95-07-070
Abstract:
Segregation Distortion and Heteroclinic Cycles
Barbel Maria Regina Stadler
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.
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