Thou Shall not Diversify: Why Two of Every Sort?

The present paper sheds a new light on the notorious question in the evolutionary biology of why the modern species exhibit only the asexual and binary mating systems, with the clear dominance of the latter over the former. We present an in-depth study of the intertemporal propagation of the fundamental distributional properties of phenotypes in general polygenic multi-gender inheritance models with sex- and time-dependent heritability. We further analyze the implications of these models under thick-tailedness of traits' initial distributions. We obtain the results that demonstrate that, under an arbitrary multi-sex mating system with k genders, the Organism's switching to a more uniform mode of heritability leads to an increase in peakedness and concentration of traits with not extremely heavy-tailed initial distributions in its population in all the future periods. However, the decrease in the diversity of the parameters responsible for the different sexes' genetical contributions to the next period's offspring leads to an increase in concentration and peakedness of extremely long-tailed traits in all future generations. From these results it follows that switching to an inheritance system with greater diversity in heritability coeffcients and, thus, an increase in the number of genders under symmetric heritability, is advantageous in the case of extremely long-tailed traits that have negative effects on the population's fitness (say, human medical or behavioral disorders for which inheritance is significant). Such a switching or increase in the number of genders slows down or completely stops the intertemporal spread of the extremely thick-tailed negative traits in the population. On the other hand, a decrease in the number of genders in the symmetric multi-sex inheritance system and, more generally, switching to less diverse heritability parameters is advantageous in the case of not extremely thick-tailed positive traits (e.g., the trait of intelligence). Our theoretical results demonstrate that the intertemporal propagation of distributional properties of traits is, to a large extent, responsible for the dominance of the asexual and binary mating systems in nature. Namely, from the results obtained in the paper it follows that the switching between the asexual and binary inheritance mechanisms allows the population to achieve effectively a relatively fast decline (sharp concentration) of bad traits or a relatively quick spread (decrease of peakedness and concentration) of good traits, regardless of the distributional properties of the phenotypes in the initial period, in particular, regardless of the degree of heavy-tailedness of their initial densities. Furthermore, from our results it follows that, regardless of their initial distributional properties, the propagation of negative traits in a population with three or more genders can be prevented and the wide spread of positive phenotypes can be achieved immediately or in a relatively near future if the population switches to a mating system with only one or two genders. Given the high costs to species of developing and maintaining extra genders, this makes the asexual and binary inheritance mechanisms advantageous comparing to other mating systems.