Mutation, Sexual Reproduction and Survival in Dynamic Environments

TL;DR

This paper models evolution in changing environments using computational algorithms, showing mutation's critical role in survival and providing new convergence bounds for evolutionary dynamics.

Contribution

It introduces a novel computational framework for evolution in dynamic environments and proves mutation's importance for population survival, with new convergence results.

Findings

Without mutation, populations go extinct in changing environments.

Mutation enables populations to survive in dynamic settings.

Convergence of sexual evolution with mutation is guaranteed in static environments.

Abstract

A new approach to understanding evolution [Val09], namely viewing it through the lens of computation, has already started yielding new insights, e.g., natural selection under sexual reproduction can be interpreted as the Multiplicative Weight Update (MWU) Algorithm in coordination games played among genes [CLPV14]. Using this machinery, we study the role of mutation in changing environments in the presence of sexual reproduction. Following [WVA05], we model changing environments via a Markov chain, with the states representing environments, each with its own fitness matrix. In this setting, we show that in the absence of mutation, the population goes extinct, but in the presence of mutation, the population survives with positive probability. On the way to proving the above theorem, we need to establish some facts about dynamics in games. We provide the first, to our knowledge, polynomial convergence bound for noisy MWU in a coordination game. Finally, we also show that in static environments, sexual evolution with mutation converges, for any level of mutation.