Segregation Distortion and Heteroclinic Cycles

Segregation Distorters are genetic elements that disturb the meiotic segregation of heterozygous genotypes. The effect is hence often referred to as meiotic drive. The driving chromosome destroys its partner, provided the latter is not resistant against the "killer." The dynamic behavior of a meiotic drive system is in general determined by the interaction of several alleles at different gene loci. The corresponding genes are "ultra-selfish" in that they force their own spreading in the population without contributing positively to the fitness of the organisms carrying them. In this work we consider only autosomal drive systems with two or three loci, one or two "killer loci" and a single "target locus." We mostly restrict ourselves to models with the minimum number of different genotypes, commonly three or four. the only exception is a six-species model for the spore killer system in Neurospora intermedia. We model the population dynamcis by means of replicator equations. The dynamics of these differential equations coincides with the behavior of the difference equations which are more common in population genetics as far as the stability of fixed points and the existence of heteroclinic cycles is concerned. We show here that heteroclinic cycles are abundant in models of segregation distortion systems. Their stability properties are analyzed in detail for a variety of models. In particular we investigate heteroclinic cycles in the population dynamics of the SD-locus of Drosophila melanogaster and the relative stability of heteroclinic cycles in the competition of two killer alleles at the same gene locus. Finally, we find a large number of heteroclinic cycles in a game dynamical model of the spore killer system of the fungus Neurospora intermedia.