Evolvability (in our sense of the possible evolutionary growth of complexity) certainly requires the bare existence of an indefinitely large set of potential reproducers, interconnected by a mutational network (``unlimited heredity''). This is enough to assure that there will be potential mutational trajectories from simpler to more complex entities. This can, of course, be achieved by genetic reproduction; but as illustrated by Tierra, it can be achieved even by template reproduction.
However, which mutational trajectories will actually be followed will depend critically on the detailed interconnections in this network, and the associated patterns of Darwinian selective displacement; should these result in relatively simple entities being selectively favored over their more or less immediately accessible mutational neighbors, then longer term evolutionary potential will be effectively blocked.
Now, in this respect there seems to be a significant difference between template and genetic reproduction. In a system relying on template reproduction, there is a fixed, essentially isomorphic, relationship between genotype and phenotype. Accordingly, the mutational connectivity of particular phenotypes is identical with the mutational connectivity of the genotypes--with whatever limitations may result on long term evolutionary dynamics. But in a system based on genetic reproduction, there is a decoupling between genotype and phenotype. There is, of course, a relationship, or mapping, between genotype and phenotype, and this still means that the connectivity of the genotype space implies connectivity of the phenotype space--unless the mapping between genotypes and phenotypes can itself evolve. But if this mapping is evolvable, then, without any change to the underlying template copying process, or the corresponding connectivity of the genotype space, the connectivity in the phenotype space can change. Since it is phenotypes that give rise to Darwinian selection, this means that the potential for indefinitely long term evolution will now not necessarily be constrained by the fixed connectivity of the genotype space; and thus genetic reproduction--if it allows for variation in the genotype-phenotype mapping--might, in principle, give rise to richer evolutionary potential, or evolvability, than any template style system.
What does it mean for the genotype-phenotype mapping to be evolvable? In terms of our earlier schematic diagram of genetic reproduction (Figure 1) the key issue is whether the constructor system is, itself, subject to (unlimited) heritable variation, for it is the constructor that implements the ``decoding'' or mapping from genotype to phenotype.
This is a more subtle question than may at first appear. It is easy enough to arrange for the constructor subsystem to be constructed by virtue of decoding some particular section of the tape. Accordingly, an alternation or mutation in that section will indeed result in a variant constructor in the offspring. This offspring will thus have both a variant constructor and a corresponding variant genotype, so it would seem that the variation can now breed true, as usual: except that this ``correspondence'' is as defined by the parental genotype-phenotype mapping--and, by stipulation, the offspring no longer shares this mapping.
We should note here that von Neumann himself seems to have discounted this possibility completely. He stated explicitly that mutations affecting that part of a descriptor coding for the constructor would result in the production of ``sterile'' offspring (von Neumann, 1949, p. 86). Clearly, on this specific point, we disagree with von Neumann. We do accept that such mutations might ``typically'' result in sterile offspring; but we suggest that, in principle at least, they may sometimes result in viable offspring, thus initiating lineages with distinctly different evolutionary potential, precisely because of the altered genotype to phenotype mapping.
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