Sign-epistatic centromere drive in panmictic populations

Abstract

Comparative work has revealed a highly non-random elevation of karyotypic homogeneity within mammalian species for either telocentric chromosomes or centric fusions, and a karyotypic bimodality among species for these binary chromosome morphologies. A verbal theory developed by Pardo-Manuel de Villena and Sapienza argues that morphology-biased segregation in female meiosis explains the corresponding directional evolution in favor of one or the other chromosome form within species, and moreover, periodic reversals of meiotic spindle asymmetry explain the pattern of bimodality observed among species. Here I investigate a population genetic model in which I assume that the direction of the spindle asymmetry is under the control of a modifier gene, either linked or unlinked to a focal karyotypic mutant (linkage being to a centric fusion, say), and I derive the corresponding invasion conditions for the modifier-centric-fusion gene complex. I demonstrate that the scenario put forth in the verbal theory can be explained by a two-step process in which (1) a centric-fusion invades to fixation while the linked modifier winds up at an intermediate frequency by hitchhiking, and then (2) subsequent fixations of unlinked centric fusions occur. Via numerical iteration of the model, I demonstrate that the typical post-hitchhiking frequency of the linked modifier (from step 1) is broadly sufficient for subsequent unlinked invasions (step 2). Sign-reversing modifier evolution is therefore concluded to be a plausible mechanism instantiating the principles of a female drive theory of karyotype evolution.