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

The 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.