The population genetics of sex determination in honey bees: random mating in closed populations

Abstract

SUMMARYThe genetic load associated with the method of sex determination in honey bees has been a great deterrent to selective breeding programmes, primarily because of a lack of understanding of the population genetics of the system. In this paper we examine the distribution of diploid brood viabilities in closed, random mating populations, as a function both of the system of sex determination and of multiple mating in queens. Analytically we show that for a given number of sex alleles, an increase in the numbers of matings of queens, reduces the variance in brood viability, but does not affect the mean. The results of a computer simulation demonstrate that the equilibrium number of sex alleles is approached very slowly from above, so that small populations that start with large numbers of sex alleles will maintain high brood viability for a long time. The practical significance of this is discussed.

Effective population size in eusocial Hymenoptera with worker-produced males

“…N e has a special importance in Hymenopteran species with complementary sex determination (CSD), because it determines allelic diversity at the CSD locus (Yokoyama and Nei, 1979;Page and Marks, 1982;Zayed, 2009). Populations with a smaller N e maintain less alleles at the CSD locus, and consequently produce higher frequencies of sterile or effectively lethal diploid males.…”

“…In some species, as honey bees and army ants, a queen mates with more than one male, leading to a biased breeding sex ratio (r ¼ N m /N f ) from unity. In such species, assuming the absence of worker reproduction, N e has been predicted from equation (1) as Page and Marks, 1982). When r is large as in honey bees, 9N f /4, that is, the number of nests multiplied by 9/4, can be a good approximation of N e (Page and Marks, 1982).…”

“…This application is reasonable, as inheritance in haplodiploid species is effectively equivalent to sex-linked inheritance in diploid species (Yokoyama and Nei, 1979;Page and Marks, 1982). Colonies of eusocial Hymenoptera are characterized by a reproductive division of labour.…”

“…When r is large as in honey bees, 9N f /4, that is, the number of nests multiplied by 9/4, can be a good approximation of N e (Page and Marks, 1982).…”

“…In such species, assuming the absence of worker reproduction, N e has been predicted from equation (1) as Page and Marks, 1982). When r is large as in honey bees, 9N f /4, that is, the number of nests multiplied by 9/4, can be a good approximation of N e (Page and Marks, 1982).It is, however, known that under certain conditions, workers lay unfertilized eggs which develop into males (Crozier and Pamilo, 1996). This production of males by workers is widespread in the eusocial Hymenoptera, such as stingless bees, honey bees, bumble bees, vespine wasps and higher ants (Crozier and Pamilo, 1996).…”