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.     

Inbreeding in a natural population of Euodynerus foraminatus (Hymenoptera: Vespidae), a solitary wasp with single-locus complementary sex determination

The solitary wasp Euodynerus foraminatus has single-locus complementary sex determination (sl-CSD), which is normally incompatible with inbreeding because it increases the production of sterile or inviable diploid males. Previous field observations of E. foraminatus have suggested that high levels of sibling mating are present in this species. However, conclusions about inbreeding and its genetic consequences could be flawed if based solely upon behavioural observations. Through microsatellite DNA genotyping of 102 E. foraminatus females in southwest Michigan, we estimate that between 55% and 77% of the matings in this population take place between siblings, but the frequency of diploid males is lower than expected. Our data suggest that a mixture of inbreeding and outbreeding persists in E. foraminatus despite the presence of sl-CSD.     

Single-locus complementary sex determination absent in Heterospilus prosopidis (Hymenoptera: Braconidae)

In the haplodiploid Hymenoptera, haploid males arise from unfertilized eggs, receiving a single set of maternal chromosomes while diploid females arise from fertilized eggs and receive both maternal and paternal chromosomes. Under single-locus complementary sex determination (sl-CSD), sex is determined by multiple alleles at a single locus. Sex locus heterozygotes develop as females, while hemizygous and homozygous eggs develop as haploid and diploid males, respectively. Diploid males, which are inviable or sterile in almost all cases studied, are therefore produced in high frequency under inbreeding or in populations with low sex allele diversity. CSD is considered to be the ancestral form of sex determination within the Hymenoptera because members of the most basal taxa have CSD while some of the more derived groups have other mechanisms of sex determination that produce the haplo-diploid pattern without penalizing inbreeding. In this study, we investigated sex determination in Heterospilus prosopidis Viereck, a parasitoid from a relatively primitive subfamily of the Braconidae, a hymenopteran family having species with and without CSD. By comparing sex ratio and mortality patterns produced by inbred and outbred females, we were able to rule out sl-CSD as a sex determination mechanism in this species. The absence of sl-CSD in H. prosopidis was unexpected given its basal phylogenetic position in the Braconidae. This and other recent studies suggest that sex determination systems in the Hymenoptera may be evolutionary labile.     

No evidence for increased extinction proneness with decreasing effective population size in a parasitoid with complementary sex determination and fertile diploid males

Background  

In species with single locus complementary sex determination (sl-CSD), the sex of individuals depends on their genotype at one single locus with multiple alleles. Haploid individuals are always males. Diploid individuals are females when heterozygous, but males when homozygous at the sex-determining locus. Diploid males are typically unviable or effectively sterile, hence imposing a genetic load on populations. Diploid males are produced from matings of partners that share an allele at the sex-determining locus. The lower the allelic diversity at the sex-determining locus, the more diploid males are produced, ultimately impairing the growth of populations and jeopardizing their persistence. The gregarious endoparasitoid wasp Cotesia glomerata is one of only two known species with sl-CSD and fertile diploid males.     

Single-locus complementary sex determination in Diadegma chrysostictos (Gmelin) (Hymenoptera: Ichneumonidae)

Following the establishment of isofemale lines and subsequent inbreeding, the ichneumonid parasitoid wasp Diadegma chrysostictos (Gmelin) was shown by segregation of polymorphic alloenzyme loci to have single-locus complementary sex determination (sl-CSD). This and the biparental nature of diploid males was confirmed using two independent Mendelian recessive phenotypic markers. The existence of diploid males, sl-CSD, and the abrogation of diploid males following outbreeding was further confirmed by flow cytometry, a potentially general method that is independent of the maternal sex allocation or the need for genetic markers. Estimates of the number of sex alleles in several British populations demonstrated 17-19 alleles in Britain, with a decline toward the northerly limit of the parasitoid's range, varying from 16 in the south of England to 4-5 in central Scotland, in broad agreement with the rate of attainment of a male-biased sex ratio when used to establish en masse laboratory cultures. These data represent the second confirmation of the existence of sl-CSD in the Ichneumonidae (and the first in the Campopleginae subfamily), lending further support to the notion that sl-CSD was the ancestral condition in the Aculeata/Ichneumonoidea clade (Cook 1993a; Periquet et al. 1993).     

