that
important anyway.  In my own formulation of the \mbox{(D-)actor},
this distinction is implicit in my discussion of the requirement
that (for selection to occur) S-class must be ``predictive'' of
S-value; but, like Hull, I do not introduce a separate term to
explicitly distinguish such S-classes
\cciteAD[esp.\ Sections~6.1 and~6.4]{McMullin:DarwinianOntology}.

I may say that I consider my formulation to be marginally superior to
Dawkins' insofar as I explicitly note that S-value depends on
{\em both\/} S-mortality or S-fecundity, whereas Dawkins'
``influence over its probability of being copied'' seems to
explicitly allow only for S-fecundity effects; but having said
that, Dawkins' formulation could be easily augmented to take
account of this---I do not suggest that its omission is a
substantive defect.

I should note here that Dawkins himself adopts a very different
view of the relationship between his concepts and Hull's.  He has
not given any extended or detailed analysis, as far as I am
aware, but he seems to consider that their two versions of
``replicator'' are equivalent, and he explicitly equates
Hull's ``interactor'' with a kind of entity he now terms a {\em
vehicle\/} \cciteAD[p.~100]{Dawkins:ExtendedPhenotype}.  I will
consider the Dawkinsian ``vehicle'' concept in somewhat more
detail below; for the moment it is sufficient to record my
disagreement with Dawkins on these points.  I shall argue that
there is a subtle, but important, distinction between their
respective notions of \mbox{(A-)replicator;} and also between Hull's
``interactor'' and Dawkins' ``vehicle''. Dawkins' equation of the
latter two seems to be based on the fact that Hull recognises
organisms as more or less prototypical cases of interactors,
while Dawkins recognises them as prototypical vehicles.  That
this interpretation is too shallow is revealed, for example, by
the fact that Hull argues at length that organisms {\em also\/}
qualify as replicators in his terms, whereas Dawkins argues (at
even more length) that organisms definitely are {\em not\/}
replicators in his terms.

However, let us return to the immediate question---which is the
relationship between Dawkins' \arpls\ and my D-actors. Dawkins
explicitly recognises the idea of an \arpl\ giving rise to a copy
which is different from the parent in a way which is,
subsequently, heritable.  That is, Dawkinsian \arpls\
incorporate a distinction which is clearly related to my
distinction between S-descent (preservation of specified parental
characteristics in the offspring) and S-creation (origination of
new characteristics, not present in the parent(s), which may be
preserved in subsequent offspring).

Neither Dawkins nor Hull make the distinction between S-descent
and S-creation quite as sharply as I do; but that they have an
equivalent distinction in mind is apparent from their discussions
of the ``degree of similarity'' between parent and offspring
required for an entity to qualify as a replicator (under either
of their interpretations).  Hull requires that parent and
offspring be similar enough ``to respond similarly to similar
selection pressures''
\cciteAD[p.~321]{Hull:IndividualityAndSelection}; Dawkins expresses
himself in essentially the same terms
\cciteAD[p.~89]{Dawkins:ExtendedPhenotype}.  Both Hull
(implicitly) and Dawkins (explicitly) refer to the following comment
from Williams, as a source for their views:
\begin{quote}
  In evolutionary theory, a gene could be defined as any hereditary
  information for which there is a favorable or unfavorable selection
  bias equal to several or many times its rate of endogenous change.
  \iciteAD[p.~25]{Williams:Adaptation}
\end{quote}

I should emphasise that I accept this general position, which
envisages that both heritability and selection pressure may, in
general, form continua, and that the differentiation between
S-descent and S-creation may not be easy to definitively
establish in any particular context (subject to some caveats:
see, in particular, my discussion of ``digital'' inheritance,
\ociteAD[Section~6.5]{McMullin:DarwinianOntology}).  My point is
that, while the two may be hard to distinguish {\em
methodologically}, the distinction is {\em conceptually\/} a
fundamental one---S-descent and S-creation play entirely
different \roles\ in the Darwinian solution of \pr{d}, \roles\
which must not be confused.  It is for this reason that, in
contrast to Hull and Dawkins, I have made this distinction so
explicit, even to the point of introducing an additional
technical terminology to reflect it.

For strictly {\em Darwinian\/} evolution I have stipulated that
S-creation must be ``unjustified'', in the sense of not involving
anticipatory models of resulting S-value (this is my distinction
between ``actors'' in general, and ``\mbox{D(arwinian-)}actors''
in particular).  Dawkins has not discussed this particular issue
in terms of his abstract \arpl\ concept; however, he has dealt
with it in his more general evolutionary writings, as I have
discussed elsewhere \cciteAD[Section~3.4]{McMullin:Organismic}.
I shall not repeat that discussion, but simply adopt the
implication that, here again, Dawkinsian \arpls\ are compatible
with my notion of D-actors.

The conclusion from all these arguments is that Dawkinsian active
\arpls\ have all the required properties to qualify as D-actors
in my terms; specifically:
\begin{itemize}

\item Their offspring are generally related to the parent(s) by
both descent and similarity.

\item The similarity in question is precisely such as to allow
selection between \mbox{(similarity-)}lineages to work itself
through.

\item There is a possibility of offspring which incorporate new
characteristics, not possessed by any of its parent(s), but which are
subsequently heritable, thus founding new
\mbox{(similarity-)}lineages which may participate in selection.

\item This origination of new, heritable, characteristics is, in
some cases at least, unjustified.

\end{itemize}

I claim, furthermore, that these properties, shared by D-actors
and Dawkinsian \arpls, are the {\em only\/} properties required
for Darwinian evolution to take place.  In particular, this
establishes that when Dawkinsian \arpls\ produce ``perfect''
offspring, they are behaving as D-actors, forming S-lineages,
between which competitive elimination (etc.) may occur.  This,
precisely, is the logic to identifying \mbox{(L-)replicators} as
the ``units of selection'', and this validates my claim that
Dawkins' ``Selfish Replicator'' (or ``Selfish gene'' for that
matter) is equivalent to my ``selfish S-lineage''.

Having established that Dawkins' abstract analysis of selection
(and Darwinian evolution generally) is at least compatible with
my analysis in terms of D-actors, I now finally claim that the
latter is somewhat preferable because of its more explicit
treatment of the following points:
\begin{itemize}

\item Both S-fecundity and S-mortality must be correlated with
S-class (not just S-fecundity as implied in Dawkins' version).

\item S-fecundity and S-mortality are exclusively characteristics
of S-lineages not of D-actors (this is confusingly ambiguous in
Dawkins' version).

\item The essential requirement is that the selection dynamics
(especially complete elimination of one S-lineage by another) be
effectively {\em deterministic\/} (once the initial S-lineages are
given); at best, this is only implicit in Dawkins' treatment.

\item S-descent and S-creation play quite different and
distinctive \roles.

\item S-creation must be unjustified with respect to S-value.

\end{itemize}

\subsection{Rival D-actors?}

In contrast to ``replicator'', Dawkins does not provide a
detailed discussion of his abstract notion of ``vehicle''. This
is because he ultimately considers the concept to be of limited
value.  However, it is a convenient tool for our present
purposes.  Roughly speaking, Dawkins identifies as vehicles any
entities which, for whatever reason, are not Dawkinsian \arpls\
in themselves, but which ``contain'' \arpls, and which work
toward the propagation (replication) of those contained
\arpls.  Dawkins stipulates that, in the biological world,
organisms must be regarded as vehicles and not \arpls.  My
criticism will be directed at this latter claim, rather than at
the general or abstract notion of the Dawkinsian vehicle itself.

To outline the structure of my discussion, I must first note that
a significant point was left dangling in the previous section.  I
commented, variously, that the Dawkinsian \arpl\ was
``essentially'' ({\em not\/} exactly) equivalent to my D-actor,
and that there is a ``subtle, but important'' distinction between
the Dawkinsian \arpl\ and the Hullean replicator.  Briefly, my
position is this: all Dawkinsian \arpls\ qualify as
D-actors (and, indeed, as Hullean replicators)---but not {\it
vice versa}.

I defer, for the moment, the examination of exactly how
Dawkinsian \arpls\ and D-actors differ: the important point, at
this stage, is that not all D-actors will qualify as Dawkinsian
\arpls. Quite generally in fact, Dawkins' distinction between
\arpls\ and vehicles may be regarded as a partition of my class
of D-actors; that is, it will turn out that only certain D-actors
qualify as Dawkinsian \arpls, and all other D-actors should be
regarded, by default, as Dawkinsian vehicles.

