Reformulation of Trivers-Willard hypothesis for parental investment

The Trivers-Willard hypothesis (TWH) plays a central role in understanding the optimal investment strategies to male and female offspring. Empirical studies of TWH, however, yielded conflicting results. Here, we present models to predict optimal comprehensive multi-element parental strategies composed of primary sex ratio, brood size, resource allocation among offspring, and the resultant secondary sex ratio. Our results reveal that the optimal strategy depends on sex differences in the shape of offspring fitness function rather than in fitness variance. Also, the slope of the tangent line (through the origin) to the offspring fitness function can be used to predict the preferred offspring sex. We also briefly discuss links between the model and the empirical research. This comprehensive reformulation of TWH will offer a thorough understanding of multi-element parental investment strategies beyond the classical TWH.

Constrained sex allocation after mating in a haplodiploid thrips species depends on maternal condition

In females of haplodiploid animals, female production requires fertilization, whereas male production does not. Therefore, haplodiploid species can display extraordinary sex ratios. Constrained sex allocation occurs when a female cannot produce daughters. This can be due to virginity but may also occur after mating due to insemination failure, selfish genetic elements or physiological constraints. Here, we investigated the mechanism underlying constrained sex allocation in Pezothrips kellyanus. In this species some mated females produce highly female-biased broods, yet, for unknown reasons, others produce extremely male-biased broods. Using crossing experiments controlled for maternally inherited endosymbionts we confirmed that constrained females were successfully inseminated. Furthermore, male-biased offspring production was not paternally inherited, ruling out paternal sex ratio elements previously identified as sex ratio distorters in some parasitoid wasps. Next, we excluded mating time and paternal fitness effects (male size) on sex allocation. However, we found that constrained sex allocation only occurred in small females producing smaller eggs than large females producing larger eggs and female-biased broods. Consequently, the bimodal sex allocation pattern correlates with maternal condition, and may have arisen (adaptively or non-adaptively) in association with an egg size-mediated fertilization mechanism recently detected in some haplodiploids, with egg size positively affecting fertilization success.

Is there a Trivers-Willard effect for parental investment? Modelling evolutionarily stable strategies using a matrix population model with nonlinear mating

The Trivers-Willard hypothesis (TWH) states that parents in good condition preferentially produce the sex with a higher variation in reproductive success, whereas parents in bad condition favour the opposite sex. Theorists distinguish two variants of the TWH: (a) a biased sex-ratio at birth and (b) biased parental investment after birth. It has been argued before that the conditions stated by Trivers and Willard (good condition is inherited and affects reproductive success more strongly for one of the sexes) are sufficient for the sex-ratio version but insufficient for the investment version of the TWH. However, it has not yet been investigated how these conditions affect parental investment in high and low quality parents, depending on the life-cycle of a species. The present study aims to fill this gap by introducing a multi-stage matrix population model with nonlinear mating to describe the effects of parental investment after birth on the reproductive values of male and female individuals. Using methods from adaptive dynamics and evolutionary invasion analysis, evolutionary trajectories and evolutionarily stable strategies are derived for different parameterizations of the model. Simulation results demonstrate that the conditions given by Trivers and Willard produce a general bias of parental investment towards the sex with higher variance in reproductive value. This bias is stronger for low-quality parents than for high-quality parents and matches the expected marginal offspring reproductive values for parental investment.

The Trivers-Willard hypothesis: sex ratio or investment?

The Trivers-Willard hypothesis has commonly been considered to predict two things. First, that a mother in good condition should bias the sex ratio of her offspring towards males (if males exhibit greater variation in reproductive value). Second, that a mother in good condition should invest more per son than per daughter. These two predictions differ empirically, mechanistically and, as we demonstrate here, theoretically too. We construct a simple model of sex allocation that allows simultaneous analysis of both versions of the Trivers-Willard hypothesis. We show that the sex ratio version holds under very general conditions, being valid for a large class of male and female fitness functions. The investment version, on the other hand, is shown to hold only for a small subset of male and female fitness functions. Our results help to make sense of the observation that the sex ratio version is empirically more successful than the investment version.

Paternal condition drives progeny sex-ratio bias in a lizard that lacks parental care

Sex-allocation theory predicts that females in good condition should preferentially produce offspring of the sex that benefits the most from an increase in maternal investment. However, it is generally assumed that the condition of the sire has little effect on progeny sex ratio, particularly in species that lack parental care. We used a controlled breeding experiment and molecular paternity analyses to examine the effects of both maternal and paternal condition on progeny sex ratio and progeny fitness in the brown anole (Anolis sagrei), a polygynous lizard that lacks parental care. Contrary to the predictions of sex-allocation theory, we found no relationship between maternal condition and progeny sex ratio. By contrast, progeny sex ratio shifted dramatically from female-biased to male-biased as paternal condition increased. This pattern was driven entirely by an increase in the production of sons as paternal condition improved. Despite strong natural selection favoring large size and high condition in both sons and daughters, we found no evidence that progeny survival was related to paternal condition. Our results emphasize the importance of considering the paternal phenotype in studies of sex allocation and highlight the need for further research into the pathways that link paternal condition to progeny fitness.

