On Sex, Evolution, and the Multiplicative Weights Update Algorithm

Abstract: We consider a recent innovative theory by Chastain, Livnat, Papadimitriou and Vazirani on the role of sex in evolution [PNAS’14]. In short, the theory suggests that the evolutionary process of gene recombination implements the celebrated multiplicative weights updates algorithm (MWUA). They claim that the population dynamics induced by sexual reproduction can be precisely modeled by genes that use MWUA as their learning strategy in a particular coordination game. The result holds in the environments of weak selection, under the assumption that the population frequencies remain a product distribution.
We revisit the theory, showing that the product distribution assumption is inconsistent with the population dynamics (meaning that the conditions for the Chastain et al. result are never met). We then eliminate both the requirement of weak selection and any assumption on the distribution of the population, and prove that the marginal allele distributions induced by the population dynamics precisely match the marginals induced by a multiplicative weights update algorithm in this general setting, thereby affirming and substantially generalizing earlier results. We further revise the implications for convergence and utility or fitness guarantees in coordination games. In contrast to the claim of Chastain et al.[PNAS’14], we conclude that the sexual evolutionary dynamics does not entail any property of the population distribution, beyond those already implied by convergence.