It follows that the question of the nature or \role\ of
biological organisms in selection processes can be divided into
two subsidiary questions:
\begin{enumerate}

\item Do organisms qualify as D-actors? My answer is a simple
{\em Yes}.  Dawkins, on the other hand, distinguishes the cases
of purely asexual organisms, and organisms engaging in sexual
reproduction (with meiosis); he appears to accept that the former
would qualify as D-actors, but rejects the latter.

\item Do organisms qualify as Dawkinsian \arpls?  Dawkins and I
are agreed that the answer to this is {\em No}.  Specifically,
although I argue that all organisms qualify as D-actors, I accept
that the Dawkinsian \arpl\ is a more restrictive class than that
of D-actor, and that organisms do not qualify as belonging to
this more restrictive class.  {\em However,\/} Dawkins and I
differ fundamentally on the implications which may be drawn from
this fact. Dawkins effectively claims that the distinction
between D-actors in general, and Dawkinsian \arpls\ in
particular, is such that the latter should be preferentially
regarded as the ``true'' D-actors in selection processes---at
least as compared to formally equivalent candidates which are
{\em not\/} Dawkinsian \arpls.  I shall argue that the
distinction Dawkins identifies cannot bear the theoretical weight
he places on it; that it does not give a basis for rejecting
organisms as candidate D-actors; and that, on the contrary, the
general issues Dawkins raises may yield a mild {\em preference\/}
for organisms as D-actors (over, say, genomes or genes etc.).

\end{enumerate}

I shall consider these questions in turn, in the following
sections.

\subsubsection{Does sex {\em really\/} matter?}

\begin{quote}

  In sexually reproducing species, the individual is too large
  and too temporary a genetic unit to qualify as a significant
  unit of natural selection.  The group of individuals is an even
  larger unit.  Genetically speaking, individuals and groups are
  like clouds in the sky or dust-storms in the desert.  They are
  temporary aggregations or federations.  They are not stable
  through evolutionary time\ldots\

  Chromosomes too are shuffled into oblivion, like hands of cards
  soon after they are dealt.  But the cards themselves survive
  the shuffling.  The cards are the genes.  The genes are not
  destroyed by crossing-over, they merely change partners and
  march on.  Of course they march on.  That is their business.
  They are the replicators and we are their survival machines.
  When we have served our purpose we are cast aside.  But genes
  are denizens of geological time: genes are forever.
  \iciteAD[pp.~36--37]{Dawkins:SelfishGene}
\end{quote}

Dawkins' argument for the inadmissibility of organisms (and,
indeed, genomes and chromosomes too) even as {\em candidate\/}
D-actors, in sexually reproducing species, seems straightforward
enough at first sight.

We first accept that there is significant standing genetic
heterogeneity in natural populations (e.g.\
\ociteAD{Ayala:MechanismsOfEvolution}). It follows that, with
overwhelming probability, every organism will be genetically
unique.  If we S-classify simply on this basis, then no coherent
S-lineages can form (since no offspring will match the S-class of
either parent, so no S-descent will occur), and selection cannot
take place.  If, however, we consider, instead, relatively short
fragments of DNA, occupying some identified locus, then
(S-classifying them in the same way) there will now be a ``high''
probability that they will bear offspring of the same S-class; so
coherent S-lineages can form, and selection becomes possible.
Therefore, under conditions of sexual reproduction, nothing more
inclusive than a ``short'' fragment of DNA (not chromosomes, not
genomes, and definitely not organisms) can function as a D-actor.

Despite the seeming clarity of the argument we should already be
deeply suspicious.  For example, my reference to fragments of
DNA ``occupying some identified locus'' is immediately
problematic---for such a locus can, at best, only be defined {\em
relative\/} to a complete genome---yet genomes supposedly have no
more stability than ``dust storms in the desert'', and thus can
hardly form a context for identifying the putative ``immortals''.
Nonetheless, clearly identifying {\em exactly\/} what is wrong
with Dawkins' argument is quite tricky.  I shall critically
consider a number of attempted refutations.

Hull has considered the possibility that Dawkins may be
overstating the degree of standing genetic heterogeneity present
in natural populations---at least in the cases of most
evolutionary interest.  He cites a number of biologists as
arguing that speciation, in particular, usually occurs among sexually
reproducing organisms when a very few become isolated from the
main body of their species; he then continues:
\begin{quote}
  The effects of such a rapid reduction in population size are
  numerous and fundamental.  For example, in most populations,
  several different alleles exist at most loci.  One pregnant
  female, to mention the most extreme case, is unlikely to
  express much of the genetic heterogeneity of her population in
  her offspring.  The ensuing inbreeding characteristic of such
  small populations is likely to increase homozygosity even
  further.  It may well be true that the genomes of sexually
  reproducing organisms are `torn to smithereens' at meiosis in
  large, genetically heterogenous populations, but according to
  the model of speciation by `genetic revolutions' currently so
  popular, all that is going on in such large populations is the
  haphazard fluctuation of allele frequencies. When it really
  matters, when new species are arising, sexually reproducing
  organisms converge on functioning as replicators.
  \iciteAD[p.~36]{Hull:UnitsOfEvolution}
\end{quote}

I find this argument unconvincing, as presented. It is no doubt
true that the genetic variability represented by a single
pregnant female will generally be significantly {\em less\/} than
for the population as a whole; it is also true that heterogeneity
is likely to fall further immediately following isolation,
essentially due to the significant effects of genetic drift in
small populations (Hull's ``inbreeding characteristic''); but
this is a long way from establishing that genetic variability in
the isolated population will be reduced to just a single genetic
locus---which would seem to be what is required by Hull's
argument. Hull does not seem not to allow for the possibility
that, even though the variability present in a small
subpopulation may be small {\em relative\/} to the population as
a whole, it could still be quite large in {\em absolute\/} terms;
and that, further, the variability required to make Dawkins'
argument go through is not very large in absolute terms anyway,
due to the combinatorial explosion which is implicit in it. That
is, it does not require variability at very many loci to mean
that, with overwhelming probability, a genome will be disrupted
by recombination.

To be specific, \citeAD{Ayala:MechanismsOfEvolution} has
estimated that in the case of humans, for example, the genetic
variability present even in a single (diploid) individual (which
would be a marginally {\em more\/} restrictive case that Hull's
pregnant, diploid, female, which is effectively a ``population''
of somewhat more than a single genetic individual) is still such
as to allow for something of the order of $10^{2,000}$ (!)
genetic variations by recombination. The probability of
``perfect'' replication of a genome would be roughly of the order
of the reciprocal of this, and is obviously negligable. I doubt
that, as a general principle, inbreeding (which would presumably
be transient, as the population expands?) would materially affect
this calculation. If Dawkins' argument works at all (and Hull
makes his point explicitly in the context of {\em accepting\/}
``Dawkins' general analysis of replicators''), then it seems that
it would still work {\em even\/} in the case of very small
populations. This idea of Hull's is interesting, but ultimately
cannot go through as it stands.

A quite different, but closely related, argument could be mounted
based on the theory of {\em punctuated equilibrium\/} of
\citeAD{Eldredge:PunctuatedEquilibria}.  This is the
general idea that most species evolve little through most of
their existence; that evolutionary change in concentrated in
small, relatively short, bursts, associated with speciation
(i.e.\ the establishment of a new lineage reproductively isolated
from the predecessors). So far, this is similar to Hull's
discussion. However, Eldredge and Gould have gone further than
this, and have argued that speciation events {\em might\/} be
``essentially random'' with respect to long term evolutionary
changes \cciteAD{Gould:TempoOfEvolution}, an idea
they attribute (perhaps misleadingly) to Sewall Wright.  If this
is the case, then the decisive selection events in evolutionary
history are not between lineages {\em within\/} an interbreeding
population (or between genes in a shared gene pool) {\em at
all\/}; rather they take place between lineages which are {\em
reproductively isolated\/} from each other---separate species in
effect. Now, if this is the case, then, by definition, the
relevant genetic differences are not getting rearranged or
recombined in sexual reproduction---for the two species are
reproductively isolated. In effect we are back to the logic of
asexual reproduction and Dawkins' argument is simply not
applicable.  However, I should point out that, as far as I am
aware, neither Eldredge nor Gould have explicitly applied the
theory of punctuated equilibrium in the particular way in
which I use it here.

