Evolutionary dynamics of the Trivers–Willard effect: A nonparametric approach

The Trivers–Willard hypothesis (TWH) states that parents in good condition tend to bias their offspring sex ratio toward the sex with a higher variation in reproductive value, whereas parents in bad condition favor the opposite sex. Although the TWH has been generalized to predict various Trivers–Willard effects (TWE) depending on the life cycle of a species, existing work does not sufficiently acknowledge that sex‐specific reproductive values depend on the relative abundances of males and females in the population. If parents adjust their offspring sex ratio according to the TWE, offspring reproductive values will also change. This should affect the long‐term evolutionary dynamics and might lead to considerable deviations from the original predictions.In this paper, I model the full evolutionary dynamics of the TWE, using a published two‐sex integral projection model for the Columbian ground squirrel (Urocitellus columbianus). Offspring sex ratio is treated as a nonparametric continuous function of maternal condition. Evolutionary change is treated as the successive invasion of mutant strategies. The simulation is performed with varying starting conditions until an evolutionarily stable strategy (ESS) is reached.The results show that the magnitude of the evolving TWE can be far greater than previously predicted. Furthermore, evolutionary dynamics show considerable nonlinearities before settling at an ESS. The nonlinear effects depend on the starting conditions and indicate that evolutionary change is fastest when starting at an extremely biased sex ratio and that evolutionary change is weaker for parents of high condition. The results show neither a tendency to maximize average population fitness nor to minimize the deviation between offspring sex ratio and offspring reproductive value ratio.The study highlights the importance of dynamic feedback in models of natural selection and provides a new methodological framework for analyzing the evolution of continuous strategies in structured populations.     

Frequency‐dependent two‐sex models: a new approach to sex ratio evolution with multiple maternal conditions

Mothers that experience different individual or environmental conditions may produce different proportions of male to female offspring. The Trivers‐Willard hypothesis, for instance, suggests that mothers with different qualities (size, health, etc.) will use different sex ratios if maternal quality differentially affects sex‐specific reproductive success. Condition‐dependent, or facultative, sex ratio strategies like these allow multiple sex ratios to coexist within a population. They also create complex population structure due to the presence of multiple maternal conditions. As a result, modeling facultative sex ratio evolution requires not only sex ratio strategies with multiple components, but also two‐sex population models with explicit stage structure. To this end, we combine nonlinear, frequency‐dependent matrix models and multidimensional adaptive dynamics to create a new framework for studying sex ratio evolution. We illustrate the applications of this framework with two case studies where the sex ratios depend one of two possible maternal conditions (age or quality). In these cases, we identify evolutionarily singular sex ratio strategies, find instances where one maternal condition produces exclusively male or female offspring, and show that sex ratio biases depend on the relative reproductive value ratios for each sex.     

Sex and stochasticity affect range expansion of experimental invasions

Understanding and predicting range expansion are key objectives in many basic and applied contexts. Among dioecious organisms, there is strong evidence for sex differences in dispersal, which could alter the sex ratio at the expansion's leading edge. However, demographic stochasticity could also affect leading‐edge sex ratios, perhaps overwhelming sex‐biased dispersal. We used insects in laboratory mesocosms to test the effects of sex‐biased dispersal on range expansion, and a simulation model to explore interactive effects of sex‐biased dispersal and demographic stochasticity. Sex‐biased dispersal created spatial clines in the sex ratio, which influenced offspring production at the front and altered invasion velocity. Increasing female dispersal relative to males accelerated spread, despite the prediction that demographic stochasticity would weaken a signal of sex‐biased dispersal. Our results provide the first experimental evidence for an influence of sex‐biased dispersal on invasion velocity, highlighting the value of accounting for sex structure in studies of range expansion.     

