POPULATION-GENETICS OF A PARASITIC CHROMOSOME - THEORETICAL-ANALYSIS OF PSR IN SUBDIVIDED POPULATIONS

An assemblage of non-Mendelian sex ratio elements occurs in natural po pulations of the parasitoid wasp Nasonia vitripennis. These include Ma ternal Sex Ratio (MSR), a cytoplasmic element that causes nearly all-f emale families, and Paternal Sex Ratio (PSR), a B chromosome that caus es all-male families. The PSR chromosome is transmitted via sperm but causes destruction of the paternal chromosomes (except itself) shortly after egg fertilization. Owing to haplodiploidy, this results in the conversion of diploid (female) eggs into haploid (male) eggs. Paternal Sex Ratio is an extreme example of a selfish genetic element. Theoret ical analysis shows that subdivided population structures reduce PSR f requency. Paternal Sex Ratio cannot exist in subdivided populations (w ith temporary mating demes lasting one generation) when foundress numb er is less than three. The equilibrium frequency of PSR depends strong ly on fertilization proportion (x). In populations producing the Hamil tonian evolutionarily stable strategy (x = [(N - 1)(2N - 1)/N(4N - 1)] ), PSR never achieves frequencies over 3% for any deme size. In contra st, if the population produces a high fertilization proportion (i.e., greater than 90%, as produced by MSR), then PSR can achieve frequencie s over 90% when deme size is three or larger. Results also show that P SR selects against the MSR cytoplasmic element in populations with sma ll deme size, which results in polymorphic equilibria for both element s.