I consider that this argument is valid as far as it goes; but its
scope is explicitly limited to selection between reproductively
isolated lineages.  It represents not so much a refutation as an
avoidance of Dawkins' argument.

A separate, but related, argument has been proposed by Hull. The
idea is that there may well be ``genetic variability'' at many
loci, but this does not mean that most, or even any, of this is
significant for selection.  Thus, in discussing sexual
reproduction between genetically heterogenous organisms, Hull
states that ``Dawkins would argue that only those segments of the
genetic material which remained undisturbed can count as
replicators, while I see no reason not to consider the organisms
themselves replicators if the parents and offspring are
sufficiently similar to each other''
\cciteAD[p.~34]{Hull:UnitsOfEvolution}; this is in the context of an
earlier interpretation of ``similar enough'' as meaning to
``react similarly to similar selection pressures''
\cciteAD[pp.~32--33]{Hull:UnitsOfEvolution}.  Elsewhere, Hull makes the
more explicit claim that ``Much of the genetic heterogeneity
present in populations has little or no phenotypic effect'',
\cciteAD[p.~321]{Hull:IndividualityAndSelection}.  Thus (though Hull
does not spell this out) it may well be that there is, at any
given time, at most {\em one\/} genetic locus at which the
variability is correlated with significant differences in
S-value of the S-lineages that are labelled by the gene at that
locus.

We can distinguish two sub-cases here.  There may be genetic
variability which, though empirically detectable, simply has no
significant effect at all, in the normal environment of the
D-actor.  If it has no effect at all, it clearly has no
selectively significant effect. An alteration of a codon to
another synonymous codon (i.e.\ such that the cistron still codes
for the same protein) would seem to be a possible candidate for this
category.  The second possibility is that the genetic variability
has some effect, but this effect is either neutral or balanced
with respect to selection.  For example, a balanced genetic
polymorphism (such as the male/female dimorphism) represents
genetic variability in the population, but there is no on-going
``selection'' (in the sense of displacement of one S-lineage by
another) going on. Neglecting the possibility of non-linear
interactions between the dynamics of S-lineages anchored on
different genetic loci (i.e.\ neglecting the possibilities of
linkage and/or epistasis)---for the moment at least---this
variability will not be affected by selection at any other locus,
but will remain (statistically) constant.  It is thus not
significant from the point of view of S-classification, and can
be factored out.

In both cases, the conclusion is that if, for whatever reason,
selection is only occurring with respect to a single genetic locus
at any given time, then standing genetic ``variability'' at other
loci is irrelevant (to S-classification) and cannot be used as a
basis for arguing that whole genomes, or more inclusive entities,
are not ``replicated''.

In effect, Hull here introduces the idea that S-classification
need not respect {\em all\/} ``genetic'' differences (i.e.\ all
differences of DNA base sequence), but can (indeed must) be
limited to recognising only those differences which identify {\em
selectively\/} distinguished S-lineages.  In this way it becomes
much more plausible that the significant or relevant genetic
variability may be limited to a single locus---in which case
Dawkins' argument from disruption through recombination no longer
applies.

Again, however, while this refutation is valid as far as it goes,
it does not seem to go far enough.  It {\em still\/} succeeds
only by avoiding rather than confronting Dawkins' argument.  We
would prefer a refutation which works even in the case of
concurrent selection at multiple loci---the case where Dawkins'
argument would seem to be at its strongest.  We must now face up
squarely to this case.

By hypothesis then, we suppose that there is selectively
significant genetic variability in the population, at a number of
loci.  If we attempt to consider genomes (or organisms) as
D-actors, S-classifying them on the basis of {\em all\/} these
loci, then, due to the fragmenting effect of meiosis, every
genome (and organism) will, with overwhelming probability, be in
a unique S-class. Thus, S-lineages cannot form, and selection
cannot arise. Contrariwise, if we consider individual genes as
D-actors they will not be disrupted by meiosis, S-lineages can
form, and we can see selection in action. This is the thrust of
Dawkins' argument that {\em only\/} genes can qualify as D-actors
in this case.

The fundamental defect in Dawkins' argument can now be
identified: it is the (implicit) assumption that, if genomes or
organisms are to be considered as candidate D-actors, they must
be S-classified on the basis of {\em all\/} (variable) genetic
loci.  But there is no compelling reason why S-classification
should be restricted in this way.  This point has already been
analysed at length in section~\ref{equivalence} above, and the
analysis will not be repeated here.  In brief, the relevant point
is that we can (for example) identify genome (or organism)
S-classes relative to just a single locus; indeed, this is
precisely the typical practice of evolutionary biologists.
Genome (or organism) S-lineages identified in this way will
necessarily show essentially the selective dynamics which Dawkins
assumes for gene S-lineages. Granted, the genome (or organism)
S-lineages anchored on distinct genetic loci will intersect in
ways which the gene S-lineages do not, which {\em may\/} make the
state descriptions in terms of genomes (or organisms) somewhat
more complicated; but it doesn't seem to me that this has any
deep-seated significance.

Dawkins has not, as far as I am aware, expressly recognised, much
less disputed, this point of view.  I therefore consider that,
({\it pro tem\/}) it offers a decisive refutation of this
particular argument of Dawkins'; indeed, it may be said to
subsume the valid core of all the other attempted refutations
considered above.

This establishes the general equivalence or interchangeability of
gene, genome, and organism (for example) as candidate D-actors.
However, before finally closing this discussion I should now like
to push one step further and argue that, in fact, organisms may
be {\em preferable\/} candidates (under the assumption of sexual
reproduction).  This argument has already been outlined in
section~\ref{candidates} above. My purpose here is to
specifically review how this issue has been dealt with by
Dawkins himself, and by his critics.

Consider first the following criticism offered by Gould:
\begin{quote}

  No matter how much power Dawkins wishes to assign to genes,
  there is one thing that he cannot give them---direct visibility
  to natural selection. Selection simply cannot see genes and
  pick among them directly. It must use bodies as an
  intermediary.  A gene is a bit of DNA hidden within a cell.
  Selection views bodies.  It favours some bodies because they
  are stronger, better insulated, earlier in their sexual
  maturation, fiercer in combat, or more beautiful to behold.
  \iciteAD[Essay~8, p.~76]{Gould:PandasThumb}
\end{quote}

Gould goes on to assert that Dawkins' view could (only) work if
there were some kind of ``one-to-one'' mapping between genes and
tangible, external, bodily manifestations; and of course, there
is no such mapping.

Dawkins has taken the opportunity of a new edition of {\em The
Selfish Gene\/} to respond to this and similar criticism by
quoting, at length, from the original edition, his repeated
rejection of any such ``genetic atomism'',
\cciteAD[pp.~271-2]{Dawkins:NewSelfishGene}.  Dawkins argues,
correctly in my view, that interaction between genetic loci in
their correlation with phenotypic effects does not, {\em in
itself,} undermine his analysis in the slightest.

I suggest that Gould actually had the correct idea here, but it
unfortunately got fatally sidetracked. It is true that, {\em
if\/} there is a one-to-one mapping between genetic loci and
selectively significant phenotypic effects, it is quite possible
(likely even) that Dawkins' genes-eye view can be validated.
{\em But the converse does not follow.} The fact (as biological
fact it seems to be) that there is no such one-to-one mapping
does not, of itself, mean that the genes-eye view is at all
problematic.

I suggest that the crucial question here is precisely that of
{\em non-linear\/} interaction between the S-size dynamics of
S-lineages anchored on distinct genetic loci.  It seems to me
that this is only loosely related, if at all, to the question of
whether the mapping between genetic loci and phenotypic traits is
one-to-one, and that Gould was mistaken in compounding the two.
It is quite possible to envisage very complex interactions
between genes, but which still combine linearly in their effects
on S-value. In such cases (and only such cases) it is precisely
true that the outcome of selection can be represented in terms of
selective forces acting {\em directly\/} (and I mean this as
literally as is possible in the context) on individual genetic
loci---{\it pace\/} Gould.

