In many eusocial Hymenoptera, a proportion of males are produced by workers. To assess the effect of male production by workers on the effective population size N e , a general expression of N e in Hymenoptera with worker-produced males is derived on the basis of the genetic drift in the frequency of a neutral allele. Stochastic simulation verifies that the obtained expression gives a good prediction of N e under a wide range of conditions. Numerical computation with the expression indicates that worker reproduction generally reduces N e . The reduction can be serious in populations with a unity or female-biased breeding sex ratio. Worker reproduction may increase N e in populations with a male-biased breeding sex ratio, only if each laying worker produce a small number of males and the difference of male progeny number among workers is not large. Worker reproduction could be an important cause of the generally lower genetic variation found in Hymenoptera, through its effect on N e . Heredity (2012) 109, 261-268; doi:10.1038/hdy.2012.11; published online 5 September 2012Keywords: effective population size; Hymenoptera; worker-produced males
INTRODUCTIONEffective population size N e is a crucial parameter in population, conservation and quantitative genetics, because this parameter determines both the rate of inbreeding and the amount of genetic drift in populations (Caballero, 1994;Falconer and Mackay, 1996;Frankham et al., 2002). In haplodiploid species, N e has been predicted by applying Wright's (1933) standard formula for X-linked locus,where N f and N m are the numbers of breeding females and males, respectively. 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. Colonies are founded by mated females (queens), who produce diploid daughters (workers and young queens) and haploid males. Workers do not mate, but they retain ovaries in many species. If workers are sterile, only queens should be counted as the breeding females in the computation of N e . Furthermore, under monogamous mating system as in many Hymenopteran species, both the numbers of queens and males are approximated by the number of nests, giving from equation (1) an estimate of N e as the number of nests multiplied by 1.5 (Ellis et al., 2006). 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).It is, however, known that under certain conditions, workers lay unfertilized eggs which develop into males (Crozier and Pamilo, 1996). This production of male...