Effects of brood manipulation costs on optimal sex allocation in social hymenoptera

In eusocial Hymenoptera, queens and workers are in conflict over optimal sex allocation. Sex ratio theory, while generating predictions on the extent of this conflict under a wide range of conditions, has largely neglected the fact that worker control of investment almost certainly requires the manipulation of brood sex ratio. This manipulation is likely to incur costs, for example, if workers eliminate male larvae or rear more females as sexuals rather than workers. In this article, we present a model of sex ratio evolution under worker control that incorporates costs of brood manipulation. We assume cost to be a continuous, increasing function of the magnitude of sex ratio manipulation. We demonstrate that costs counterselect sex ratio biasing, which leads to less female-biased population sex ratios than expected on the basis of relatedness asymmetry. Furthermore, differently shaped cost functions lead to different equilibria of manipulation at the colony level. While linear and accelerating cost functions generate monomorphic equilibria, decelerating costs lead to a process of evolutionary branching and hence split sex ratios.     

Evolution of sex ratios in social hymenoptera: Consequences of finite brood size

Evolutionarily stable sex ratios are determined for social hymenoptera under local mate competition (LMC) and when the brood size is finite. LMC is modelled by the parameterd. Of the reproductive progeny from a single foundress nest, a fractiond disperses (outbreeding), while (l-d) mate amongst themselves (sibmating). When the brood size is finite,d is taken to be the probability of an offspring dispersing, and similarly,r, the proportion of male offspring, the probability of a haploid egg being laid. Under the joint influence of these two stochastic processes, there is a nonzero probability that some females remain unmated in the nest. As a result, the optimal proportion of males (corresponding to the evolutionarily stable strategy, ESS) is higher than that obtained when the brood size is infinite. When the queen controls the sex ratio, the ESS becomes more female biased under increased inbreeding (lowerd). However, the ESS under worker control shows an unexpected pattern, including anincrease in the proportion ofmales withincreased inbreeding. This effect is traced to the complex interaction between inbreeding and local mate competition.     

A sex ratio theory of gregarious parasitoids

Summary A mathematical model is constructed to explain a density-dependent increase in the progeny sex ratios of gregarious parasitoids. In the model we considered non-cooperative game between females concerned with their own inclusive fitness. Equilibrium progeny sex ratios of the first and second females ovipositing on the same host are expressed in terms of the probability of double parasitism (p), the ratio of a male to a female in contribution to resource competition (α), the clutch size ratio between the two females (β), the crowding effect on female reproductive success (γ), and the inbreeding coefficient (f). Major predictions from the model are: 1) the progeny sex ratios of both the first and second females increase withp, 2) as β becomes smaller, the progeny sex ratios of the first females decrease, while those of the second females dramatically increases, 3) when a host is attacked by at most two wasps, the sex ratio of the total number of eggs laid on the host does not exceed 0.25. The effects of α and preferential death by female progeny in doubly parasitized hosts are considered as factors responsible for an excess number of males at emergence. Some possible modes of density-dependent increase in the sex ratios of the overall progeny populations is also discussed on the basis of the present model.     

Sex ratio changes and the evolution of eusociality in the hymenoptera: Simulation and games theory studies

Computer simulations of the evolution of altruistic (worker) behaviour with concomitant sex ratio biasing by female Hymenoptera were used to calculate K_min, the minimum K preventing selection against altruism. K is the ratio of the number of siblings raised by a worker, to the number of offspring she would have raised otherwise. The results were compared to a games theory analysis of the same system.The simulation results agreed exactly with games theory predictions under Hardy-Weinberg conditions, but deviated from them somewhat during selection. K_min varied with P (the proportion of altruists). If altruists made the sex ratio more female-biased, K_min < 1 at low P, but with reasonable brood sizes K_min > 1 at high P. If queens raised a second brood, simultaneously with brood raised by altruists, the value of K_min at high P was reduced with decreasing brood size. Decreasing the degree of female-bias generally caused a decrease in K_min with increasing P; altruism with sex ratio biasing toward males was always selected against. Simulations confirmed that selection is positive when K > K_min and negative when K < K_min. Thus altruism can be favoured by sex ratio biasing while P is low, but as P increases it becomes increasingly disadvantaged relative to altruism without sex ratio biasing (when K ? 1 at all P). It is concluded that sex ratio biasing is not particularly favourable for the evolution of social behaviour in Hymenoptera.     

