Abstract
BackgroundMany hypotheses have been proposed for how sexual reproduction may facilitate an increase in the population mean fitness, such as the Fisher-Muller theory, Muller’s ratchet and others. According to the recently proposed mixability theory, however, sexual recombination shifts the focus of natural selection away from favoring particular genetic combinations of high fitness towards favoring alleles that perform well across different genetic combinations. Mixability theory shows that, in finite populations, because sex essentially randomizes genetic combinations, if one allele performs better than another across the existing combinations of alleles, that allele will likely also perform better overall across a vast space of untested potential genotypes. However, this superiority has been established only for a single-locus diploid model.ResultsWe show that, in both haploids and diploids, the power of randomization by sex extends to the multilocus case, and becomes substantially stronger with increasing numbers of loci. In addition, we make an explicit comparison between the sexual and asexual cases, showing that sexual recombination is the cause of the randomization effect.ConclusionsThat the randomization effect applies to the multilocus case and becomes stronger with increasing numbers of loci suggests that it holds under realistic conditions. One may expect, therefore, that in nature the ability of an allele to perform well in interaction with existing genetic combinations is indicative of how well it will perform in a far larger space of potential combinations that have not yet materialized and been tested. Randomization plays a similar role in a statistical test, where it allows one to draw an inference from the outcome of the test in a small sample about its expected outcome in a larger space of possibilities—i.e., to generalize. Our results are relevant to recent theories examining evolution as a learning process.ReviewersThis article was reviewed by David Ardell and Brian Golding.
Highlights
Many hypotheses have been proposed for how sexual reproduction may facilitate an increase in the population mean fitness, such as the Fisher-Muller theory, Muller’s ratchet and others
Mixability theory has already had an unexpected consequence in the interdisciplinary realm: it has served as a motivation in the development of a key advance [30, 31] that contributed to the phenomenal leap of deep learning in 2012 [32, p.440] and to the global artificial intelligence revolution (e.g., [33])
It is shown that the simulated P value is close to the theoretical one. In both haploid and diploid cases, we find that sex has the power of randomization: by essentially randomizing genetic combinations, the allele that is favored by natural selection in its interactions with the existing genetic combinations in a current, finite population is likely to perform better overall across the much larger space of untested, potential genotypes
Summary
Many hypotheses have been proposed for how sexual reproduction may facilitate an increase in the population mean fitness, such as the Fisher-Muller theory, Muller’s ratchet and others. According to the mixability theory for the role of sex in evolution, in the presence of sexual reproduction, natural selection favors not the best specific combinations of genes; i.e., not those genotypes of highest fitness, but rather alleles that perform well in interaction with a wide variety of different genetic combinations — “mixable alleles” [21]. This theory offers an alternative view on the role of sex in evolution to the more familiar lines of work on this topic from the 20th century, such as the Fisher-Muller theory [17, 18], the deterministic mutation hypothesis. Previous theory in evolution and in particular on the role of sexual reproduction has inspired developments in computing through the genetic algorithm work of John Holland [34], while mixability theory has inspired innovation in the science of deep learning
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