A spatially explicit model of sex ratio evolution in response to sex-biased dispersal

Sex-biased dispersal occurs in all seed plants and many animal species. Theoretical models have shown that sex-biased dispersal can lead to evolutionarily stable biased sex ratios. Here, we use a spatially explicit chessboard model to simulate the evolution of sex ratio in response to sex-biased dispersal range and sex-biased dispersal rate. Two life cycles are represented in the model: one in which both sexes disperse before mating (DDM), the other in which males disperse before mating and mated females or zygotes disperse after mating (DMD). Model parameters include factors like dispersal rate, dispersal range, number of individuals per patch, and habitat heterogeneity.When dispersal range is sex biased, we find that, in a homogeneous environment, the sex ratio is generally biased towards the sex that disperses more widely (sex ratio range: 0.47–0.52). In a heterogeneous environment, the sex ratio is generally biased towards the more dispersive sex in good habitats, and towards the less dispersive sex in poor habitats (sex ratio range: 0–1). This is opposite to the effect of sex-biased dispersal rate, which favours the production of the more dispersive sex in poor habitats and the less dispersive sex in good habitats (sex ratio range: 0–1). To allow for a comparison with theoretical predictions, data concerning sex-biased dispersal and habitat-dependent sex ratios should thus incorporate information about the spatial scale of both dispersal and environmental heterogeneity.     

Mating system and sex allocation in the gregarious parasitoid Cotesia glomerata

The gregarious parasitoid Cotesia glomerata (L.) is often presumed to possess the characteristic attributes of a species that manifests local mate competition (LMC), as it commonly produces female-biased broods. However, our field surveys of sex ratio and laboratory observations of adult behaviour showed that this species is subject to partial local mate competition caused by natal dispersal. On average, 30% of males left their natal patch before mating, with the proportion of dispersing males increasing with an increase in the patch's sex ratio (i.e. proportion of males). Over 50% of females left their natal patch before mating, and only 27.5% of females mated with males emerging from the same natal patch. Although females showed no preference between males that were and were not their siblings, broods from females that mated with siblings had a significantly higher mean brood sex ratio (0.56) than broods from females that mated with nonsiblings (0.39). Furthermore, brood sex ratios increased as inbreeding was intensified over four generations. A field population of this wasp had a mean brood sex ratio of 0.35 over 3 years, which conformed well to the evolutionarily stable strategy sex ratio (r=0.34) predicted by Taylor's partial sibmating model for haplodiploid species. These results suggest that the sex allocation strategy of C. glomerata is based on both partial local mate competition in males and inbreeding avoidance in females. In turn, this mating system plays a role in the evolution of natal dispersal behaviour in this species.Copyright 2003 Published by Elsevier Ltd on behalf of The Association for the Study of Animal Behaviour.      

Sex differences in dispersal and the evolution of helping and harming

In this article, we explore the impact of sex-biased dispersal on local relatedness and on selection for helping and harming behavior among males and females. We show that in a patch-structured population, when there is a marked sex bias in dispersal, selection will almost always favor harming behavior among individuals of the sex more prone to dispersal. This result holds regardless of the effects of mating skew or overlapping generations. Selection may well also favor helping behavior among individuals of the philopatric sex, particularly if there is generational overlap, but this is less likely to occur if individuals of the philopatric sex compete more intensely for fewer breeding opportunities. In this last case, if generational overlap is low and mating skew pronounced, the result may be selection for harming behavior among both males and females. In general, the rate of dispersal and the level of relatedness among individuals of one sex do not reliably predict their level of helping or harming behavior; selection on either males or females depends on the dispersal of both sexes.     

