Algorithms, games, and evolution

Significance Theoretical biology was founded on the mathematical tools of statistics and physics. We believe there are productive connections to be made with the younger field of theoretical computer science, which shares with it an interest in complexity and functionality. In this paper, we find that the mathematical description of evolution in the presence of sexual recombination and weak selection is equivalent to a repeated game between genes played according to the multiplicative weight updates algorithm, an algorithm that has surprised computer scientists time and again in its usefulness. This equivalence is informative for the pursuit of two key problems in evolution: the role of sex and the maintenance of variation. Even the most seasoned students of evolution, starting with Darwin himself, have occasionally expressed amazement that the mechanism of natural selection has produced the whole of Life as we see it around us. There is a computational way to articulate the same amazement: “What algorithm could possibly achieve all this in a mere three and a half billion years?” In this paper we propose an answer: We demonstrate that in the regime of weak selection, the standard equations of population genetics describing natural selection in the presence of sex become identical to those of a repeated game between genes played according to multiplicative weight updates (MWUA), an algorithm known in computer science to be surprisingly powerful and versatile. MWUA maximizes a tradeoff between cumulative performance and entropy, which suggests a new view on the maintenance of diversity in evolution.

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