I think that this point---that the genes-eye is perfectly
compatible with arbitrarily ``complicated'' interaction effects,
{\em provided\/} that they do not give rise to non-linearity in
the coupling between S-lineages anchored on different loci---has
been central to at least some of Dawkins' analysis.  In
particular, it is implicit in his {\em initial\/} formulation of
an analogy for natural selection based on the selection of a
rowing crew:
\begin{quote}

  One oarsman on his own cannot win the Oxford and Cambridge boat
  race.  He needs eight colleagues.  Each one is a specialist who
  always sits in a particular part of the boat---bow or stroke or
  cox etc.  Rowing the boat is a cooperative venture, but some
  men are nevertheless better at it than others.  Suppose a coach
  has to choose his ideal crew from a pool of candidates, some
  specializing as cox, and so on.  Suppose that he makes his
  selection as follows.  Every day he puts together three new
  trial crews, by random shuffling of the candidates for each
  position, and he makes the three crews race against each other.
  After some weeks of this it will start to emerge that the
  winning boat often tends to contain the same individual men.
  These are marked up as good oarsmen.  Other individuals seem
  consistently to be found in slower crews, and these are
  eventually rejected.  But even an outstandingly good oarsman
  might sometimes be a member of a slow crew, either because of
  the inferiority of the other members, or because of bad
  luck---say a strong adverse wind.  It is only {\em on
  average\/} that the best men tend to be in the winning boat.
  \iciteAD[p.~40]{Dawkins:SelfishGene}
\end{quote}

While Dawkins does not explicitly refer to ``linearity'' (or even
``additive'' effects) here, I suggest that this particular
formulation is clearly based on an assumption that, in fact, the
performance of a crew is linearly related to characteristics of
its members.

Let us stipulate then that, in the absence of non-linearity, the
genes-eye view is perfectly satisfactory (and may even offer some
formal simplification relative to viewing genomes or organisms as
the D-actors, at least for diploid or polyploid organisms).  The
question is to assess the significance of non-linearity for the
dynamics of selection, under sexual reproduction.

As with most questions dealing with non-linear dynamical systems,
there are no simple or universal answers, though we may be able to
make progress by considering special cases.  As far as I am aware,
there are essentially just two relevant special cases which have
been considered in the literature, though they are not
all that easy to characterise precisely.

I consider first the case introduced by Dawkins, via an
extension of his rowing analogy:
\begin{quote}

  Suppose it is important in a really successful crew that the
  rowers should coordinate their activities by means of speech.
  Suppose further that, in the pool of oarsmen at the coach's
  disposal, some speak only English and some speak only German.
  The English are not consistently better or worse rowers than
  the Germans.  But because of the importance of communication, a
  mixed crew will tend to win fewer races that either a pure
  English crew or a pure German crew.

  The coach does not realize this.  All he does is shuffle his
  men around, giving credit points to individuals in winning
  boats, marking down individuals in losing boats.  Now if the
  pool available to him just happens to be dominated by
  Englishmen it follows that any German who gets into a boat is
  likely to cause it to lose, because communications break down.
  Conversely, if the pool happened to be dominated by Germans, an
  Englishman would tend to cause any boat in which he found
  himself to lose.  What will emerge as the overall best crew
  will be one of the two stable states---pure English or pure
  German, but not mixed.
  \iciteAD[p.~91]{Dawkins:SelfishGene}
\end{quote}

Again, Dawkins does not explicitly refer to linearity here;
indeed, he generally phrases his discussion of this issue in
terms closer to {\em frequency dependent selection}.  This is
presumably because he expresses and justifies his conclusions by
reference to Maynard~Smith's {\em Evolutionary Game Theory},
which is, indeed, typically introduced in just these terms
\cciteAD[Chapter~7]{MaynardSmith:EvolutionaryGenetics}. My
understanding of the situation is that, under sexual
reproduction, non-linear interactions between the dynamics of
S-lineages anchored on distinct loci can give rise to a form of
frequency dependent selection; and that this is, in fact, the
implicit mechanism in Dawkins' discussion of the issue; in
particular, it is the mechanism in the mixed-language rowing crew
analogy quoted above.  I think it may be better to explicitly
identify the \role\ of non-linear interactions (between loci) in
this context, as frequency dependent ``selection'' {\em can\/}
also arise in the context of a single genetic locus.

In any case, in the particularly simple circumstances described
by Dawkins above, the outcome is relatively clear---even though
the mechanism, and the detailed dynamics, may be rather
complicated.  Dawkins attempts to generalise this lesson as
follows:
\begin{quote}

  The interesting question is what makes a gene good.  As a first
  approximation I said that what makes a gene good is the ability
  to build efficient survival machines---bodies.  We must now
  amend that statement.  The gene pool will become an {\em
  evolutionarily stable set\/} of genes, defined as a gene pool
  that cannot be invaded by any new gene.  Most new genes that
  arise, either by mutation or reassortment or immigration, are
  quickly penalized by natural selection: the evolutionarily
  stable set is restored. Occasionally a new gene does succeed in
  invading the set: it succeeds in spreading through the gene
  pool.  There is a transitional period of instability,
  terminating in a new evolutionarily stable set---a little bit
  of evolution has occurred. \ldots\ Progressive evolution may be
  not so much a steady upward climb as a series of discrete steps
  from stable plateau to stable plateau.
  \iciteAD[pp.~92--93]{Dawkins:SelfishGene}
\end{quote}

This is obviously not a formal or quantitative analysis; but,
informally, Dawkins' suggestion seems to be that, in some cases
at least, non-linearity can have the effect of stabilising the
presence of certain genetic combinations in the
population---which is to say, preventing the kind of concurrent,
gene-level, selective displacements {\em at multiple loci\/} that
might otherwise be expected.  It is thus difficult (if not
impossible) for concurrent selection (at least in the sense of
displacement) to occur at multiple loci; but it still leaves open
the possibility for selective displacement to occur at any {\em
single\/} locus at one time, coupled with {\em sequential\/}
displacements at different loci. {\em This\/} kind of single
locus selection dynamics (possibly associated with a shift in the
dynamic equilibrium at other loci) can operate in essentially the
same manner as in the absence of non-linear interactions.

But if this is truly a fair interpretation of Dawkins' analysis,
then it undermines precisely his strongest case.  The positive
argument for regarding genes as D-actors (under sexual
reproduction) seemed to be that it could provide a somewhat
simpler formal description of concurrent selection at multiple
loci.  If the selection events of long term significance (i.e.\
selective displacements) at distinct loci are constrained by
non-linearity to be sequential rather than concurrent, then this
argument loses most if not all of its force.  For selection going
on at only a single locus, the genes-eye view offers little, if
any, formal simplification over a view based on genomes or
organisms; in fact, in these circumstances, the latter viewpoints
will not even be marred by the need to track intersecting
S-lineages anchored on different loci. Moreover, the distinctive
S-value associated with a particular gene, at a particular locus,
will (as always) only be manifest by taking account of the
particular genetic background prevalent in the population---which
is to say by looking at whole genomes or organisms.

Notwithstanding all this, Dawkins still states a preference for
the genes-eye view; but his argument now seems to become much weaker,
or even obscure. Thus, in a final version of the
rowing analogy, he could conclude only that he found it more
``parsimonious'' to think of the coach selecting at the level of
the independent candidates rather than whole crews
\cciteAD[p.~92]{Dawkins:SelfishGene}. On the face of it this is a
substantive retreat from his original claim that {\em only\/}
genes could qualify as D-actors, under sexual reproduction.