膜翅目昆虫补偿性性别决定机制

膜翅目昆虫单双倍体性别决定机制(雄性是单倍体、雌性是二倍体)在昆虫纲的进化中有非常重要的作用。通常膜翅目昆虫的性别由单一位点的等位基因决定,杂合体发育成雌性,半合体发育成雄性。在近亲繁殖的情况下,一定数目的雄性会出现纯合二倍体,由于遗传阻隔这种二倍体的雄性通常是不育的。csd基因的发现为膜翅目昆虫性别决定机制提供了分子生物学证据。文章探讨CSD的分子生物学基础,对膜翅目昆虫sl-CSD的分布进行综述并且探讨膜翅目昆虫降低二倍体雄性消耗的策略以及可能存在的进化机制,最后提出几点建议以便从遗传学、生态学以及进化生物学角度全面的了解sl-CSD。     

Effective population size of a population with stochastically varying size

For a Wright–Fisher model with mutation whose population size fluctuates stochastically from generation to generation, a heterozygosity effective population size is defined by means of the equilibrium average heterozygosity of the population. It is shown that this effective population size is equal to the harmonic mean of population size if and only if the stochastic changes of population size are uncorrelated. The effective population size is larger (resp. smaller) than the harmonic mean when the stochastic changes of population size are positively (resp. negatively) autocorrelated. These results and those obtained so far for other stochastic models with fluctuating population size suggest that the property that effective population sizes are always larger than the harmonic mean under the fluctuation of population size holds only for continuous time models such as diffusion and coalescent models, whereas effective population sizes can be equal to or smaller than the harmonic mean for discrete time models.     

Single-locus complementary sex determination in the inbreeding wasp Euodynerus foraminatus Saussure (Hymenoptera: Vespidae)

The Hymenoptera have arrhenotokous haplodiploidy in which males normally develop from unfertilized eggs and are haploid, while females develop from fertilized eggs and are diploid. Multiple sex determination systems are known to underlie haplodiploidy, and the best understood is single-locus complementary sex determination (sl-CSD) in which sex is determined at a single polymorphic locus. Individuals heterozygous at the sex locus develop as females; individuals that are hemizygous (haploid) or homozygous (diploid) at the sex locus develop as males. sl-CSD can be detected with inbreeding experiments that produce diploid males in predictable proportions as well as sex ratio shifts due to diploid male production. This sex determination system is considered incompatible with inbreeding because the ensuing increase in homozygosity increases the production of diploid males that are inviable or infertile, imposing a high cost on matings between close relatives. However, in the solitary hunting wasp Euodynerus foraminatus, a species suspected of having sl-CSD, inbreeding may be common due to a high incidence of sibling matings at natal nests. In laboratory crosses with E. foraminatus, we find that sex ratios and diploid male production (detected as microsatellite heterozygosity) are consistent with sl-CSD, but not with other sex determination systems. This is the first documented example of sl-CSD in a hymenopteran with an apparent natural history of inbreeding, and thus presents a paradox for our understanding of hymenopteran genetics.     

Effective population size and population subdivision in demographically structured populations

A fast-timescale approximation is applied to the coalescent process in a single population, which is demographically structured by sex and/or age. This provides a general expression for the probability that a pair of alleles sampled from the population coalesce in the previous time interval. The effective population size is defined as the reciprocal of twice the product of generation time and the coalescence probability. Biologically explicit formulas for effective population size with discrete generations and separate sexes are derived for a variety of different modes of inheritance. The method is also applied to a nuclear gene in a population of partially self-fertilizing hermaphrodites. The effects of population subdivision on a demographically structured population are analyzed, using a matrix of net rates of movement of genes between different local populations. This involves weighting the migration probabilities of individuals of a given age/sex class by the contribution of this class to the leading left eigenvector of the matrix describing the movements of genes between age/sex classes. The effects of sex-specific migration and nonrandom distributions of offspring number on levels of genetic variability and among-population differentiation are described for different modes of inheritance in an island model. Data on DNA sequence variability in human and plant populations are discussed in the light of the results.     