Sexual dimorphism,survival, and parental investment in relation to offspring sex in a precocial bird

Differential growth rate between males and females, owing to a sexual size dimorphism, has been proposed as a mechanism driving sex‐biased survival. How parents respond to this selection pressure through sex ratio manipulation and sex‐biased parental investment can have a dramatic influence on fitness. We determined how differential growth rates during early life resulting from sexual size dimorphism affected survival of young and how parents may respond in a precocial bird, the black brant Branta bernicla nigricans. We hypothesized that more rapidly growing male goslings would suffer greater mortality than females during brood rearing and that parents would respond to this by manipulating their primary sex ratio and parental investment. Male brant goslings suffered a 19.5% reduction in survival relative to female goslings and, based on simulation, we determined that a female biased population sex ratio at fledging was never overcome even though previous work demonstrated a slight male‐biased post‐fledging survival rate. Contrary to the Fisherian sex ratio adjustment hypothesis we found that individual adult female brant did not manipulate their primary sex ratio (50.39% male, n = 645), in response to the sex‐biased population level sex ratio. However, female condition at the start of the parental care period was a good predictor of their primary sex ratio. Finally, we examined how females changed their behavior in response to primary sex ratio of their broods. We hypothesized that parents would take male biased broods to areas with increased growth rates. Parents with male biased primary sex ratios took broods to areas with higher growth rates. These factors together suggest that sex‐biased growth rates during early life can dramatically affect population dynamics through sex‐biased survival and recruitment which in turn affects decisions parents make about sex allocation and sex‐biased parental investment in offspring to maximize fitness.     

REPLICATED ORIGIN OF FEMALE‐BIASED ADULT SEX RATIO IN INTRODUCED POPULATIONS OF THE TRINIDADIAN GUPPY (POECILIA RETICULATA)

There are many theoretical and empirical studies explaining variation in offspring sex ratio but relatively few that explain variation in adult sex ratio. Adult sex ratios are important because biased sex ratios can be a driver of sexual selection and will reduce effective population size, affecting population persistence and shapes how populations respond to natural selection. Previous work on guppies (Poecilia reticulata) gives mixed results, usually showing a female‐biased adult sex ratio. However, a detailed analysis showed that this bias varied dramatically throughout a year and with no consistent sex bias. We used a mark‐recapture approach to examine the origin and consistency of female‐biased sex ratio in four replicated introductions. We show that female‐biased sex ratio arises predictably and is a consequence of higher male mortality and longer female life spans with little effect of offspring sex ratio. Inconsistencies with previous studies are likely due to sampling methods and sampling design, which should be less of an issue with mark‐recapture techniques. Together with other long‐term mark‐recapture studies, our study suggests that bias in offspring sex ratio rarely contributes to adult sex ratio in vertebrates. Rather, sex differences in adult survival rates and longevity determine vertebrate adult sex ratio.     

The evolution of sex roles in mate searching

Searching for mates is a critical stage in the life cycle of most internally, and many externally, fertilizing species. Males usually invest more in this costly activity than females, but the reasons for this are poorly understood. Previous models have shown that female‐biased parental investment, including anisogamy, does not by itself select for male‐biased mate searching, so it requires additional explanations. Here, we correct and expand upon earlier models, and present two novel hypotheses that might explain the evolution of male‐biased mate searching. The “carry‐over hypothesis” states that females benefit less from searching if the associated costs affect other stages of the life cycle, rather than arising only while searching. It is relevant to the evolution of morphological traits that improve searching efficiency but are also expressed in other contexts. The “mating window hypothesis” states that females benefit less from searching if their life cycle includes intervals during which the exact timing of mating does not matter for the appropriate timing of reproduction (e.g., due to sperm storage or delayed embryo implantation). Such intervals are more likely to exist for females given the general pattern of greater female parental investment. Our models shed new light on classic arguments about sex role evolution.     

Effect of paternal age on the birth sex ratio in captive populations of aye‐aye (Daubentonia madagascariensis (Gmelin))

For the management of captive populations of zoo animals, it is important to elucidate factors that affect the offspring birth sex ratio. On the basis of the sex allocation theory, the Trivers–Willard and mate attractive/quality hypotheses predict that maternal and paternal conditions affect offspring birth sex ratios. We examined these predictions for the birth sex ratio of aye‐aye Daubentonia madagascariensis (Gmelin) by analyzing the pedigree information in the International Studbook. We found that the birth sex ratio of the aye‐aye was affected by the paternal age, but not maternal age and other environmental factors (birth year, season, and institution). The younger the sire, the more the offspring sex ratio was biased toward males. These results are useful for the effective population management of captive aye‐aye and illustrated the usefulness of the sex allocation theory in the sex ratio management of zoo animals.     