Even this is not the final conclusion however.  If I have
interpreted him correctly, Dawkins has suggested one possible
view of the significance of this kind of non-linearity for the
phyletic evolution of sexual populations---namely that it may
force selective displacements at multiple loci to occur
sequentially rather than concurrently; but it is by no means
clear that this is the only possibility. Wright's Shifting
Balance theory (e.g.\ \ociteAD{Wright:ShiftingBalanceTheory})
provides another, quite different, possibility. Roughly speaking,
Wright suggests the possibility that genome or organism
S-lineages, distinguished from each other (S-classified) by
differences at {\em multiple\/} genetic loci, may selectively
displace each other---and, indeed, that this may be the
predominant process in phyletic evolution. While such selection
processes {\em could\/} be formally modelled at a gene level,
such a description would necessarily {\em obscure\/} the
selection process, relative to a description at the genome or
organism level.  That is, under shifting balance, genomes or
organisms actually provide a significantly {\em simpler\/} (and
thus preferable) formal description of selection, as compared to
a gene level description.\footnote{It should be emphasised (as
  Wright himself has done) that the shifting balance process is
  {\em not\/} a form of ``group selectionism'', as normally
  construed; and arguments against group selectionism are not
  {\it ipso facto\/} arguments against shifting balance. For a
  more detailed discussion of this point see, for example,
  \citeAD[Chapter~9]{MaynardSmith:EvolutionaryGenetics}.}

Wright has presented essentially this criticism of genic
selectionism, as a specific response to Dawkins, in his paper
{\em Genic and Organismic Selectionism\/}
\cciteAD{Wright:GenicAndOrganismic}. Dawkins is
certainly aware of this paper, having cited it in, for example,
\cciteAD{Dawkins:ExtendedPhenotype} and
\cciteAD{Dawkins:UniversalDarwinism}.  The former is worth quoting
at some length:
\begin{quote}

  I think this [\ociteAD{Wright:GenicAndOrganismic}] is a valuable
  paper, even though its ostensible purpose is to attack the view
  that `with respect to natural selection \ldots\ it is the gene,
  not the individual or group, that is the unit'.  Wright
  concludes that `The likelyhood of organismic, instead of merely
  genic, selection goes far toward meeting one of the most
  serious objections to the theory of natural selection
  encountered by Darwin.'  He attributes the `genic selection'
  view to Williams, Maynard Smith and me, and traces it back to
  R.A.Fisher, I think correctly.  All of which must lead him to
  be somewhat bemused by the following accolade from
  Medawar [\ociteAD{Medawar:BackToEvolution}]: `The most important
  single innovation in the modern synthesis was however the new
  conception that a population that was deemed to undergo
  evolution could best be thought of as a population of
  fundamental replicating units---of genes---rather than as a
  population of individual animals or of cells.  Sewall Wright
  \ldots\ was a principal innovator in this new way of
  thinking\ldots'
  \iciteAD[pp.~238--239]{Dawkins:ExtendedPhenotype}
\end{quote}

At face value, this passage seems to dismiss Wright's attack on
genic selectionism simply on the basis that a third party
(Medawar) has identified Wright as one of the originators of
genic selectionism in the first place; which is to suggest that
Medawar knows what Wright thinks better than Wright himself. This
is not an argument, and Dawkins cannot mean to rely on it.

Dawkins goes on:
\begin{quote}

  In the rest of this chapter, I hope to show that the version of
  `genic selectionism' that can be attacked as naively atomistic
  and reductionistic is a straw man; that it is not the view that
  I am advocating; and that if genes are correctly understood as
  being selected {\it for their capacity to cooperate\/} with
  other genes in the gene-pool, we arrive at a theory of genic
  selection which Wright and Mayr will recognize as fully
  compatible with their own views.  Not only compatible but, I
  would claim, a truer and clearer expression of their views.
  \iciteAD[p.~239]{Dawkins:ExtendedPhenotype}
\end{quote}

Dawkins indicates here that he is going to rebut, or at least
disarm, arguments (against genic selectionism) presented by both
Wright and Mayr.  Unfortunately, that is the last explicit
reference to Wright which appears in the chapter (or the book,
for that matter)---Dawkins' subsequent treatment deals explicitly
only with points raised by Mayr.  I shall not consider any
details of the latter, for I have no strong disagreement with
Dawkins on those issues (indeed, Dawkins' own claim is that he
himself has no substantive disagreement with Mayr).  The
significant point is that the structure of Dawkins' presentation
here seems positively misleading. Although he has promised to
confront Wright's argument, he never does so---or, at least, not
{\em explicitly}. One must suppose that Dawkins intends his
comments on Mayr to also apply {\it mutatis mutandis\/} to
Wright, but I am not convinced that this can be made to work.

More specifically, Dawkins makes no mention of the shifting
balance process {\it per se}, whereas it is central to Wright's
criticism. The point which Dawkins emphasises repeatedly is that
genes should be understood as being selected for their ``capacity
to cooperate''---but this seems to mean, in each particular case,
cooperation with whichever genes {\em already\/} dominate the
gene pool.  If this is a fair interpretation, then it misses
Wright's claim that, under shifting balance, there may be
evolutionarily significant selection events which simply cannot
be decomposed into such separate ``selection'' of individual
(sexually segregating) genes---in the sense that genes at
distinct loci are either selected {\em as\/} a co-dependent set
(in competition with alternative, allelomorphic, co-dependent
sets) or not at all.  If I have grasped it correctly, Wright's
point is that, with a suitable population structure, this can be
an effective process {\em despite\/} the ongoing disruption of
the co-dependent set through recombination.  By contrast, Dawkins
seems to hold that such concurrent selection of a co-dependent
set can arise only if disruption through
recombination can be neglected---which is to say, ``only if the
genes \ldots\ were linked tightly in a supergene''
\cciteAD[p.~244]{Dawkins:ExtendedPhenotype}.  This, of course,
would effectively mean a return to the gene's eye view, except
now in terms of a ``supergene''.  Dawkins seems to be implicitly
denying that the shifting balance process can be effective---but
without giving specific arguments as to why not.

In terms of the rowing analogy again, shifting balance envisages
a situation somewhat like the following.  Suppose that, for
whatever reason, a mixed crew is always better if there are more
English rowers in it, but that an all German crew will beat an
all English crew.  Suppose, further, that the initially selected
crew is all English.  Now all perturbations of this, short of
forming an all German crew, will make it worse, and in Dawkins'
view of evolution it would seem that an all German crew could
never become established; and even if it were, it would be
immediately broken up. Wright's point is that, if we made the
model more biologically plausible by imagining that a population
of such crews existed, all initially dominated by English
speakers, but geographically dispersed, with limited migration (of
whole crews), and that they ``reproduced'' with
``recombination'', then a statistical fluctuation might allow a
small, but viable, subpopulation of all German crews to become
established in some local geographical area; this would then be
able to expand and selectively eliminate the all English crews.
This is a very rough and qualitative argument, and I have omitted
to specify many details which would be necessary to make it work;
but if, as Wright suggests, some such outcome is possible at all,
it seems that it simply cannot be interpreted in terms of
individual crew members being selected (for their ``ability to
cooperate'' or otherwise).

% This next bit is a bit cheap, and unreliable. Leave it out!
%
% I may say that, as far as I am aware, Dawkins has not
% confronted Wright's argument more substantively in any other
% writing.  In particular, in the New Edition (1989) of {\em The
% Selfish Gene\/} his only comment on the issue is the following:
% \begin{quote}
%
%   I think it is clear that Williams never thought of
%   himself as advocating anything new or revolutionary in his
%   `genic selectionism', and no more did I in 1976.  We both
%   thought we were simply reasserting a fundamental principle of
%   Fisher, Haldane, and Wright, the founding fathers of
%   `neo-Darwinism' in the 1930s. Nevertheless, perhaps because of
%   our uncompromising language, some people, including Sewall
%   Wright himself, apparently take exception to our view that `the
%   gene is the unit of selection'.  Their basic reason is that
%   natural selection sees organisms, not the genes inside them.
%   My reply to views such as Wright's is in {\em The Extended
%   Phenotype} [\ociteAD{Dawkins:ExtendedPhenotype}],
%   especially pp.~238--47.
%
%   \iciteAD[p.~273]{Dawkins:NewSelfishGene}
% \end{quote}
%
% This is simply a reference back to the discussion already
% dealt with above, and adds nothing new.  Again, there is no
% explicit recognition of the significance of Wright's unique
% formulation of the evolutionary {\em process\/} (in the form of
% shifting balance), and certainly no substantive response to it.

To conclude finally on the relevance of sex to the candidacy of
D-actors: under sexual reproduction with meiosis, individual
genes {\em may\/} qualify as candidate D-actors; in certain
circumstances they may even be preferred candidates; however, in
all the cases considered, genomes (and organisms) are viable
alternative candidates; and in some cases (notably under Wright's
shifting balance process) genomes (and organisms) are {\em
much\/} preferable candidates.  Dawkins' simple claim that, as a
logical consequence of meiosis, genes should be decisively favoured
as candidate D-actors, must be rejected.

\subsubsection{Causal Arrows\ldots}

In the previous section I considered whether genomes (and
organisms) could, in general, be regarded as satisfactory
candidate D-actors.  I now come to a superficially similar, but
actually quite different question, which is whether organisms can
qualify as Dawkinsian replicators.  Dawkins' answer to this
question is `No'.  I shall actually agree with this, which
necessarily involves finally identifying the distinction between
my {\em D-actor\/} and Dawkins' {\em replicator}.  It should then
become clear that the substantive question is not whether
organisms can qualify as Dawkinsian replicators as such, but
whether Dawkinsian replicators play a peculiarly distinguished
evolutionary \role, which cannot be played by D-actors in
general.

