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In a recent series of papers a surprisingly strong connection was discoveredbetween standard models of evolution in mathematical biology and MultiplicativeWeights Updates Algorithm, a ubiquitous model of online learning andoptimization. These papers establish that mathematical models of biologicalevolution are tantamount to applying discrete Multiplicative Weights UpdatesAlgorithm, a close variant of MWUA, on coordination games. This connectionallows for introducing insights from the study of game theoretic dynamics intothe field of mathematical biology. Using these results as a stepping stone, weshow that mathematical models of haploid evolution imply the extinction ofgenetic diversity in the long term limit, a widely believed conjecture ingenetics. In game theoretic terms we show that in the case of coordinationgames, under minimal genericity assumptions, discrete MWUA converges to pureNash equilibria for all but a zero measure of initial conditions. This resultholds despite the fact that mixed Nash equilibria can be exponentially (or evenuncountably) many, completely dominating in number the set of pure Nashequilibria. Thus, in haploid organisms the long term preservation of geneticdiversity needs to be safeguarded by other evolutionary mechanisms such asmutations and speciation.

Natural Selection as an Inhibitor of Genetic Diversity: Multiplicative Weights Updates Algorithm and a Conjecture of Haploid Genetics