REDUCTION OF GENE FLOW DUE TO THE PARTIAL STERILITY OF HETEROZYGOTES FOR A CHROMOSOME MUTATION. I. STUDIES ON A "NEUTRAL" GENE NOT LINKED TO THE CHROMOSOME MUTATION IN A TWO POPULATION MODEL.

Abstract

The primary role of chromosome mutations that cause partial sterility of the heterozygote in triggering some processes of speciation is supported by an increasing amount of data. This type of speciation seems to have played a particularly important role in animal species with limited vagility. Among the more extensively studied examples are the Australian Morabinae (White, 1968, 1974), the complex Didymuria violescens (Bocquet, 1953; Lecher, 1964, 1967, 1968), the isopods Jaera (Lecher and Prunus, 1972) and the Mexican lizards of the complex Sceloporus grammicus (Hall and Selander, 1973). Besides these exemplary cases, there are numerous other situations of closely related species with different karyotypes in numerous groups of animals which have been interpreted in terms of chromosomal speciation mechanisms (see White, 1978a, 1978b, for a complete review). The mechanisms of chromosomal speciation are open to discussion. The stasipatric speciation model, proposed and developed by White (1968, 1978a, 1978b), envisages the production of a heterozygote mutant, the fixation of the mutation by genetic drift and the subsequent spread of the mutant homozygote population due to systematic factors advantageous to the mutation. Clarification and quantification of the processes and mechanisms involved with regard to sequence and hierarchy are necessary: besides further knowledge of individual examples, theoretical models are important to explain the onset, fixation (see Hedrick, 198 1), spread and accumulation of chromosome mutations and their role in reproductive isolation. We address here the efficiency, as a mechanism of reproductive isolation, of the partial sterility of heterozygotes for chromosome mutations. In this paper we quantify the efficiency of a single chromosome mutation that causes partial sterility of the heterozygote in reducing the gene flow. We use a model similar to the loci systems on which an extensive literature exists (see Hedrick et al., 1978), but which scarcely addresses the problem of chromosomal speciation. The model consists of two populations of the same size which come into contact and are initially monomorphic, one with a normal form and the other a mutated form of one specific chromosome. These populations differ in frequency for a pair of selectively neutral alleles, not linked to the chromosome involved in the mutation. We propose a model with non-overlapping generations based on the following parameters: 1) constant symmetrical migration rate between the two populations in the diploid stage (m); and 2) reduction of fitness, caused by the partial sterility of the heterozygote for the chromosome mutation (s). Our model will be based upon the following quantities: 1) the difference in frequency of the mutated chromosome in populations 1 and 2 at the nth generation (p ,n p2(n)); 2) the difference in frequen-