First I must explain the distinction between D-actors and
Dawkinsian replicators.  Briefly, both involve a combination of
similarity and descent; but Dawkinsian \arpls\ have an {\em
additional\/} property not necessarily exhibited by my
D-actors (or Hullean replicators for that matter). This
additional property is a constraint on the {\em mechanism\/}
whereby similarity is achieved (i.e.\ on how S-class is preserved
in S-descent): namely that this mechanism must be one of
``copying''.

Now, it is not all that easy to formalise exactly what is meant
by a ``copying'' process, and I shall not even try to do so here.
For the moment, let me simply stipulate that genes (or even whole
genomes, in the case of asexual organisms) are, indeed,
``copied'' during biological reproduction, whereas organisms (or
``phenotypes'' generally) are not.

This qualification on the mechanism of S-descent underlies
Dawkins' concept of ``vehicle''.  In effect, both Dawkinsian
\arpls\ {\em and\/} Dawkinsian vehicles qualify as D-actors in my
terms---which is to say that they are alternative candidates for
the \role\ of D-actor in discussing selection
processes.\footnote{Note, again, that this distinction is not
  related to the relative merits of S-lineages versus D-actors as
  the ``unit of selection'', but is purely about the relative
  merits of two candidate D-actors.}  Dawkins concludes, in fact,
that his \arpls\ should be preferred; whereas I conclude that, if
anything, his vehicles should be preferred.  But we are both
agreed that genes (and perhaps genomes) are Dawkinsian
replicators, whereas organisms are Dawkinsian vehicles.

It should be noted at this stage that Dawkins' notion of the
abstract {\em replicator\/} has, itself, evolved somewhat.

In his earliest explicit consideration of rival candidates for
the \role\ of \arpls\ Dawkins accepted that {\em certain\/}
organisms could play this part
\cciteAD[p.~69]{Dawkins:ReplicatorSelection}.\footnote{Specifically:
  those organisms employing asexual reproduction. This
  restriction to asexual reproduction was to take account of the
  argument relating to fragmentation of the genome at meiosis,
  detailed in the previous section.  On my analysis, such a
  restriction is now seen as an unnecessary distraction.}
At this point, while he had defined replication in terms of
copying, he was placing no particular stress on this fact; in
effect, his replicator was still more or less synonymous with my
D-actor, requiring only similarity and descent to characterise
it.

However, Dawkins subsequently changed his mind, deciding that
nothing more inclusive than the ``genome'' could ever operate as
an \arpl\ \cciteAD[p.~50]{Dawkins:ReplicatorsAndVehicles}.  This
applied to organisms as such (whether sexual or asexual), and
generally to any more inclusive entities.  It was at this point
that he identified {\em copying\/} as an {\em essential\/}
ingredient of replication, and started to claim a unique
evolutionary \role\ for replicators in this more restricted sense
(i.e.\ restricted relative to D-actor, or Hullean replicator). It
is precisely his basis for this step which is the target for
critical discussion here.

Dawkins has summarised his argument as follows:
\begin{quote}

  \samepage
  To regard an organism as a replicator, even an asexual organism
  like a female stick insect, is tantamount to a violation of the
  `central dogma' of the non-inheritance of acquired
  characteristics.  A stick insect looks like a replicator, in
  that we may lay out a sequence consisting of daughter,
  granddaughter, great-granddaughter, etc., in which each appears
  to be a replica of the preceding one in the series.  But
  suppose a flaw or blemish appears somewhere in the chain, say a
  stick insect is unfortunate enough to lose a leg.  The blemish
  may last for the whole of her lifetime, but it is not passed on
  to the next link in the chain.  Errors that affect stick
  insects but not their genes are not perpetuated.  Now lay out a
  parallel series consisting of daughter's genome,
  granddaughter's genome, great-granddaughter's genome, etc.  If
  a blemish appears somewhere along {\it this\/} series it will
  be passed on to all subsequent links in the chain, because in
  each generation there are causal arrows leading from genes from
  body.
  \pagebreak
  But there is no causal arrow leading from body to genes.
  No part of the stick insect's phenotype is a replicator.  Nor
  is her body as a whole.
  \iciteAD[p.~97]{Dawkins:ExtendedPhenotype}
\end{quote}

The reference here to ``causal arrows'' should presumably not be
taken too literally.  It is manifestly the case that there {\em
are\/} ``causal'' relationships directed from organisms to their
genomes, as evidenced (for example) by the fact that a naked
genome, in the absence of some minimal set of phenotypic products
(including at least the enzymes associated with its replication),
cannot actually replicate. But let us accept Dawkins' substantive
point: there exist possible modifications of genomes which, if
they arise, will be preserved in offspring, whereas this is not the
case for modifications which do not affect genomes.  To put it
another way (a way which does not rely on causal ``arrows''), it
is true that non-genetic modification may result in {\em some\/}
modification of the offspring---but such resulting modification
of the offspring will not be the {\em same\/} modification as
that originally applied to the parent.  The {\em only\/} kind of
modification which can persist through generations is a
modification including, or anchored upon, a genetic
modification.\footnote{Actually, it seems to me that even this is
  probably not {\em strictly\/} correct.  If it is accepted that
  the mapping from genotype to phenotype is, in some respects,
  {\em arbitrary}, then, by implication, there exist alternative,
  self-consistent, phenotypes which could viably correspond to
  any given genotype. It follows that a ``modification'' of any
  one of these into any other would be a purely phenotypic
  modification which would be preserved in subsequent
  generations.  However, the ``modification'' in question now
  amounts to a thorough rebuilding of the existing phenotype, and
  could not conceivably arise by a process of unjustified
  variation (compare the more detailed discussion in
  \ociteAD[Chapter~27]{Hofstadter:Metamagical}).  Thus, I happily
  stipulate that the only modifications which need be practically
  considered in a properly Darwinian evolutionary process are
  just those which Dawkins calls genetic.}

Accepting all this, the question which arises is what
significance should we attribute to these facts.  Dawkins' view
clearly is that entities which have this property---that
(specified) modifications to them will be preserved in subsequent
generations---play some unique evolutionary \role, which cannot
be played by any entity lacking this property.  But what {\em
is\/} this unique \role?  Dawkins does not, unfortunately, spell
it out explicitly, and we must therefore be satisfied with
attempting more or less plausible inferences.

The first possibility is this: Dawkins may be claiming simply
that any D-actor must incorporate what is, in effect, some kind
of ``information storage'' mechanism (whose information content
is duplicated in reproduction) in order to ``stabilise'' the
preservation of S-class in S-descent.  This information storage
mechanism is then, precisely, what Dawkins calls a {\em
replicator\/} (I should note that there seems no intrinsic reason
which this mechanism should be ``neatly'' separable from the rest
of the putatively ``reproducing'' entity).  This is an
interesting claim, which I am inclined to accept.  In fact, I
believe that the credit for this insight, and its important
ramifications for the possibility of a Darwinian growth of
``complexity'', is properly due to John von~Neumann
\cciteD{VonNeumann:TSRAutomata}; but that is not a discussion
which I wish to pursue in the current context. For my present
purposes, in trying to contrast different candidate D-actors, it
still amounts simply to focusing on the requirement that S-class
be preserved in S-descent, while more or less ignoring the
requirement that S-class be predictive of S-value (in given
environmental conditions).  As discussed in section~\ref{pragma}
above, this might sometimes yield a pragmatic preference for a
gene-level choice of D-actor, but it is, at best, a weak
preference, contingent on the particular circumstances. In any
case, this pragmatic interpretation of Dawkins' position is not
actually sustainable. In his general development of the
replicator concept, he has stipulated that it is ``active''
replicators which are of evolutionary significance---and
``active'' replicators are precisely entities whose
characteristics are not just preserved in reproduction but are
predictive of S-value also.

The second possible interpretation is that Dawkins means to
propose what I have earlier called {\em genetic absolutism}.
That is the view that there is an absolute mapping from genotypes
to phenotypes.  If this were so, then, since we grant that all
evolutionarily significant changes {\em include\/} genetic
changes, the entire evolutionary story can be told in terms of
genomes alone---the phenotypic implications can be ``calculated''
back in at any time, if desired.  I repeat that this does not
involve any claim that the genotype-phenotype mapping be
deterministic (or ``atomistic'' for that matter).