The influence of demography and local mating environment on sex ratios in a wind‐pollinated dioecious plant

Negative frequency‐dependent selection should result in equal sex ratios in large populations of dioecious flowering plants, but deviations from equality are commonly reported. A variety of ecological and genetic factors can explain biased sex ratios, although the mechanisms involved are not well understood. Most dioecious species are long‐lived and/or clonal complicating efforts to identify stages during the life cycle when biases develop. We investigated the demographic correlates of sex‐ratio variation in two chromosome races of Rumex hastatulus, an annual, wind‐pollinated colonizer of open habitats from the southern USA. We examined sex ratios in 46 populations and evaluated the hypothesis that the proximity of males in the local mating environment, through its influence on gametophytic selection, is the primary cause of female‐biased sex ratios. Female‐biased sex ratios characterized most populations of R.  hastatulus (mean sex ratio = 0.62), with significant female bias in 89% of populations. Large, high‐density populations had the highest proportion of females, whereas smaller, low‐density populations had sex ratios closer to equality. Progeny sex ratios were more female biased when males were in closer proximity to females, a result consistent with the gametophytic selection hypothesis. Our results suggest that interactions between demographic and genetic factors are probably the main cause of female‐biased sex ratios in R. hastatulus. The annual life cycle of this species may limit the scope for selection against males and may account for the weaker degree of bias in comparison with perennial Rumex species.     

Sex ratio evolution under probabilistic sex determination

Sex allocation theory has been remarkably successful at explaining the prevalence of even sex ratios in natural populations and at identifying specific conditions that can result in biased sex ratios. Much of this theory focuses on parental sex determination (SD) strategies. Here, we consider instead the evolutionary causes and consequences of mixed offspring SD strategies, in which the genotype of an individual determines not its sex, but the probability of developing one of multiple sexes. We find that alleles specifying mixed offspring SD strategies can generally outcompete alleles that specify pure strategies, but generate constraints that may prevent a population from reaching an even sex ratio. We use our model to analyze sex ratios in natural populations of Tetrahymena thermophila, a ciliate with seven sexes determined by mixed SD alleles. We show that probabilistic SD is sufficient to account for the occurrence of skewed sex ratios in natural populations of T. thermophila, provided that their effective population sizes are small. Our results highlight the importance of genetic drift in sex ratio evolution and suggest that mixed offspring SD strategies should be more common than currently thought.     

Cross‐fostering eggs reveals that female collared flycatchers adjust clutch sex ratios according to parental ability to invest in offspring

Across animal taxa, reproductive success is generally more variable and more strongly dependent upon body condition for males than for females; in such cases, parents able to produce offspring in above‐average condition are predicted to produce sons, whereas parents unable to produce offspring in good condition should produce daughters. We tested this hypothesis in the collared flycatcher (Ficedula albicollis) by cross‐fostering eggs among nests and using the condition of foster young that parents raised to fledging as a functional measure of their ability to produce fit offspring. As predicted, females raising heavier‐than‐average foster fledglings with their social mate initially produced male‐biased primary sex ratios, whereas those raising lighter‐than‐average foster fledglings produced female‐biased primary sex ratios. Females also produced male‐biased clutches when mated to males with large secondary sexual characters (wing patches), and tended to produce male‐biased clutches earlier within breeding seasons relative to females breeding later. However, females did not adjust the sex of individuals within their clutches; sex was distributed randomly with respect to egg size, laying order and paternity. Future research investigating the proximate mechanisms linking ecological contexts and the quality of offspring parents are able to produce with primary sex‐ratio variation could provide fundamental insight into the evolution of context‐dependent sex‐ratio adjustment.     