A theory of Fisher's reproductive value

The formal Darwinism project aims to provide a mathematically rigorous basis for optimisation thinking in relation to natural selection. This paper deals with the situation in which individuals in a population belong to classes, such as sexes, or size and/or age classes. Fisher introduced the concept of reproductive value into biology to help analyse evolutionary processes of populations divided into classes. Here a rigorously defined and very general structure justifies, and shows the unity of concept behind, Fisher's uses of reproductive value as measuring the significance for evolutionary processes of (i) an individual and (ii) a class; (iii) recursively, as calculable for a parent as a sum of its shares in the reproductive values of its offspring; and (iv) as an evolutionary maximand under natural selection. The maximand is the same for all parental classes, and is a weighted sum of offspring numbers, which implies that a tradeoff in one aspect of the phenotype can legitimately be studied separately from other aspects. The Price equation, measure theory, Markov theory and positive operators contribute to the framework, which is then applied to a number of examples, including a new and fully rigorous version of Fisher's sex ratio argument. Classes may be discrete (e.g. sex), continuous (e.g. weight at fledging) or multidimensional with discrete and continuous components (e.g. sex and weight at fledging and adult tarsus length).     

Male work and sex ratio in social crab spiders

Summary: Biased sex ratios may alter the contribution that individuals of either sex make to group living. Such a possibility has not been examined in social spiders, in part as adult male spider anatomy and behaviour are focussed on mating. Subadult male behaviour was examined in two congener social crab spiders that have similar ecological niches, Diaea ergandros with an equal sex ratio and D. socialis with a female-biased sex ratio. A laboratory experiment that varied sex ratios of groups of subadults of the two species found that nest construction in D. ergandros did not vary with sex ratio, but that of D. socialis did as males did not contribute to nest construction. This may suggest that among social species, biased sex ratios might influence the appearance of drone-like behaviour.     

Evolution of sex ratios in social hymenoptera: kin selection,local mate competition,polyandry and kin recognition

A model is constructed to study the effects of local mate competition and multiple mating on the optimum allocation of resources between the male and female reproductive brood in social hymenopteran colonies from the ‘points of view’ of the queen (parental manipulation theory) as well as the workers (kin selection theory). Competition between pairs of alleles specifying different sex investment ratios is investigated in a game theoretic frame work. All other things being equal, local mate competition shifts the sex allocation ratio in favour of females both under queen and worker control. While multiple mating has no effect on the queen’s optimum investment ratio, it leads to a relatively male biased investment ratio under worker control. Under queen control a true Evolutionarily Stable Strategy(ess) does not exist but the ‘best’ strategy is merely immune from extinction. A trueess exists under worker control in colonies with singly mated queens but there is an asymmetry between the dominant and recessive alleles so that for some values of sex ratio a recessive allele goes to fixation but a dominant allele with the same properties fails to do so. Under multiple mating, again, a trueess does not exist but a frequency dependent region emerges. The best strategy here is one that is guaranteed fixation against any competing allele with a lower relative frequency. Our results emphasize the need to determine levels of local mate competition and multiple mating before drawing any conclusions regarding the outcome of queen-worker conflict in social hymenoptera. Multiple mating followed by sperm mixing, both of which are known to occur in social hymenoptera, lower average genetic relatedness between workers and their reproductive sisters. This not only shifts the optimum sex ratio from the workers’ ‘point of view’ in favour of males but also poses problems for the kin selection theory. We show that kin recognition resulting in the ability to invest in full but not in half sisters reverts the sex ratio back to that in the case of single mating and thus completely overcomes the hurdles for the operation of kin selection.     

Persistence conditions of symmetric social hybridogenesis in haplo-diploid hymenoptera

In eusocial Hymenoptera species, females variably develop into either alate females (queens) or workers, and in most cases, caste differentiation is determined environmentally. Recently, however, female castes in two harvester ant species, Pogonomyrmex rugosus and P. barbatus, were found to be determined genetically in hybrid zones of these two species. In the hybrid populations, homozygous females (e.g. AA or BB) and heterozygous females (AB) develop into alate females and workers, respectively. This genetic caste determination system is called symmetric social hybridogenesis (SSH). It is clear that populations with SSH can persist only if all four genotypes (AA and BB females, and A and B males) coexist simultaneously. However, it is not obvious that these populations are always persistent when the four genotypes simultaneously exist. Here, we examined the stability and persistence of an SSH population using a simple mathematical model. According to the analysis of the model, the SSH population persists only when some conditions are satisfied: (1) each female mates with more than two males, and (2) male production increases less steeply than linearly with increasing numbers of workers in a colony, and alate female production increases more steeply than linearly with increasing numbers of workers, or (2') male production increases more steeply than linearly with increasing numbers of workers in a colony, and alate female production increases much more steeply than male production. Therefore, it is not obvious that SSH populations are maintained and are stable for long periods. We discuss whether these conditions are satisfied in real SSH populations.     

