Sex and Portfolio Investment

We attempt to answer why sex is nearly ubiquitous when asexual reproduction is ostensibly more efficient than sexual reproduction. From the perspective of a genetic allele, each individual bearing that allele is akin to a stock share yielding dividends equal to that individual’s number of offspring, and the totality of individuals bearing the allele is its portfolio investment. Alleles compete over portfolio growth. Evolutionary reproduction strategies can essentially be seen as on-line learning algorithms seeking improved portfolio growth, with sexual reproduction a goal-directed algorithmic exploration of genotype space by sampling in each generation. We show that in finite population models the algorithm of sexual reproduction yields, with high probability, higher expected growth than the algorithm of asexual reproduction does. We thus seek to explain why a majority of species reproduce sexually. The model assumes a stochastically changing environment but not weak selection.