Population Genetics of a Parasitic Chromosome: Theoretical Analysis of PSR in Subdivided Populations

An assemblage of non-Mendelian sex ratio elements occurs in natural populations of the parasitoid wasp Nasonia vitripennis. These include Maternal Sex Ratio (MSR), a cytoplasmic element that causes nearly all-female families, and Paternal Sex Ratio (PSR), a B chromosome that causes 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. Theoretical analysis shows that subdivided population structures reduce PSR frequency. Paternal Sex Ratio cannot exist in subdivided populations (with temporary mating demes lasting one generation) when foundress number is less than three. The equilibrium frequency of PSR depends strongly on fertilization proportion (x). In populations producing the Hamiltonian evolutionarily stable strategy (x = [(N - 1)(2N - 1)/N(4N - 1)]), PSR never achieves frequencies over 3% for any deme size. In contrast, if the population produces a high fertilization proportion (i.e., greater than 90%, as produced by MSR), then PSR can achieve frequencies over 90% when deme size is three or larger. Results also show that PSR selects against the MSR cytoplasmic element in populations with small deme size, which results in polymorphic equilibria for both elements.