Sexual conflict in action: An antagonistic relationship between maternal and paternal sex allocation in the tammar wallaby,Notamacropus eugenii

Sex ratio biases are often inconsistent, both among and within species and populations. While some of these inconsistencies may be due to experimental design, much of the variation remains inexplicable. Recent research suggests that an exclusive focus on mothers may account for some of the inconsistency, with an increasing number of studies showing variation in sperm sex ratios and seminal fluids. Using fluorescent in‐situ hybridization, we show a significant population‐level Y‐chromosome bias in the spermatozoa of wild tammar wallabies, but with significant intraindividual variation between males. We also show a population‐level birth sex ratio trend in the same direction toward male offspring, but a weaning sex ratio that is significantly female‐biased, indicating that males are disproportionately lost during lactation. We hypothesize that sexual conflict between parents may cause mothers to adjust offspring sex ratios after birth, through abandonment of male pouch young and reactivation of diapaused embryos. Further research is required in a captive, controlled setting to understand what is driving and mechanistically controlling sperm sex ratio and offspring sex ratio biases and to understand the sexually antagonistic relationship between mothers and fathers over offspring sex. These results extend beyond sex allocation, as they question studies of population processes that assume equal input of sex chromosomes from fathers, and will also assist with future reproduction studies for management and conservation of marsupials.     

Male‐specific mortality biases secondary sex ratio in Eurasian tree sparrows Passer montanus

Sex allocation theory predicts that parents bias the offspring sex ratio strategically. In avian species, the offspring sex ratio can be biased at multiple growth stages, although the mechanisms are not well known. It is crucial to reveal a cause and timing of biased offspring sex ratio. We investigated (i) offspring sex ratio at multiple growth stages, from laying to fledging; and (ii) the stage at which offspring sex ratio became biased; and (iii) the cause of biased offspring sex ratio in Eurasian tree sparrows Passer montanus. Sex determination of 218 offspring, including hatchlings and unhatched eggs from 41 clutches, suggested that the offspring sex ratio was not biased at the egg‐laying stage but was significantly female‐biased after the laying stage due to higher mortality of male embryos. Half of the unhatched eggs showed no sign of embryo development (37/74, 50.00%), and most undeveloped eggs were male (36/37, 97.30%). Additional experiments using an incubator suggested that the cause of embryo developmental failure was a lack of developmental ability within the egg, rather than a failure of incubation. This study highlights the importance of clarifying offspring sex ratio at multiple stages and suggests that offspring sex ratio is adjusted after fertilization.     

Flexible mate choice when mates are rare and time is short

Female mate choice is much more dynamic than we once thought. Mating decisions depend on both intrinsic and extrinsic factors, and these two may interact with one another. In this study, we investigate how responses to the social mating environment (extrinsic) change as individuals age (intrinsic). We first conducted a field survey to examine the extent of natural variation in mate availability in a population of threespine sticklebacks. We then manipulated the sex ratio in the laboratory to determine the impact of variation in mate availability on sexual signaling, competition, and mating decisions that are made throughout life. Field surveys revealed within season heterogeneity in mate availability across breeding sites, providing evidence for the variation necessary for the evolution of plastic preferences. In our laboratory study, males from both female‐biased and male‐biased treatments invested most in sexual signaling late in life, although they competed most early in life. Females became more responsive to courtship over time, and those experiencing female‐biased, but not male‐biased sex ratios, relaxed their mating decisions late in life. Our results suggest that social experience and age interact to affect sexual signaling and female mating decisions. Flexible behavior could mediate the potentially negative effects of environmental change on population viability, allowing reproductive success even when preferred mates are rare.     