I do not believe that Dawkins really means to advocate genetic
absolutism; but there is no doubt that he implies something very
close to this in much of his writings, and he could easily be
(mis-?)understood in this way. Consider the following passages, for
example:
\begin{quote}

  We are survival machines---robot vehicles blindly programmed to
  preserve the selfish molecules known as genes.
  \iciteAD[p.~ix]{Dawkins:SelfishGene}

  \bigskip
  What weird engines of self-preservation would the millenia
  bring forth? Four thousand million years on, what was to be the
  fate of the ancient replicators?  They did not die out, for
  they are past masters of the survival arts.  But do not look
  for them floating loose in the sea; they gave up that cavalier
  freedom long ago. Now they swarm in huge colonies, safe inside
  gigantic lumbering robots, sealed off from the outside world,
  communicating with it by tortuous indirect routes, {\em
  manipulating it by remote control.}  They are in you and in me;
  they created us, body and mind; and their preservation is the
  ultimate rationale for our existence.  They have come a long
  way, those replicators.  Now they go by the name of genes, and
  we are their survival machines.
  \iciteAD[p.~21, \\emphasis added]{Dawkins:SelfishGene}

  \bigskip
  The genes too {\em control\/} the behaviour of their survival
  machines, not directly with their fingers on puppet strings,
  but indirectly like the computer programmer.
  \iciteAD[p.~56, \\emphasis added]{Dawkins:SelfishGene}
\end{quote}

This last quotation is particularly suggestive.  It is excerpted
from a longer discussion, in which Dawkins compares genes (or,
more generally, replicators) to computer programs, saying {\it
inter alia\/} that a program ``is not fussy which physical
computer it uses to act out its skills''
\cciteAD[p.~55]{Dawkins:SelfishGene}.  This is, of course, true
as far as it goes, but could easily be read as meaning that
computer programs have {\em intrinsic\/} or absolute
interpretations, which are merely realised by plugging them into
{\em any\/} (arbitrary) computer. This would be
nonsense---programs have well defined meanings or behaviours only
relative to a specified computer (or class of computers).  In
terms of the analogy to genes, we should imagine instead the
possibility of programmed
computers which, in executing their programs, actually cause the
construction of new computers, and also equip such offspring
computers with a copy of the parental program.\footnote{Again,
  this idea was essentially pioneered
  by \citeAD{VonNeumann:TSRAutomata}.}
The important point is that, following a ``mutation'', the
offspring computer may differ from the parental computer, so that
even though the offspring has (more or less) the ``same'' program
(in some kind of {\em informational\/} or {\em syntactic\/}
sense), its {\em function\/} may be arbitrarily different.
Thus, an evolutionary story expressed solely in terms of the
lineage of computer {\em programs\/} would definitely not allow
the ``phenotypic'' details to be calculated back in.\footnote{It
  should also, incidentally, be clear from this discussion that a
  phenotype cannot be considered merely as part of the
  ``environment'' of the genotype.}

I should emphasise here that Dawkins consistently recognises that
individual (sexually segregating) genes do not have absolute
interpretations or meanings; unfortunately, in doing so, he can
seem to imply that, by contrast, complete genomes, in given
(extra-organismic) environmental conditions {\em do\/} have
absolute interpretations.  Thus, we have the following, for
example:
\begin{quote}

  \ldots\ the relationship between a gene and its phenotypic
  effect is not an intrinsic property of the gene, but a property
  of the forward developmental consequences of the gene when
  interacting with the consequences of many other genes and many
  external factors.
  \iciteAD[p.~176]{Dawkins:ExtendedPhenotype}
\end{quote}

Dawkins explicitly states that the effect of any one gene is
contingent on the other genes in the genome, and on ``external''
(presumably extra-{\em organismic\/}?) factors, thus implying, by
omission, that it does {\em not\/} depend on any non-genetic, but
internal (organismic) factors; which is to say, he again implies
some form of genetic absolutism.

Dawkins most definite commitment to something very like genetic
absolutism appears in his book {\em The Blind Watchmaker}, where
it implicitly underlies his so-called {\em biomorph\/} computer
model of evolution:
\begin{quote}

  There is another mathematical space filled, not with nine-gened
  biomorphs but with flesh and blood animals made of millions of
  cells, each containing tens of thousands of genes.  This is not
  biomorph space but real genetic space.  The actual animals that
  have ever lived on Earth are a tiny subset of the theoretical
  animals that {\it could\/} exist.  These real animals are the
  products of very small number of evolutionary trajectories
  through genetic space.  The vast majority of theoretical
  trajectories through animal space give rise to impossible
  monsters.  Real animals are dotted around here and there among
  the hypothetical monsters, each perched in its own unique place
  in genetic hyperspace.  Each real animal is surrounded by a
  little cluster of neighbours, most of whom have never existed,
  but a few of whom are its ancestors, its descendants and its
  cousins.
  \iciteAD[p.~73]{Dawkins:BlindWatchmaker}
\end{quote}

Dawkins' clear implication here is that there is some universal
mapping from genomes to ``animals'' (phenotypes).  He is perhaps even
more explicit in a more or less parenthetical discussion in {\em
The Extended Phenotype}, where he essentially claims that
if a genetic change is reversed the phenotypic consequences will
necessarily be reversed also
\cciteAD[pp.~3--4]{Dawkins:ExtendedPhenotype}; but, as already
commented upon in section~\ref{relativism}, this conclusion would
seem to be warranted only under an assumption of genetic
absolutism.

In any case, my objective here has simply been to establish that
Dawkins can reasonably be interpreted as espousing genetic
absolutism.  The arguments {\em against\/} such a view have
already been adequately rehearsed in section~\ref{absolutism}\
and need not be repeated here.  The more interesting question is
whether there is any basis for supposing that Dawkins should {\em
not\/} be interpreted in this way.  As it happens, there is at
least fragmentary evidence to this effect.  Thus, in Dawkins'
more recent discussion of his {\em biomorph\/} model, we find the
following:
\begin{quote}

  \ldots\ we need to make a preliminary distinction between two
  kinds of mutation: ordinary changes within an existing genetic
  system, and changes to the genetic system itself.  Ordinary
  changes within an existing genetic system are the standard
  mutations that may or may not be selected in normal evolution
  within a species.  One allele is replaced by an alternative
  allele at the same locus, as in the famous case of industrial
  melanism where a gene for blackness spread through moth
  populations in industrial areas (see any biology textbook).
  This is how all normal evolutionary change happens.  But it is
  an inescapable fact that different species, to a greater or
  lesser extent, have different genetic systems from one another,
  even if this only means that they have different numbers of
  chromosomes. ``The same locus,'' when we are talking about an
  elephant and a human, may not even be a meaningful thing to
  say.  Humans and elephants employ basically the same {\it
  kind\/} of genetic system, but they don't have the same genetic
  system.  They have different numbers of chromosomes and you
  can't make a locus-for-locus mapping between them like you can
  between two individual humans.  Yet humans and elephants
  undoubtedly have a common ancestor.  Therefore, during their
  evolutionary divergence, there must have been changes to the
  genetic systems, as well as changes within the genetic systems.
  These changes to genetic systems must have been, at least in
  one sense, major changes, changes of a different order from the
  normal allele substitutions that go on within a genetic system.
  \iciteAD[p.~217]{Dawkins:Evolvability}
\end{quote}

Dawkins is here coming very close to renouncing genetic
absolutism, which I naturally agree with.  However, I should note
that I disagree with Dawkins on several substantive details.

Thus, while I agree that humans and elephants almost certainly
have different ``genetic systems'', I disagree that this can be
reliably inferred merely from the fact that there have different
numbers of chromosomes (by analogy, computer programs may differ
widely---length, organisation and number of subprograms etc.---
and yet be still valid, or functional, programs for the same
computer).  Indeed, attempting to distinguish ``genetic systems''
by appeal to purely genetic differences (such as chromosome
number) is essentially to relapse back into genetic absolutism.

