A Two Locus Haploid Population with Overlapping Generations

The rates and probabilities of fixation in pure homozygous states are obtained for a finite size, two linked loci population of monoecious haploid individuals (e.g. bacteria) reproducing by mechanisms that may be loosely termed random and nonrandom matings. Birth-death events occur one at a time so that the generations are overlapping. It is foulnd that the degree of nonrandom mating does not affect the fixatioii probabilities and, indeed, these probabilities are identical to the fixation probabilities for a certain discrete generations model well known in the literature. Furthermore, if N birth-death events of the overlapping generations model are identified with one discrete generation and the nonrandom mating condition is dropped, then this rate is asymptotically equal to the known rate. The rate of approach to fixation of the first allele to be fixed is found exactly for all population sizes when the recombination fraction is at its extreme values. This rate is also determined numerically for certain small population sizes and specific values of the recombination fraction. It appears that this rate is made quicker by increasing the valtue of recombination fraction and that for large population sizes there exists a critical value of the recombination fraction after which the rate is effectively constant.