Sex ratios of Sitodiplosis mosellana (Diptera: Cecidomyiidae): implications for pest management in wheat (Poaceae)

Sex ratios of populations of the wheat midge Sitodiplosis mosellana Gehin, developing on wheat Triticum aestivum L., were determined at reproduction, adult emergence, and dispersal. The patterns of sex ratio through the life cycle of S. mosellana result from: (i) a genetic mechanism that causes all or nearly all of the progeny of individual females to be a single sex, with an overall sex ratio that is slightly biased at 54-57% females; (ii) a differential mortality during diapause that increases the sex ratio to 60-65% females; (iii) mating which occurs near the emergence site followed by female dispersal which causes the post-dispersal sex ratio to rise to nearly 100% females; and (iv) oviposition which spreads eggs among different plants and assures that the next generation has a local sex ratio close to the population average. These changes in sex ratio through the life cycle have implications for using crop resistance or pheromones to manage S. mosellana, because mating takes place quickly near emergence sites, and because mated females but not males disperse from emergence sites to oviposition sites. Crop refuges used to protect resistance genes against the evolution of virulence by S. mosellana must be interspersed to prevent assortative mating that would occur in separate blocks of resistant and susceptible plants. Monitoring or mating disruption using a pheromone would be ineffective when wheat is grown in rotation with a non-host crop.     

Factors influencing the optimum sex ratio in a structured population

W. D. Hamilton (1967, Science 156, 477-488) calculated the optimum sex-ratio strategy for a population subdivided into local mating groups. He made three important assumptions: that the females founding each group responded precisely to the number of them initiating the group; that ail broods within a group matured synchronously; and that males were incapable of dispersing between groups. We have examined the effects of relaxing each of these assumptions and obtained the following results: (1) When broods mature asynchronously the optimum sex ratio is considerably more female biased than the Hamiltonian prediction. (2) Increasing male dispersal always decreases the optimum female bias to the sex ratio, but it is of particular interest that when moderate levels of dispersal are coupled with asynchrony of brood maturation then the optimum strategy is relatively insensitive to changes in foundress number. (3) When females cannot precisely determine the number of other foundresses initiating the group then the optimum strategy is almost exactly the strategy appropriate to a group of average size. These effects can be most easily understood in terms of local parental control (LPC) of the sex ratio. Through LPC a founding female can alter the mating success of her sons by altering the sex ratio of her brood. Asynchrony in the maturation of broods within a group increases the control that a founding female has over the mating success of her sons, whereas male dispersal reduces it. We have shown that the role of LPC and the role of inbreeding, which favors a female-biased sex ratio in haploidiploid species, are independent and that their effects can be combined into a single general formula r = (1-(r2/z2) E(alpha z/alpha r]/(1 + I). The concept of LPC can also be used to interpret two factors which have been proposed to select for the Hamiltonian sex ratios: local mate competition is LPC acting through sons; and sib mating is LPC acting through daughters.     

Optimal sex ratios in structured populations

In this paper, we develop a general method to determine evolutionary equilibrium sex ratios and to check evolutionary stability, continuous stability and invadability in exact genetic models with or without dominance. This method is then applied to three kinds of models for structured populations: the first one concerns Hamilton's LMC model, except that only a fraction beta of female offspring mate with male offspring born in the same colonies, while a fraction 1-beta mate with male offspring chosen at random within the whole population; in the second model, it is assumed that partial dispersal of inseminated females occurs after mating; in the third model, partial dispersal of male and female offspring occurs before mating. In the first model, the effect of population regulation is studied while, in the other models, two kinds of dispersal are considered: proportional and uniform.     

Sex-biased dispersal and the speed of two-sex invasions

Population models that combine demography and dispersal are important tools for forecasting the spatial spread of biological invasions. Current models describe the dynamics of only one sex (typically females). Such models cannot account for the sex-related biases in dispersal and mating behavior that are typical of many animal species. In this article, we construct a two-sex integrodifference equation model that overcomes these limitations. We derive an explicit formula for the invasion speed from the model and use it to show that sex-biased dispersal may significantly increase or decrease the invasion speed by skewing the operational sex ratio at the invasion's low-density leading edge. Which of these possible outcomes occurs depends sensitively on complex interactions among the direction of dispersal bias, the magnitude of bias, and the relative contributions of females and males to local population growth.     