There again, while agreeing with Dawkins that there must have
been evolutionary changes to ``genetic systems'' I reject his
suggestion that genetic changes might be neatly divided into
those which affect this ``genetic system'' and those which do not.  I
think Dawkins has, in this case, been badly misled by the
simplifications inherent in his computer models.  In the latter
it is easy (even convenient) for the ``genetic system'' to be a
distinguishable subsystem of his actors, ``coded for'' by a
definite fragment of the genome. But there is no reason to
suppose that real organisms incorporate any such neat
subdivisions.  Instead, given the prevalence of pleiotropic
effects, I conjecture that many (perhaps even most) genetic
modifications have {\em both\/} kinds of effect identified by
Dawkins (``changes within an existing genetic system'' and
``changes to the genetic system itself''). If this conjecture is
even close to the truth then Dawkins' attempted distinction
between ``normal'' evolutionary steps, and steps ``of a different
order'' is mistaken and misleading.  What Dawkins would regard as
``normal'' evolutionary steps could actually have the automatic
side-effect of changing (``incrementally'' or otherwise) the
``genetic system''.

I have elaborated my detailed disagreement with this passage of
Dawkins' for a definite reason.  Taking the passage as it
stands, the implication is that, in discussing biological
evolution, we need to track both genetic changes, as such, and
the ``genetic system'' which is appropriate to any given genome.
Dawkins implies that this ``genetic system'' can be thought of as
constant (read ``absolute'') for the purposes of considering
most (``normal'') evolutionary change; and that it can be
distinguished as a sub-system of the organism (I again ignore the
counter-productive idea that the ``genetic system'' could itself
be inferred from the genome).  If Dawkins grants even this much,
he would surely admit that a ``minimal sufficient'' candidate
D-actor must consist of a genome plus its genetic system (as
opposed to a genome on its own).  To my knowledge, Dawkins has
not recognised this implication.  But, in any case, if my further
qualifications are valid---that the ``genetic system'' is neither
constant over long periods of evolutionary time, nor a neatly
distinguishable subsystem in itself---then one will be forced to
recognise essentially the whole {\em organism\/} as being the
best available approximation to a minimally sufficient D-actor.

The thrust of this last argument has been to suggest that, if
Dawkins does {\em not\/} embrace genetic absolutism, then the
only possible, remaining, interpretation of his position would seem to
be some form of genetic relativism.  But the above analysis,
derived from Dawkins' own admissions about the maleability of
``genetic systems'', essentially retraces the rejection of
genetic relativism already presented in section~\ref{relativism}.
I conclude that Dawkins' concept of replicator, {\em insofar as it
differs from my concept of D-actor,} is a misleading distraction,
and should be dispensed with.

\subsubsection{A Resolution?}

There is, however, one final comment worth making here.  While I
have gone to some length to trace Dawkins' arguments for some
kind of preeminence of the genetic D-actor, it seems to me that
Dawkins himself is ultimately ambivalent about this. This may
be illustrated by the following two highly suggestive quotations:
\begin{quote}

  It is the incidence of phenotypes that we are interested in
  explaining, not the incidence of molecular configurations of
  DNA. And if any reader thinks that last remark contradicts my
  basic thesis, I must have failed to make my basic thesis clear.
  \iciteAD[p.~154]{Dawkins:ExtendedPhenotype}

  \bigskip
  I see the world as populated by competing replicators in germ
  lines.  Each replicator, when compared with its alleles, {\em
  can be thought of as being attached to a suite of characters,
  outward and visible tokens of itself.}  These tokens are its
  phenotypic consequences, in comparison with its alleles, upon
  the world. They determine its success or failure in continuing
  to exist.
  \iciteAD[pp.~59--60, emphasis added]{Dawkins:ReplicatorsAndVehicles}
\end{quote}

If this last passage is read in the light of a rejection of genetic
absolutism, then it identifies a Dawkinsian replicator {\em
plus\/} some attached ``suite of characters'', as the preferred
candidate for the \role\ of D-actor.  On {\em this\/}
interpretation, Dawkins and I would finally speak with one voice.

\section{Conclusion}

This has been a long and technical essay.  In conclusion I
should like to try to distil out the central point more concisely.

We have two apparently complementary and exhaustive ways of
looking at the evolutionary \roles\ of genes and organisms:
\begin{description}

\item[{\em 1: Organisms subserve Genes.}]

This is Genic Selectionism in its purest form.  It holds that
genes have no ``function'' other than to ensure their propagation
into future generations---i.e.\ to replicate---and organisms are
merely tools or ``vehicles'' constructed and maintained by the
genes to facilitate this process.  The most explicit and
provocative proponent of this view has been Richard
Dawkins---hence the extended discussion devoted to his ideas
in this essay.

\item[{\em 2: Genes subserve Organisms.}]

This is Organismic Selectionism in its purest form.  It holds
that organisms have no function other than to ensure their
propagation into future generations, and genes are merely a tool
(an information storage mechanism) constructed and maintained by
the organisms to facilitate this process.

\end{description}

My claim is that this is ultimately a false and sterile
dichotomy; that both claims are better replaced by the following
synthesis:
\begin{description}

\item[{\em 3: Organisms and Genes both subserve S-lineages.}]

That is, neither genes nor organisms have functions in themselves
other than to facilitate the success of S-lineage(s) of which
they are members, in competition with other S-lineage(s).  This is
the point of saying that the S-lineage is the unit of selection.

Both genes and organisms may qualify as more or less satisfactory
D-actors, depending on the precise circumstances.  But {\em if\/}
we wish to identify the {\em minimal sufficient\/} D-actor, then
genes (and genomes) definitely do not qualify, and organisms are
probably the uniquely best approximation which is typically
available.

\end{description}

Does this actually make any difference?  Well, quite apart from
any aesthetic appeal of this formulation, I think that the
forthright, detailed, and comprehensive, rejection of Genic
Selectionism, which I have attempted here, is a necessary
prerequisite for the {\em satisfactory\/} realisation of
artificial Darwinism.  For Genic Selectionism is strongly linked
to Genetic Absolutism; and Genetic Absolutism reduces the
Darwinian evolution of adaptive complexity to a trajectory
through a predetermined genetic vector space.  By contrast, real
Darwinian growth of adaptive complexity (and, by implication, any
worthwhile artificial growth of adaptive complexity) is just not
that simple.

In closing, there is one last crucial point to be made.  I have
argued elsewhere that Organismic Darwinism (where organisms are
treated as D-actors) offers a more or less satisfactory solution
to the problem of the phylogenetic growth of organismic
complexity \cciteAD{McMullin:Organismic}.  I have argued here
that, to the extent that that previous analysis was correct, then
it may, in some cases at least, be equally satisfactory, and
essentially equivalent, to regard certain other entities,
especially genes or genomes, as D-actors---although I have argued
that the organism level is still the most generally satisfactory
choice.  But I must emphasise now that I do not pretend that the
organismic view offers, in any sense, a complete or final
explanatory framework for all growth of complexity in the
biological world. In particular, even in
\cciteAD{McMullin:Organismic} I acknowledged that quite distinct
new kinds of D-actors {\em could\/} emerge, which would {\em
not\/} be formally equivalent to organismic D-actors; and that
the distinct D-systems which result might interact in significant
ways, which would render any explanation phrased in terms of only
a single kind of such D-actor quite inadequate; and, indeed, that
this {\em may\/} already have been a significant phenomenon in
biological evolution to date.  I have in mind here the kind of
hierarchical Darwinian theory described, for example, by
\citeAD{Gould:Darwinism}. In terms of such an hierarchical
theory, my purpose has been restricted to the attempted
clarification of Darwinian theory within {\em one\/}
hierarchical level; but I do not imply, and do not suppose,
that such a single level theory exhausts the scope of Darwinism.

This is an internal Technical Report; as with the previous essays
in the series, I rely on the informality of that medium to excuse
the rough edges remaining. In any case, I would greatly
appreciate comments and criticism of any sort.

\section*{Acknowledgements}

This series of essays form part of an ongoing attack on the
problem of realising the spontaneous growth of Artificial
Knowledge by Darwinian (or any other!) means.  In this pursuit, I
have benefited greatly from discussions with colleagues,
particularly Noel Murphy in DCU, and John Kelly of University
College Dublin. Paul~McKevitt also made useful comments on
earlier drafts of this material. I am indebted to the School of
Electronic Engineering in DCU (particularly through the agency of
its Head, Charles \mbox{McCorkell}) for continuing encouragement,
not to mention material support. All errors remain, of course, my
own responsibility.

\clearpage
\bibliography{phd}
\bibliographystyle{citeAD}

\end{document}
