Population dynamics of sperm and pollen killers

Abstract

A model of segregation distortion is assumed in which the action of the distorter when heterozygous is to render dysfunctional those gametes that carry its allele. Two gamete killers when homozygous are assumed to distort each other. Individuals that carry the gamete killer suffer a reduction in the number of functional gametes they produce, but this deleterious effect is counterbalanced by the segregation ratio advantage of the distorter. The dynamics of such a system are analyzed in terms of a generalized fecundity function, which is defined as a function which assigns to any individual his relative fecundity in terms of the fraction of functional gametes he produces. Three general classes of fecundity functions are considered: (a) proportionality, in which the relative fecundity of an individual is proportional to the fraction of functional gametes he produces, (b) compensation, in which the relative fecundity of an individual is always greater than the fraction of functional gametes he produces, and (c) mass action, in which the relative fecundity of an individual is less than or greater than the fraction of functional gametes he produces according to whether the fraction of functional gametes is less than or greater than some threshold. In case (a) all gamete killers are always at neutral equilibria and gene frequency changes at the locus are governed by random drift. In case (b) all gamete killers will be fixed if the fecundity function is such that its second derivative is negative, whenever its argument is greater than one-half. And in case (c) some gamete killers will converge to stable equilibria, others will be fixed. If a gamete killer is homozygous lethal it will almost always converge to a stable equilibrium.