Local Mating,Dispersal and Sex Ratio in a Gregarious Parasitoid Wasp

Parasitoid sex ratios can be greatly influenced by mating and dispersal behaviour. Many sex ratio models assume that mating is strictly local (only mated females disperse from the natal patch) and that a single male is sufficient to inseminate all females in a brood. Bethylids (aculeate parasitoids) have been used to test predictions of these models, but less attention has been paid to testing their underlying assumptions. We investigated the timing of eclosion, mating and dispersal in mixed-sex and single-sex broods of the bethylid wasp Goniozus nephantidis. In mixed-sex broods, almost all females mate before dispersal and a single male is sufficient to inseminate virtually all females, even when brood sizes are large. Males disperse from both mixed-sex and all-male broods, but males in all-male broods disperse more slowly. Virgin females disperse from all-female broods, which are common. Virgin females can produce a brood, mate with their own sons and subsequently produce mixed-sex broods, but their success rate is very low. Virgin females could potentially circumvent sex allocation constraints by superparasitizing mixed-sex broods, but when presented with hosts bearing mixed-sex broods they destroy all members of the initial brood before ovipositing. Because of the high prevalence of single-sex broods and dispersal of both sexes, the mating structure of G. nephantidis is unlikely to conform to the assumption of strict local mating.     

Insemination Capacity and Dispersal in Relation to Sex Allocation Decisions in Goniozus legneri (Hymenoptera: Bethylidae): Why Are There More Males in Larger Broods?

Models considering sex ratio optima under single foundress strict local mate competition predict that female bias will be reduced by stochasticity in sex allocation, developmental mortality of males and limited insemination capacity of males. In all three cases the number of males per brood is expected to increase with brood size. Sex ratio optima may also be less female biased when several mothers contribute offspring to local mating groups or if non‐local mating occurs between members of different broods; again more males are expected in larger broods. In the parasitoid wasp Goniozus legneri (Hymenoptera: Bethylidae), sex allocation has only a small stochastic component, developmental mortality is low and non‐siblings are unlikely to develop in the same brood. However, the number of males per brood increases with the size of the brood (produced by a single mother). We investigated the further possibilities of limited insemination capacity and non‐local mating using a naturalistic experimental protocol. We found that limited insemination capacity is an unlikely general explanation for the increase in number of males with brood size. All males and females dispersed from both mixed and single sex broods. Although most females in mixed sex broods mated prior to dispersal, these data suggest that non‐local mating is possible, for instance via male immigration to broods containing virgin females. This may influence sex ratio optima and account for the trend in male number.     

Female-biased dispersal under conditions of low male mating competition in a polygynous mammal

Sex-biased dispersal is a common phenomenon in birds and mammals. Competition for mates has been argued to be an important selective pressure favouring dispersal. Sexual differences in the level of intrasexual competition may produce asymmetries in the costs-benefits balance of dispersal and philopatry for males and females, which may favour male-biased dispersal in polygynous species such as most mammals. This being the case, condition-dependent dispersal predicts that male-bias should decrease if mating competition relaxes. We test this expectation for red deer, where male-biased dispersal is the norm. In southwestern Spain, red deer populations located in nonfenced hunting estates presented altered structures with sex ratio strongly biased to females and high proportion of young males. As a consequence, mate competition in these populations was lower than in other, most typical red deer populations. We found that, under such conditions of altered population structure, dispersal was female-biased rather than male-biased. Additionally, mate competition positively related to male dispersal but negatively to female dispersal. Other factors such as resource competition, age of individuals and sex ratio were not related to male or female dispersal. Males may not disperse if intrasexual competition is low and then females may disperse as a response to male philopatry. We propose hypotheses related to female mate choice to explain female dispersal under male philopatry. The shift of the sex-biased dispersal pattern along the gradient of mate competition highlights its condition-dependence as well as the interaction between male and female dispersal in the evolution of sex-biased dispersal.     