Factors influencing brood sex ratios in polyembryonic Hymenoptera

Copidosoma sp. is a polyembryonic encyrtid wasp which parasitizes isolated hosts. Most broods of this wasp are unisexual, but some contain both sexes and the secondary sex ratio of these is usually highly female biased. The overall population secondary sex ratio is female biased. Walter and Clarke (1992) argue that because the majority of individuals must mate outside the natal patch, the bias in the population secondary sex ratio contradicts predictions made by Hamilton's (1967) theory of local mate competition (LMC). We suggest that the primary sex ratio is unbiased and that Walter and Clarke's results do not cast doubt on LMC. Instead these results imply that ovipositing females make a combined clutch size and sex ratio decision influencing whether individuals developing from a particular brood will outbreed or largely inbreed; for each case the predictions of LMC theory are not violated. If this interpretation is correct, what is of interest is the basis on which this decision is made rather than the population secondary sex ratio. We show that host encounter rate influences the proportions of mixed and single sex broods laid by Copidosoma floridanum, a related polyembryonic parasitoid. Among single-sex broods the primary sex ratio is female biased, but our results are in agreement with LMC theory since offspring developing from these broods will probably mate with siblings from adjacent hosts. We consider the egg load of females to be of major influence on oviposition behaviour, and that the mating structure of parasitoid offspring, potentially differential costs of male and female broods and the natural distributions of hosts both at oviposition and eclosion, require further study.     

Daphnia females adjust sex allocation in response to current sex ratio and density

Cyclical parthenogenesis presents an interesting challenge for the study of sex allocation, as individuals’ allocation decisions involve both the choice between sexual and asexual reproduction, and the choice between sons and daughters. Male production is therefore expected to depend on ecological and evolutionary drivers of overall investment in sex, and those influencing male reproductive value during sexual periods. We manipulated experimental populations, and made repeated observations of natural populations over their growing season, to disentangle effects of population density and the timing of sex from effects of adult sex ratio on sex allocation in cyclically parthenogenetic Daphnia magna. Male production increased with population density, the major ecological driver of sexual reproduction; however, this response was dampened when the population sex ratio was more male‐biased. Thus, in line with sex ratio theory, we show that D. magna adjust offspring sex allocation in response to the current population sex ratio.     

Assessment of costs of reproduction in a pelagic seabird using multistate mark-recapture models

We used a long‐term population band‐resight survey database, a parallel reproduction database, and multistate mark–recapture analysis to assess the costs of reproduction, a keystone concept of life‐history evolution, in Nazca boobies (Sula granti) from Punta Cevallos, Isla Española, Galápagos, Ecuador. We used eight years of resight and breeding data to compare models that included sex‐ and state‐specific survival probabilities and probabilities of transition between reproductive states using multistate mark–recapture models. Models that included state‐specific effects were compared with models lacking such effects to evaluate costs of reproduction. The top model, optimizing the trade‐off of model simplicity and fit to the data using the Akaike Information Criterion (AIC), showed evidence of a temporally varying survival cost of reproduction: nonbreeders showed higher annual survival than breeders did in some years. Because increasing investment among breeders showed no negative association with survival and subsequent breeding success, this evidence indicates a cost to both males and females of initiating, but not of continuing, a reproductive attempt. In some cases, breeders reaching the highest reproductive state (fledging an offspring) showed higher survival or subsequent breeding success than did failed breeders, consistent with differences in overall quality that promote both survival and reproduction. Although a male‐biased adult sex ratio was observed in this population of Nazca boobies, models of state‐ and sex‐specific survival and transition probabilities were not supported, indicating that males and females do not incur different costs of reproduction, and that the observed sex ratio bias is not due to sex‐specific adult mortality.     

EVOLUTIONARILY STABLE SEX RATIOS AND MUTATION LOAD

Frequency‐dependent selection should drive dioecious populations toward a 1:1 sex ratio, but biased sex ratios are widespread, especially among plants with sex chromosomes. Here, we develop population genetic models to investigate the relationships between evolutionarily stable sex ratios, haploid selection, and deleterious mutation load. We confirm that when haploid selection acts only on the relative fitness of X‐ and Y‐bearing pollen and the sex ratio is controlled by the maternal genotype, seed sex ratios evolve toward 1:1. When we also consider haploid selection acting on deleterious mutations, however, we find that biased sex ratios can be stably maintained, reflecting a balance between the advantages of purging deleterious mutations via haploid selection, and the disadvantages of haploid selection on the sex ratio. Our results provide a plausible evolutionary explanation for biased sex ratios in dioecious plants, given the extensive gene expression that occurs across plant genomes at the haploid stage.     

