Bias in the arrival of variation can dominate over natural selection in Richard Dawkins’s biomorphs
Fig 5
Structure in the GP map—The phenotypic effect of mutations.
In every panel, the computational results are shown in blue and the analytic relationships from the constrained-unconstrained model are shown as red lines, with markers indicating the discrete allowed values. (A) Point mutations of a genotype with initial phenotype q can either leave q intact or lead to a phenotypic change to a new phenotype p. The likelihood of the first outcome is given (on average) by the phenotype robustness of q, ρq; the likelihood of the latter outcome is given by the mutation probability from q to p, denoted as ϕpq (see Table 1). (B) Phenotype robustness ρp vs. phenotype frequency fp: the computational results (blue) are compared to the analytic calculation of Eq 5 (red). The black line (ρp = fp) shows the prediction from the uncorrelated null model from ref [40]. The robustness is much higher than this random null model, i.e. there are genetic correlations. (C) Genotype evolvability vs genotype robustness
for both the computational (blue) and analytic (red, Eq 6) approach: we find the expected trade-off between robustness and evolvability at the genotype level. (D) Phenotype evolvability ϵp vs phenotype robustness ρp for both the computational (blue) and analytic (red, Eq 7) approach. As observed more widely [32], robust phenotypes have large neutral sets and are connected with many other neutral networks, so there is a positive correlation. (E) Mutation probability ϕpq vs. phenotype frequency fp for a fixed initial phenotype q (shown in the corner). Again, the computational data is shown in blue, the analytic data in red (given by a parametric equation from section A.7 in S1 Text), and the black line shows the null model from ref [40], which gives ϕpq = fp, Data points with ϕpq = 0 are excluded due to the logarithmic scale, even though 99.997% of all biomorph phenotypes have ϕpq = 0 for this particular initial phenotype q.