Sex allocation and dispersal in a heterogeneous two-patch environment

We investigate the evolution of sex allocation and dispersal in a two-habitat environment using a game theoretic analysis. One habitat is of better quality than the other and increased habitat quality influences the competitive ability of offspring in a sex-specific manner. Unlike previous work, we allow incomplete mixing of the population during mating. We discuss three special cases involving the evolution of sex allocation under fixed levels of dispersal between habitats. In these special cases, stable sex-allocation behaviors can be both biased and unbiased. When sex-allocation behavior and dispersal rates co-evolve we identify two basic outcomes. First-when sex-specific differences in the consequences of spatial heterogeneity are large-we predict the evolution of biased sex-allocation behavior in both habitats, with dispersal by males in one direction and dispersal by females in the other direction. Second-when sex-specific differences are small-unbiased sex-allocation is predicted with no dispersal between habitats.

Reproductive rates of wild and captive Vancouver Island marmots (Marmota vancouverensis)

I evaluated reproductive rates of the critically endangered Vancouver Island marmot (Marmota vancouverensis Swarth, 1911) using data from captive and wild populations over the 1980–2004 period. Results were similar to those reported for other alpine-dwelling marmots, including the closely related Marmota caligata (Eschscholtz, 1829) and Marmota olympus (Merriam, 1898). Most females in captivity first bred at age 3 or 4 (Tbreed = 4.3 years, SD = 1.15, n = 9), an age not significantly different from that observed in the wild (Tbreed = 3.6 years, SD = 1.2, n = 16). Numbers of pups weaned per litter were similar in captivity (Npups = 3.0, SD = 1.4, n = 25) and in the wild (Npups = 3.4, SD = 1.1, n = 58). Females were capable of weaning pups in consecutive years (46.4%, n = 13) but often skipped 1 year (39.3%, n = 11) or 2 years (14.3%, n = 4) between litters. Two-year-old females weaned pups infrequently (Pbreed = 0.09, n = 43) and older females were far more likely to breed (Pbreed = 0.40, n = 200); in neither case were significant captive-wild differences found. The oldest breeding female was 10 years old, but sample sizes for marmots older than 8 years were small and maximum breeding age may be underestimated. Between-litter intervals in captivity (Tbetween = 1.4 years, SD = 0.7, n = 11) were significantly shorter than in the wild (Tbetween = 1.9 years, SD = 0.7, n = 17). Sex ratios of weaned pups did not differ from 1:1 in the wild (female/male = 1.04) but were significantly skewed towards males in captivity (female/male = 0.56). I conclude that reproductive performance in Vancouver Island marmots is limited both by body condition and social constraints.

Sexual Selection Favors Female‐Biased Sex Ratios: The Balance between the Opposing Forces of Sex‐Ratio Selection and Sexual Selection

In a verbal model, Trivers and Willard proposed that, whenever there is sexual selection among males, natural selection should favor mothers that produce sons when in good condition but daughters when in poor condition. The predictions of this model have been the subject of recent debate. We present an explicit population genetic model for the evolution of a maternal-effect gene that biases offspring sex ratio. We show that, like local mate competition, sexual selection favors female-biased sex ratios whenever maternal condition affects the reproductive competitive ability of sons. However, Fisherian sex-ratio selection, which favors a balanced sex ratio, is an opposing force. We show that the evolution of maternal sex-ratio biasing by these opposing selection forces requires a positive covariance across environments between the sex-ratio bias toward sons (b) and the mating success of sons (r). This covariance alone is not a sufficient condition for the evolution of maternal sex-ratio biasing; it must be sufficiently positive to outweigh the opposing sex-ratio selection. To identify the necessary and sufficient conditions, we partition total evolutionary change into three components: (1) maternal sex-ratio bias, (2) sexual selection on sons, and (3) sex-ratio selection. Because the magnitude of the first component asymmetrically affects the strength of the second, biasing broods toward females in a poor environment evolves faster than the same degree of bias toward males in a good environment. Consequently, female-biased sex ratios, rather than male-biased sex ratios, are more likely to evolve. We discuss our findings in the context of the primary sex-ratio biases observed in strongly sexually selected species and indicate how this perspective can assist the experimental study of sex ratio evolution.