Statistical theory of phenotype abundance distributions: a test through exact enumeration of genotype spaces

TL;DR

This paper tests a statistical theory predicting phenotype abundance distributions in genotype spaces by exact enumeration, confirming that in navigable spaces, abundance follows a log-normal distribution with high accuracy.

Contribution

It provides a rigorous test of a theory predicting phenotype abundance and distribution using exact enumeration of genotype-phenotype maps, highlighting the log-normal pattern in navigable spaces.

Findings

Phenotype abundance can be accurately predicted by the theory.

In navigable genotype spaces, abundance distributions converge to a log-normal form.

Exact enumeration confirms the theory's predictions across multiple GP maps.

Abstract

The evolutionary dynamics of molecular populations are strongly dependent on the structure of genotype spaces. The map between genotype and phenotype determines how easily genotype spaces can be navigated and the accessibility of evolutionary innovations. In particular, the size of neutral networks corresponding to specific phenotypes and its statistical counterpart, the distribution of phenotype abundance, have been studied through multiple computationally tractable genotype-phenotype maps. In this work, we test a theory that predicts the abundance of a phenotype and the corresponding asymptotic distribution (given the compositional variability of its genotypes) through the exact enumeration of several GP maps. Our theory predicts with high accuracy phenotype abundance, and our results show that, in navigable genotype spaces ---characterised by the presence of large neutral networks---, phenotype abundance converges to a log-normal distribution.