A genetic perspective on mating systems and sex ratios of parasitoid wasps

Parasitoid sex ratios are influenced by mating systems, whether complete inbreeding, partial inbreeding, complete inbreeding avoidance, or production of all-male broods by unmated females. Population genetic theory demonstrates that inbreeding is possible in haplodiploids because the purging of deleterious and lethal mutations through haploid males reduces inbreeding depression. However, this purging does not act quickly for deleterious mutations or female-limited traits (e.g., fecundity, host searching, sex ratio). The relationship between sex ratio, inbreeding, and inbreeding depression has not been explored in depth in parasitoids. The gregarious egg parasitoid, Trichogramma pretiosum Riley, collected from Riverside, CA (USA) produced a female-biased sex ratio of 0.24 (proportion of males). Six generations of sibling mating in the laboratory uncovered considerable inbreeding depression (∼ 20%) in fecundity and sex ratio. A population genetic study (based upon allozymes) showed the population was inbred (F _it = 0.246), which corresponds to 56.6% sib-mating. However, average relatedness among females emerging from the same host egg was only 0.646, which is less than expected (0.75) if ovipositing females mate randomly. This lower relatedness could arise from inbreeding avoidance, multiple mating by females, or superparasitism. A review of the literature in general shows relatively low inbreeding depression in haplodiploid species, but indicates that inbreeding depression can be as high as that found in Drosophila. Finally, mating systems and inbreeding depression are thought to evolve in concert (in plants), but similar dynamic models of the joint evolution of sex ratio, mating systems, and inbreeding depression have not been developed for parasitoid wasps. Received: November 13, 1998 /Accepted: January 8, 1999     

Limited male dispersal in a social spider with extreme inbreeding

Cooperatively breeding animals commonly avoid incestuous mating through pre-mating dispersal. However, a few group-living organisms, including the social spiders, have low pre-mating dispersal, intra-colony mating, and inbreeding. This results in limited gene flow among colonies and sub-structured populations. The social spiders also exhibit female-biased sex ratios because survival benefits to large colonies favour high group productivity, which selects against 1 : 1 sex ratios. Although propagule dispersal of mated females may occasionally bring about limited gene flow, little is known about the role of male dispersal. We assessed the extent of male movement between colonies in natural populations both experimentally and by studying colony sex ratios over the mating season. We show that males frequently move to neighbouring colonies, whereas only 4% of incipient nests were visited by dispersing males. Neighbouring colonies are genetically similar and movement within colony clusters does not contribute to gene flow. Post-mating sex ratio bias was high early in the mating season due to protandry, and also in colonies at the end of the season, suggesting that males remain in the colony when mated females have dispersed. Thus, male dispersal is unlikely to facilitate gene flow between different matrilineages. This is consistent with models of non-Fisherian group-level selection for the maintenance of female biased sex ratios, which predict the elimination of male dispersal.  © 2009 The Linnean Society of London, Biological Journal of the Linnean Society 2009, 97 , 227–234.     

Mating ecology of the nonpollinating fig wasps of Ficus ingens

The males of many fig wasps fight fatally for mating opportunities. The concentration of females in space has been proposed as one factor selecting for their aggressive behaviour. We studied the temporal distribution of receptive females to obtain a clearer impression of the operational sex ratio in figs. Females of nonpollinating species emerged from figs over a protracted period of time and this resulted in an extremely male-biased operational sex ratio, conducive to extreme fighting. Since there were so few receptive females at any one time, a male could defend an eclosing female. Consequently, the largest, Otitesella longicauda male in a fig had a much higher mating success than smaller males. This suggests that larger males have a larger fitness advantage than larger females and a Trivers-Willard effect could have important implications for sex allocation. Apterous and seemingly nondispersing males routinely left their figs. Such dispersal can affect both (1) sex allocation by reducing the degree of local mate competition between brothers and (2) male dimorphism by reducing the mating opportunities of males with a dispersing morphology. We show that the wingless digitata males of the Otitesella digitata species group disperse on to leaves close to their natal fig. An extremely male-biased sex ratio resulted in almost all O. longicauda females being mated. These findings suggest that the classical concept of the fig wasp mating system is too simplistic and that important assumptions of sex allocation models are violated. Copyright 1999 The Association for the Study of Animal Behaviour.     