Balancing selection maintains sex determining alleles in multiple‐locus complementary sex determination

Hymenopteran species in which sex is determined through a haplo‐diploid mechanism known as complementary sex determination (CSD) are vulnerable to a unique form of inbreeding depression. Diploids heterozygous at one or more CSD loci develop into females but diploids homozygous at all loci develop into diploid males, which are generally sterile or inviable. Species with multiple polymorphic CSD loci (ml‐CSD) may have lower rates of diploid male production than species with a single CSD locus (sl‐CSD), but it is not clear if polymorphism is consistently maintained at all loci. Here, we assess the rate of diploid male production in a population of Cotesia rubecula, a two‐locus CSD parasitoid wasp species, approximately 20 years after the population was introduced for biological control. We show that diploid male production dropped from 8–13% in 2005 and 2006 to 3–4% by 2015. We also show from experimental crosses that the population maintained polymorphism at both CSD loci in 2015. We use theory and simulations to show that balancing selection on all CSD alleles promotes polymorphism at several loci in ml‐CSD populations. Our study supports the hypothesis that ml‐CSD populations have lower diploid male production and are more likely to persist than comparable sl‐CSD populations.     

Unexpectedly low frequencies of diploid males in an inbreeding parasitoid with complementary sex determination

In hymenopterans with single locus complementary sex determination, sex depends on the genotype at one polymorphic locus. Haploids are always male, while diploids are female when heterozygous and male when homozygous at the sex‐determining locus. Brothers and sisters have a 50% chance of sharing a sex allele (i.e. of being ‘matched’), and hence half of all sibling matings are expected to produce diploid males at the expense of females. Nevertheless, observed frequencies of diploid males are often lower than predicted, as diploid males may succumb to pre‐imaginal mortality, or because unmatched mates or sperm enjoy a competitive advantage. We counted diploid males in broods of the parasitoid wasp Cotesia glomerata sampled in the field, and in broods produced through controlled laboratory crosses. Consistently, the frequency of diploid males fell below expectations based upon the estimated occurrence of sibling mating. In the staged broods with diploid males, females made up a disproportionately large share of the diploids. Broods with and without diploid males were of similar size. Hence, the shortage of diploid males cannot be accounted for by differential pre‐imaginal mortality alone. Instead, we postulate the existence of a mechanism that leads to preferential fertilization of eggs by sperm bearing unmatched alleles. © 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, ●● , ●●–●●.     

Effective population size for culturally evolving traits

Population size has long been considered an important driver of cultural diversity and complexity. Results from population genetics, however, demonstrate that in populations with complex demographic structure or mode of inheritance, it is not the census population size, N, but the effective size of a population, N_e, that determines important evolutionary parameters. Here, we examine the concept of effective population size for traits that evolve culturally, through processes of innovation and social learning. We use mathematical and computational modeling approaches to investigate how cultural N_e and levels of diversity depend on (1) the way traits are learned, (2) population connectedness, and (3) social network structure. We show that one-to-many and frequency-dependent transmission can temporally or permanently lower effective population size compared to census numbers. We caution that migration and cultural exchange can have counter-intuitive effects on N_e. Network density in random networks leaves N_e unchanged, scale-free networks tend to decrease and small-world networks tend to increase N_e compared to census numbers. For one-to-many transmission and different network structures, larger effective sizes are closely associated with higher cultural diversity. For connectedness, however, even small amounts of migration and cultural exchange result in high diversity independently of N_e. Extending previous work, our results highlight the importance of carefully defining effective population size for cultural systems and show that inferring N_e requires detailed knowledge about underlying cultural and demographic processes.     

Effective size of a fluctuating age-structured population

Previous theories on the effective size of age-structured populations assumed a constant environment and, usually, a constant population size and age structure. We derive formulas for the variance effective size of populations subject to fluctuations in age structure and total population size produced by a combination of demographic and environmental stochasticity. Haploid and monoecious or dioecious diploid populations are analyzed. Recent results from stochastic demography are employed to derive a two-dimensional diffusion approximation for the joint dynamics of the total population size, N, and the frequency of a selectively neutral allele, p. The infinitesimal variance for p, multiplied by the generation time, yields an expression for the effective population size per generation. This depends on the current value of N, the generation time, demographic stochasticity, and genetic stochasticity due to Mendelian segregation, but is independent of environmental stochasticity. A formula for the effective population size over longer time intervals incorporates deterministic growth and environmental stochasticity to account for changes in N.     

