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An End to Endless Forms: Epistasis, Phenotype Distribution Bias, and Nonuniform Evolution

Figure 3

Localization of the visible phenotypic subspace.

(A) A loglog plot of the distribution of degeneracy levels among visible phenotypes. Each point denotes the expected number of distinct phenotypes with a certain degeneracy level for a given developmental plan and is an average over 10,000 different plans. Note that the point associated with degeneracy level 0 (i.e., hidden phenotypes) is not included. These developmental plans frequently give rise to phenotypes with degeneracy levels higher than 103, and in rare cases, higher than 103.5. Given that the total number of genotypes is 214 a single phenotype can be produced by 6%–20% genotypes. (B) A contour plot of the gain function induced by a given developmental plan (all developmental plans produce qualitatively similar results). The gain function, gain(dg,dp), denotes the probability that the Hamming distance between two phenotypes is dp, given that the distance between the two genotypes that produced them is dg. (C) The distribution of pairwise phenotypic Hamming distances among randomly selected phenotypes (not produced by a developmental plan), distinct visible phenotypes (considering every visible phenotype only once, regardless of frequency), and visible phenotypes including all occurrences of each phenotype. The pairwise Hamming distances between randomly selected phenotypes follows a binomial distribution, with mean distance 7 (for phenotypes of length 14). Distinct visible phenotypes are closer to one another, with the mean distance 5.976. When weighting by the frequency of the visible phenotypes, the distance is reduced, with a mean distance 4.607.

Figure 3