Statistical Mechanics of Convergent Evolution

The aim of this work was to try to understand some of the fundamental constraints of evolution from a physics perspective - given a life history of an organism, how reproducible is evolution over an ensemble of identical (aside from stochastic variation) evolutionary experiments. We explore this question of convergent evolution by analysis of the genotype to phenotype map in biology using a simple model of spatial patterning for embryonic development. Building upon the work of Sella and Hirsh (PNAS, (2005), 102, 9541-9546) who identified a direct analogy between the statistical mechanics of the canonical ensemble and the Wright-Fisher evolutionary process, we probe the phenotypic structure that emerges from an underlying genotype. Using Monte Carlo simulations, we show that the emergent evolutionary landscapes share many analogous features to the thermodynamics of physical systems and we highlight some of the unexpected biological consequences in the context of convergent or divergent evolution. In particular, we demonstrate the importance of population size in determining the probability of different evolutionary solutions; the number of ways a phenotype is realised from different genotypes (mutational entropy) and the local roughness of landscapes can make dramatic changes to evolutionary outcomes.