Haldane rules: costs of outbreeding at production of daughters in sand lizards

Haldane's rule is one of the most widely applicable paradigms in evolutionary biology, stating that in species crossings, the heterogametic sex will suffer more severely in terms of sterility and inviability. We address this in a within‐species outbreeding situation by assessing the risk of producing inviable offspring depending on the sex ratio of the clutch produced in between‐population crossings in the laboratory. In crossings between male and female sand lizards (Lacerta agilis) from two different sampling regions, one in Sweden, one in central Europe, risk of gametic incompatibility is unaffected by outbreeding, but offspring from between‐population crossings show 300% higher malformation frequency and 10% lower hatching success. The risk of having inviable offspring increases with the production of daughters, i.e. the hemizygous sex in this species (ZW). Such sex‐specific genetic costs of offspring production need to be incorporated into life history ecology, e.g. sex allocation theory.     

Sex reversal and primary sex ratios in the common frog (Rana temporaria)

Sex reversal has been suggested to have profound implications for the evolution of sex chromosomes and population dynamics in ectotherms. Occasional sex reversal of genetic males has been hypothesized to prevent the evolutionary decay of nonrecombining Y chromosomes caused by the accumulation of deleterious mutations. At the same time, sex reversals can have a negative effect on population growth rate. Here, we studied phenotypic and genotypic sex in the common frog (Rana temporaria) in a subarctic environment, where strongly female‐biased sex ratios have raised the possibility of frequent sex reversals. We developed two novel sex‐linked microsatellite markers for the species and used them with a third, existing marker and a Bayesian modelling approach to study the occurrence of sex reversal and to determine primary sex ratios in egg clutches. Our results show that a significant proportion (0.09, 95% credible interval: 0.04–0.18) of adults that were genetically female expressed the male phenotype, but there was no evidence of sex reversal of genetic males that is required for counteracting the degeneration of Y chromosome. The primary sex ratios were mostly equal, but three clutches consisted only of genetic females and three others had a significant female bias. Reproduction of the sex‐reversed genetic females appears to create all‐female clutches potentially skewing the population level adult sex‐ratio consistent with field observations. However, based on a simulation model, such a bias is expected to be small and transient and thus does not fully explain the observed female‐bias in the field.     

The paradox of obligate sex: The roles of sexual conflict and mate scarcity in transitions to facultative and obligate asexuality

The maintenance of obligate sex in animals is a long‐standing evolutionary paradox. To solve this puzzle, evolutionary models need to explain why obligately sexual populations consistently resist invasion by facultative strategies that combine the benefits of both sexual and asexual reproduction. Sexual antagonism and mate availability are thought to shape the occurrence of reproductive modes in facultative systems. But it is unclear how such factors interact with each other to influence facultative invasions and transitions to obligate asexuality. Using individual‐based models, we clarify how sexually antagonistic coevolution and mate availability affect the likelihood that a mutant allele that gives virgin females the ability to reproduce parthenogenetically will invade an obligately sexual population. We show that male coercion cannot stop the allele from spreading because mutants generally benefit by producing at least some offspring asexually prior to encountering males. We find that effects of sexual conflict can lead to positive frequency‐dependent dynamics, where the spread of the allele is promoted by effective (no‐cost) resistance when males are common, and by mate limitation when sex ratios are female‐biased. However, once the mutant allele fixes, effective coercion prevents the complete loss of sex unless linkage disequilibrium can build up between the allele and alleles for effective resistance. Our findings clarify how limitations of female resistance imposed by the genetic architecture of sexual antagonism can promote the maintenance of sexual reproduction. At the same time, our finding of widespread obligate sex when costs of parthenogenesis are high suggests that developmental constraints could contribute to the rarity of facultative reproductive strategies in nature.