A mathematical model for recessive lethal segregation distorters with differential viabilities in the sexes.

Abstract

ETAILED examinations of gene frequency changes at loci which show Dnon-Mendelian segregation are generally unavailable because realistic models are analytically intractable. Most naturally occurring examples of meiotic drive occur in only one sex. In at least one case, that of segregation distorter in Drosophila melanogaster (HARTL, HIRAIZUMI and CROW 1967), the sexes also differ in fecundity. Considered separately. neither complication creates a serious problem. The sexual inequality in segregation ratio can be handled quite easily (PROUT 1953; BRUCK 1957; LEWONTIN and DUNN 1960; DUNN and LEVENE 1961; SCUDO 1967). LEWONTIN (1968) has obtained numerical solutions to the equations of a general model of meiotic drive in which the reproductive values are different between genotypes but equal in the two sexes. The literal solutions to his equations are also available ( HARTL 1970a). Similarly, gene frequency equilibria have been found for models in which there is no segregation distortion but in which the reproductive values differ between the sexes (HALDANE 1924,1926; OWEN 1953; BODMER 1965; CANNINGS 1969). When the inequalities in segregation and fitness are considered simultaneously, however, then there arises a formidable problem in analysis. This paper presents the evolutionary dynamics of a locus having a recessive lethal allele which shows meiotic drive in heterozygotes. That the segregation distorter is assumed to be a recessive lethal is not an unreasonable restriction, for several important examples found in nature are lethal when homozygous (SANDLER, HIRAIZUMI and SANDLER 1959; CHESLEY and DUNN 1936). Population genetic models of this kind have been treated previously (BRUCK 1957; HIRAIZUMI, SANDLER and CROW 1960; CROW and KIMURA 1970), but the models in the present paper are more realistic in that they allow the sexes to differ in reproductive value.