Conflict over multiple-partner mating between males and females of the polygynandrous common lizards

The optimal number of mate partners for females rarely coincides with that for males, leading to a potential sexual conflict over multiple-partner mating. This suggests that the population sex ratio may affect multiple-partner mating and thus multiple paternity. We investigate the relationship between multiple paternity and the population sex ratio in the polygynandrous common lizard (Lacerta vivipara). In six populations the adult sex ratio was biased toward males, and in another six populations the adult sex ratio was biased toward females, the latter corresponding to the average adult sex ratio encountered in natural populations. In males the frequency and the degree of polygyny were lower in male-biased populations, as expected if competition among males determines polygyny. In females the frequency of polyandry was not different between treatments, and polyandrous females produced larger clutches, suggesting that polyandry might be adaptive. However, in male-biased populations females suffered from reduced reproductive success compared to female-biased populations, and the number of mate partners increased with female body size in polyandrous females. Polyandrous females of male-biased populations showed disproportionately more mating scars, indicating that polyandrous females of male-biased populations had more interactions with males and suggesting that the degree of multiple paternity is controlled by male sexual harassment. Our results thus imply that polyandry may be hierarchically controlled, with females controlling when to mate with multiple partners and male sexual harassment being a proximate determinant of the degree of multiple paternity. The results are also consistent with a sexual conflict in which male behaviors are harmful to females.     

Constrained sex allocation in a parasitoid due to variation in male quality

The theory of constrained sex allocation posits that when a fraction of females in a haplodiploid population go unmated and thus produce only male offspring, mated females will evolve to lay a female-biased sex ratio. I examined evidence for constrained sex ratio evolution in the parasitic hymenopteran Uscana semifumipennis. Mated females in the laboratory produced more female-biased sex ratios than the sex ratio of adults hatching from field-collected eggs, consistent with constrained sex allocation theory. However, the male with whom a female mated affected her offspring sex ratio, even when sperm was successfully transferred, suggesting that constrained sex ratios can occur even in populations where all females succeed in mating. A positive relationship between sex ratio and fecundity indicates that females may become sperm-limited. Variation among males occurred even at low fecundity, however, suggesting that other factors may also be involved. Further, a quantitative genetic experiment found significant additive genetic variance in the population for the sex ratio of offspring produced by females. This has only rarely been demonstrated in a natural population of parasitoids, but is a necessary condition for sex ratio evolution. Finally, matings with larger males produced more female-biased offspring sex-ratios, suggesting positive selection on male size. Because the great majority of parasitic hymenoptera are monandrous, the finding of natural variation among males in their capacity to fertilize offspring, even after mating successfully, suggests that females may often be constrained in the sex allocation by inadequate number or quality of sperm transferred.     

Simultaneous failure of two sex-allocation invariants: implications for sex-ratio variation within and between populations

Local mate competition (LMC) occurs when male relatives compete for mating opportunities, and this may favour the evolution of female-biased sex allocation. LMC theory is among the most well developed and empirically supported topics in behavioural ecology, clarifies links between kin selection, group selection and game theory, and provides among the best quantitative evidence for Darwinian adaptation in the natural world. Two striking invariants arise from this body of work: the number of sons produced by each female is independent of both female fecundity and also the rate of female dispersal. Both of these invariants have stimulated a great deal of theoretical and empirical research. Here, we show that both of these invariants break down when variation in female fecundity and limited female dispersal are considered in conjunction. Specifically, limited dispersal of females following mating leads to local resource competition (LRC) between female relatives for breeding opportunities, and the daughters of high-fecundity mothers experience such LRC more strongly than do those of low-fecundity mothers. Accordingly, high-fecundity mothers are favoured to invest relatively more in sons, while low-fecundity mothers are favoured to invest relatively more in daughters, and the overall sex ratio of the population sex ratio becomes more female biased as a result.     

