Effective population size in eusocial Hymenoptera with worker-produced males

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.