Experimentally increased testosterone affects social rank and primary sex ratio in the spotless starling

It has been suggested that the amount of maternal testosterone allocated into the eggs might be implicated in the process of sex determination. However, recent findings on the effect that female social rank has on the level of egg testosterone suggest that reported associations between male-biased sex ratios and yolk testosterone may represent an indirect hormonal effect mediated by the interdependence among maternal hormones, female social rank, and sex ratio. Here, we report the results of a field experiment in which we manipulated the circulating levels of testosterone in female spotless starlings (Sturnus unicolor) before egg formation. Focal females were controlled in subsequent years to explore possible delayed effects of hormone manipulation on primary sex ratio and social status that could persist because of permanent hormonal change or through hormone-dominance interactions. The results indicate that testosterone-implanted females (T-females) produced significantly more sons than control females (C-females) in the year in which they were manipulated. These differences in offspring sex ratio between T- and C-females persisted in the next 3 years, although no additional hormone treatments were given. These results were not mediated by an eventual effect of testosterone treatment on the quality of the females' mates. A similar proportion of T- and C-females acquired a nest box and bred either in the manipulation year or in Year 1 after manipulation, but T-females tended to be more successful in acquiring a nest box than C-females in Years 2 and 3 after manipulation. These results suggest that added testosterone had a direct role on the acquisition and maintenance of high social rank. Delayed effects of testosterone on primary sex ratio might have been caused by altered endogenous production of T-females. Alternatively, the maintenance of sex ratio differences between T- and C-females long after having being implanted might be attributed to the positive effect that enhanced social rank of T-females has on their circulating testosterone levels.     

A theory of gene-culture coevolution of parental preference and sex ratio in humans

A theory on the evolution of human primary sex ratio is proposed. Effects of parental preference for sons, reflected in birth control based on offspring sex ratio and female biased infanticide, on the evolution of primary sex ratio are analyzed. Both are shown to select for female bias in primary sex ratio. The gene-culture coevolution of female infanticide and primary sex ratio is also studied and it is shown that female infanticide develops more in societies in which the father plays a more important role in the transmission of culture than the mother does.     

2nd to 4th digit ratio and offspring sex ratio

There is evidence that the ratio of the length of the 2nd and 4th digit (2D:4D) is negatively related to prenatal and adult concentrations of testosterone. It has also been reported that high levels of testosterone at conception in both fathers and mothers are associated with an increased sex ratio (proportion of males at birth). It follows from these observations that low values of 2D:4D may be related to high sex ratio. We present evidence from three populations (English, Spanish and Jamaican) that 2D:4D is negatively related to sex ratio, independent of the sex and ethnicity of the parents.     

Seasonal sex ratio and unbalanced investment sex ratio in the Banksia bee Hylaeus alcyoneus

Abstract 1. Hylaeus alcyoneus is an endemic solitary bee common on coastal heaths of Western Australia. The bee is unusual in that males are larger than females. This size dimorphism presents an opportunity to test the theory of resource-dependent sex allocation, in which theory predicts that when resources are low the sex ratio should be biased towards the smaller sex. In most bees, females are larger than males and, in line with theoretical prediction, sex ratios are male biased when resources are scarce.
2. The emerging sex ratio and brood mass from a natural population of H. alcyoneus using trap nests was studied over two seasons (1999, 2000). A switch from a male- to a female-biased sex ratio through the season was found, which was related to a reduced floral resource.
3. Fisherian sex ratio theory predicts that total investment in each sex throughout a season should be equal and that the sex ratio should be biased towards the smaller sex. By measuring the mass of the emerging progeny, the total investment was found to favour males. Possible explanations for this bias in investment are discussed.     