Contest versus scramble competition for mates: The composition and spatial structure of a population of gray mouse lemurs (Microcebus murinus) in North-west Madagascar

The modes of intrasexual competition interacting in many dispersed societies of nocturnal solitary foragers are still poorly understood. In this study we investigate the spatial structure within a free-living population of gray mouse lemurs (Microcebus murinus) in order to test for the first time the predictions from two contrasting models of male intrasexual competition on the population level. The contest competition model predicts an uneven distribution of the sexes in a population nucleus with a female biased sex ratio in the center and a male biased sex ratio in the periphery. In contrast the scramble competition model predicts males and females being distributed evenly throughout their habitat with a constant sex ratio. Nine capture/recapture periods within three consecutive mating seasons revealed a continuous male biased sex ratio in the adult population with even trapping rates for the sexes. The male biased sex ratio could either be explained with postnatal female biased mortality or with a male biased natal sex ratio. This male biased sex ratio was apparent in all parts of the study site, indicating that the population was not subdivided into a female biased core and a male biased periphery. Furthermore, the majority of adult males have been captured at the same site as or in vicinity to females. Consequently, a large proportion of males had spatial access to females during the mating season. No signs of monopolization of females by certain dominant males could be detected. These data support the predictions from the scramble competition model and the concept of a promiscuous mating system for this species.     

Modelling the mating system of polar bears: a mechanistic approach to the Allee effect

Allee effects may render exploited animal populations extinction prone, but empirical data are often lacking to describe the circumstances leading to an Allee effect. Arbitrary assumptions regarding Allee effects could lead to erroneous management decisions so that predictive modelling approaches are needed that identify the circumstances leading to an Allee effect before such a scenario occurs. We present a predictive approach of Allee effects for polar bears where low population densities, an unpredictable habitat and harvest-depleted male populations result in infrequent mating encounters. We develop a mechanistic model for the polar bear mating system that predicts the proportion of fertilized females at the end of the mating season given population density and operational sex ratio. The model is parametrized using pairing data from Lancaster Sound, Canada, and describes the observed pairing dynamics well. Female mating success is shown to be a nonlinear function of the operational sex ratio, so that a sudden and rapid reproductive collapse could occur if males are severely depleted. The operational sex ratio where an Allee effect is expected is dependent on population density. We focus on the prediction of Allee effects in polar bears but our approach is also applicable to other species.     

Persistence of females that produce only female progeny in lepidoptera

In Lepidoptera females that produce only female progeny, can be found in wild populations of at least 11 species. The genetic variation is passed on to each generation of female offspring. If genetically abnormal females produce more female offspring than normal females do and mating is random, then populations containing these abnormal females will have a biased population sex ratio. Unmated females will increase due to the scarcity of males and so the population as a unit will die out. Several possible biological explanations for the persistence of the genetic variation have been proposed. But experiments and observations have not verified those hypotheses. Simulations of Heuch's model (1978), however, have shown that the variation persists if the population is distributed, in patches and there is dispersal among patches, even when insects disperse at random. Abnormal females tend to persist at both low and high migration rates, but the probability of persistence is higher at high migration rates. It has been suggested that abnormal females in a population are an adaptation, but the results of this investigation show that this explanation, may not be plausible.     

Partial local mate competition and the sex ratio: A study on non-pollinating fig wasps

In many species, mating takes place in temporary patches where only a small number of females produce offspring. In this situation Local Mate Competition (LMC) theory predicts that the optimal sex ratio (defined as proportion males) should become increasingly female biased as the number of females contributing offspring to a patch decreases. However, in a large number of these species, some mating is also likely to occur away from the natal patch (termed partial LMC). In this case the degree of LMC is reduced, and theory predicts a relatively less female biased sex ratio. We tested these two predictions with field data from 17 species of New World non-pollinating fig wasps representing three genera. We present a model which suggests that the average number of females ovipositing in a fruit (i.e. patch) is positively correlated with the proportion of fruit of a given tree species in which that species of wasp occurs. Across species, the overall sex ratio was positively correlated with the proportion of fruit in which that species occurs. Furthermore, the males of some species are wingless, and in these species all mating must take place before females disperse from their natal fruit. In contrast, the males of other species are winged, and in these species mating may also take place away from the natal fruit. Species with winged males had less female biased sex ratios than species with wingless males that occurred in a similar proportion of fruit. Finally, the correlation between sex ratio and the proportion of fruit in which a species occurs was also observed within species when comparing between the fruit crops of different trees. This suggests that individual females facultatively adjust the sex ratio of their offspring in response to variable LMC.