Between-year variation in population sex ratio increases with complexity of the breeding system in Hymenoptera

While adaptive adjustment of sex ratio in the function of colony kin structure and food availability commonly occurs in social Hymenoptera, long-term studies have revealed substantial unexplained between-year variation in sex ratio at the population level. In order to identify factors that contribute to increased between-year variation in population sex ratio, we conducted a comparative analysis across 47 Hymenoptera species differing in their breeding system. We found that between-year variation in population sex ratio steadily increased as one moved from solitary species, to primitively eusocial species, to single-queen eusocial species, to multiple-queen eusocial species. Specifically, between-year variation in population sex ratio was low (6.6% of total possible variation) in solitary species, which is consistent with the view that in solitary species, sex ratio can vary only in response to fluctuations in ecological factors such as food availability. In contrast, we found significantly higher (19.5%) between-year variation in population sex ratio in multiple-queen eusocial species, which supports the view that in these species, sex ratio can also fluctuate in response to temporal changes in social factors such as queen number and queen-worker control over sex ratio, as well as factors influencing caste determination. The simultaneous adjustment of sex ratio in response to temporal fluctuations in ecological and social factors seems to preclude the existence of a single sex ratio optimum. The absence of such an optimum may reflect an additional cost associated with the evolution of complex breeding systems in Hymenoptera societies.     

Ladies last: diel rhythmicity of adult emergence in a parasitoid with complementary sex determination

Protandry, the earlier adult emergence of males, is explained as either an adaptive strategy maximizing male mating opportunities at the same time as minimizing female pre‐reproductive mortality, or as an incidental by‐product of sexual dimorphism fuelled by selection for other life‐history traits. Adult emergence sequences are monitored of broods of the gregarious larval endoparasitoid Cotesia glomerata L. (Hymenoptera: Braconidae) undergoing pupal development under different temperature regimes. As a haplodiploid species with single‐locus complementary sex determination, gender in C. glomerata is determined by the genotype at one sex locus. Haploids are always male, whereas diploids are female when heterozygous but male when homozygous at the sex locus. Sibling mating promotes homozygosity and thus the production of diploid males. Diploid males are produced at the expense of females, and impose a genetic burden on individuals and populations, despite their exceptional fertility in C. glomerata. Emergence of broods is typically completed within 2 days. Irrespective of temperature, males emerge earlier and within a shorter time interval than females, and a majority of the males in a cluster emerge before the first female. The implications of an incomplete temporal segregation of the sexes on the incidence of inbreeding in C. glomerata are discussed in the light of its sex determination mechanism and its patterns of mating, host exploitation and natal dispersal.     

Experimental support for multiple-locus complementary sex determination in the parasitoid Cotesia vestalis

Despite its fundamental role in development, sex determination is highly diverse among animals. Approximately 20% of all animals are haplodiploid, with haploid males and diploid females. Haplodiploid species exhibit diverse but poorly understood mechanisms of sex determination. Some hymenopteran insect species exhibit single-locus complementary sex determination (sl-CSD), where heterozygosity at a polymorphic sex locus initiates female development. Diploid males are homozygous at the sex locus and represent a genetic load because they are inviable or sterile. Inbreeding depression associated with CSD is therefore expected to select for other modes of sex determination resulting in fewer or no diploid males. Here, we investigate an alternative, heretofore hypothetical, mode of sex determination: multiple-locus CSD (ml-CSD). Under ml-CSD, diploid males are predicted to develop only from zygotes that are homozygous at all sex loci. We show that inbreeding for eight generations in the parasitoid wasp Cotesia vestalis leads to increasing proportions of diploid males, a pattern that is consistent with ml-CSD but not sl-CSD. The proportion of diploid males (0.27 ± 0.036) produced in the first generation of inbreeding (mother–son cross) suggests that two loci are likely involved. We also modeled diploid male production under CSD with three linked loci. Our data visually resemble CSD with linked loci because diploid male production in the second generation was lower than that in the first. To our knowledge, our data provide the first experimental support for ml-CSD.