Calving sex ratio as related to the predicted Y-chromosome-bearing spermatozoa ratio in bull ejaculates

The first objective was to correlate calving sex-ratio data from semen lots with the semen sex ratio obtained by two duplex polymerase chain reaction (PCR)/gel electrophoresis techniques. The two techniques involved different starting DNA amounts, PCR conditions, agarose gel concentrations, sample placement on the gels, lane size, number of lanes per gel, and duration of electrophoresis. The second objective was to sequence the duplex PCR products to verify their match to genes and chromosomes for which they were designed. Thirty-six ejaculates (lots) from eight Holstein sires were collected. Semen straws were distributed among dairies in three states. Ten straws per lot were used for the different PCR techniques. Sperm DNA was extracted and PCR analysis was done using one primer set to amplify a single copy section of the factor IX precursor (X-chromosome only) and another primer set to amplify a single copy section the sex determining region (Y-chromosome only). The glyceraldehyde phosphate dehydrogenase gene was amplified as an internal control. Standard curves were designed using PCR products in known ratios. Gel electrophoresis and image analysis were used to determine predicted %Y-chromosome-bearing spermatozoa (PredPtY). Sex (male=1, female=0) was reported on 526 calves and the ratio of the number of male to total calves (proportion of male calves (PMC)) was determined between sire and lot within sire. The PredPtY and PMC were significantly correlated (r=0.82, P<0.0002). No significant variance between sires was found in PredPtY or PMC, but lots within sires was a significant variance source for both. The two PCR technologies adequately determined semen sex ratio. The technology-by-lot-within-sire interaction was a significant variance source for PredPtY. Acrosomal integrity (after a 2-h) incubation, was correlated with both PMC and PredPtY; other semen quality characteristics had no significant correlations with PMC or PredPtY. Therefore, calf crop sex ratio skewness could be controlled by screening semen for PredPtY through the use of PCR.     

Do females adjust the sex of their offspring in relation to the breeding sex ratio?

When the adult sex ratio differs between years in local populations, but still is predictable between adjacent years, it has been proposed that the best strategy would be to bias the offspring sex ratio in favour of the rare sex. We tested this hypothesis using a data set of great reed warbler offspring, sexed by molecular techniques, that were collected over 11 breeding seasons at two adjacent reed marshes. Three important assumptions for this hypothesis are fulfilled in the studied great reed warbler population. First, a substantial proportion of great reed warblers are living in small local populations where sex ratio distortions would be sufficiently large and common. Second, breeding adults and their offspring return to breed in the local population to a high degree. Third, females have a possibility to assess the breeding sex ratio before laying their eggs. At our study site, the breeding sex ratio was positively correlated between successive years. However, contrary to our prediction, female great reed warblers seemed not to adjust their offspring sex ratio in relation to the local breeding sex ratio.     

Budding dispersal and the sex ratio

There is much interest in understanding how population demography impacts upon social evolution. Here, we consider the impact of rate and pattern of dispersal upon a classic social evolutionary trait--the sex ratio. We recover existing analytical results for individual dispersal, and we extend these to allow for budding dispersal. In particular, while a cancelling of relatedness and kin competition effects means that the sex ratio is unaffected by the rate of individual dispersal, we find that a decoupling of relatedness and kin competition means that budding dispersal favours increasingly female-biased sex ratios. More generally, our analysis illustrates the relative ease with which biological problems involving class structure can be solved using a kin selection approach to social evolution theory.     

Towards a genetic theory for the evolution of the sex ratio II. Haplodiploid and diploid models with sibling and parental control of the brood sex ratio and brood size

Population genetic models involving sister, brother, and father control of the brood sex ratio and brood size in both the haplodiploid and diploid cases are constructed and analyzed. The results are interpreted in light of the verbal theories which predict the evolution of the sex ratio to a value which is proportional to the ratio of relatedness of the controlling members of the family to males and to females produced in the brood. In our models, the sex ratio in a certain class of polymorphic equilibria evolves to equal investment in males and females in those cases where the controlling members of the family are symmetrically related to males and females as predicted by the verbal theory. However, the sex ratio in the case of sister control in haploidiploids does not evolve to 1:3, but rather to a value proportional to the ratio of the regression coefficients of additive genotypes. Even so, the predicted sex ratio, which is proportional to 1:3, is in fact an “ESS” in the sense that fixation of a genotype specifying that sex ratio is resistant to the initial increase of all other genotypes.