Effective population size in eusocial Hymenoptera with worker-produced males

Abstract

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...

Prediction and estimation of effective population size

“…For example, in many eusocial Hymenoptera species, males can be produced by workers rather than only by queens. Predictions of N e for this scenario have been developed by Nomura and Takahashi (2012).…”

Workers' sons rescue genetic diversity at the sex locus in an invasive honey bee population

“…The basis of this prediction is that worker‐produced males introduce an additional round of gametic sampling per generation that increases the rate of allele loss to drift (Crozier & Pamilo, ). However, when the breeding sex ratio is male‐biased and variance in offspring production among workers is low, worker reproduction instead increases Ne (Nomura & Takahashi, ). Honey bees in general, and A. cerana in particular, are an archetype for these latter life history traits (Holmes, Tan, Wang, Oldroyd, & Beekman, ; Nomura & Takahashi, ), meaning that worker reproduction is predicted to increase Ne in A. cerana .…”

“…Among hymenopteran eusocial insects (ants, some bees and wasps), worker sterility can be absolute (workers lack functional ovaries), but typically is not; that is, workers have lost the ability to mate but remain capable of laying unfertilized haploid eggs that produce males (Ronai, Vergoz, & Oldroyd, ). Theory predicts that direct male production by workers has consequences for population genetics (Crozier, ; Crozier & Pamilo, ; Nomura & Takahashi, ; Owen, ; Owen & Owen, ). For example, where sex ratios are equal, reproductive workers should decrease genetic diversity in a population, relative to populations where only queens produce sons, because they introduce an additional round of gametic sampling and thereby increase the loss of alleles due to drift (Crozier & Pamilo, ; Nomura & Takahashi, ; Owen & Owen, ).…”

“…Theory predicts that direct male production by workers has consequences for population genetics (Crozier, ; Crozier & Pamilo, ; Nomura & Takahashi, ; Owen, ; Owen & Owen, ). For example, where sex ratios are equal, reproductive workers should decrease genetic diversity in a population, relative to populations where only queens produce sons, because they introduce an additional round of gametic sampling and thereby increase the loss of alleles due to drift (Crozier & Pamilo, ; Nomura & Takahashi, ; Owen & Owen, ). In contrast, where sex ratios are male‐biased, worker reproduction may lead to higher genetic diversity (Nomura & Takahashi, ).…”

“…For example, where sex ratios are equal, reproductive workers should decrease genetic diversity in a population, relative to populations where only queens produce sons, because they introduce an additional round of gametic sampling and thereby increase the loss of alleles due to drift (Crozier & Pamilo, ; Nomura & Takahashi, ; Owen & Owen, ). In contrast, where sex ratios are male‐biased, worker reproduction may lead to higher genetic diversity (Nomura & Takahashi, ). However, how such population‐level effects of fertile workers influence a species' ecology is poorly understood.…”