Sex Ratio in a Stepping-Stone Population with Sex-Specific Dispersal

doi:10.1006/tpbi.1994.1011

Theoretical Population Biology

Volume 45, Issue 2, April 1994, Pages 203-218

https://doi.org/10.1006/tpbi.1994.1011 Get rights and content

Abstract

The theoretical hypothesis that the sex-ratio should be biased towards the sex with the wider and/or more even dispersal pattern is tested and confirmed with an inclusive fitness model in a one-dimensional diploid stepping-stone population in which offspring can remain on their home site or disperse one site to the right or left. Two models are examined, dispersal of both sexes before mating and male dispersal before mating followed by dispersal of mated females.

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Cited by (35)

Dispersal evolution and resource matching in a spatially and temporally variable environment
2015, Journal of Theoretical Biology
Metapopulations may consist of patches of different quality, and are often disturbed by extrinsic processes causing variation of patch quality. The persistence of such metapopulations then depends on the species׳ dispersal strategy. In a temporally constant environment, the evolution of dispersal rates follows the resource matching rule, i.e. at the evolutionarily stable dispersal strategy the number of competitors in each patch matches the resource availability in each patch. Here, we investigate how the distribution of individuals resulting from convergence stable dispersal strategies would match the distribution of resources in an environment which is temporally variable due to extrinsic disturbance. We develop an analytically tractable asexual model with two qualities of patches. We show that convergence stable dispersal rates are such that resource matching is predicted in expectation before habitat quality variation, and that the distribution of individuals undermatches resources after habitat quality variation. The overall flow of individuals between patches matches the overall flow of resources between patches resulting from environmental variation. We show that these conclusions can be generalized to organisms with sexual reproduction, and to a metapopulation with three qualities of patches when there is no mutational correlation between dispersal rates.
Evolutionary and convergence stability for continuous phenotypes in finite populations derived from two-allele models
2012, Journal of Theoretical Biology
Citation Excerpt :
The concept of evolutionary stability (Maynard-Smith, 1982; Eshel, 1983) is born out of the aim of characterizing long-term phenotypic evolution directly from payoff functions, devoid of the intricacies of population genetics considerations. The strength of the concept of evolutionary stability has been forcefully revealed when analyzing the evolution of continuously varying phenotypes, where it has been applied to investigate the evolution of many of different traits, from the sex-ratio in spatially structured populations, to body size in prey–predator systems, to the evolution of other-regarding preferences (e.g., Parker and Maynard Smith, 1990; Bulmer, 1994; Taylor, 1994; Geritz et al., 1998; Vincent and Brown, 2005; Dercole and Rinaldi, 2008; Leimar, 2009; Akçay and Van Cleve, 2012). Although much attention has been paid to theoretical aspects of selection in finite population with and without frequency-dependent selection (e.g., Wright, 1931; Crow and Kimura, 1970; Gandon and Rousset, 1999; Ewens, 2004; Rousset and Ronce, 2004; Otto and Day, 2007; Lessard, 2005; Lessard and Ladret, 2007; Tarnita et al., 2009; Ohtsuki, 2010), there are few studies (Rousset and Billiard, 2000; Rousset, 2004) addressing the theoretical question of the stability of continuous phenotypes in finite populations (for discrete strategies, see Nowak et al., 2004; Wild and Taylor, 2004; Lessard, 2005).
The evolution of a quantitative phenotype is often envisioned as a trait substitution sequence where mutant alleles repeatedly replace resident ones. In infinite populations, the invasion fitness of a mutant in this two-allele representation of the evolutionary process is used to characterize features about long-term phenotypic evolution, such as singular points, convergence stability (established from first-order effects of selection), branching points, and evolutionary stability (established from second-order effects of selection). Here, we try to characterize long-term phenotypic evolution in finite populations from this two-allele representation of the evolutionary process. We construct a stochastic model describing evolutionary dynamics at non-rare mutant allele frequency. We then derive stability conditions based on stationary average mutant frequencies in the presence of vanishing mutation rates. We find that the second-order stability condition obtained from second-order effects of selection is identical to convergence stability. Thus, in two-allele systems in finite populations, convergence stability is enough to characterize long-term evolution under the trait substitution sequence assumption. We perform individual-based simulations to confirm our analytic results.
Sex ratio dependent dispersal when sex ratios vary between patches
2011, Journal of Theoretical Biology
Citation Excerpt :
This may lead one to conclude that males will not evolve to disperse more from patches with higher sex ratios. However, Wild and Taylor’s (2004) finding is, in part, an artefact of a simplifying assumption that most analytical sex ratio models make, namely, that sex ratios are precise (Motro, 1982; Frank, 1986; Taylor, 1988, 1994; Gandon and Michalakis, 2001; Leturque and Rousett, 2003; Ronce, 2007; but see Green et al., 1982; Griffiths and Godfray, 1988; Nagelkerke, 1996). Hence, a male finding himself in a patch with a high sex ratio will encounter the exact same sex ratio in all other patches because sex ratios are invariable.
Female biased sex ratios reduce competition between brothers when mating takes place within local patches. Male dispersal prior to mating is another strategy that reduces competition between brothers. One may thus expect these two traits to co-evolve and this is partially met in that sex ratios becomes less female biased as dispersal increases. However, the evolutionary stable degree of dispersal is unaffected by the sex ratio. The analytical models developed to reach these conclusions ignored variance in sex ratios, since this increases the structural complexity of models. For similar reasons finite clutch sizes are also routinely ignored. To overcome these shortfalls, we developed individual based simulations that allowed us to incorporate realistic clutch sizes and binomial variance in sex ratios between patches. We show that under variable sex ratios, males evolve to more readily disperse away from patches with higher sex ratios than lower sex ratios. We show that, while the dispersal rate is insensitive to the sex ratio when sex ratios are precise, it is affected by the number of males with dispersal decreasing as the number of males decreases.
Sexual conflict in viscous populations: The effect of the timing of dispersal
2011, Theoretical Population Biology
Citation Excerpt :
Alternatively, we might suppose that both males and females disperse prior to mating, so that mating occurs on the same site where offspring are produced. Taylor (1994) and Wild and Taylor (2004) have called the former situation the ‘DMD life history’ (males Disperse, then Mating occurs, then inseminated females Disperse, hence the acronym DMD), and have called the latter situation the ‘DDM life history’ (males Disperse and females Disperse, both before Mating occurs, hence the acronym DDM). Both DMD and DDM life histories are investigated below.
In recent years, there has been increasing theoretical and empirical examination of how sexual conflict can arise between males and females. However, much this work has implicitly assumed that interactions take place in panmictic populations with complete dispersal, where interactions are between unrelated individuals. Here, we examine the consequences of limited dispersal and population structure for the evolution of a male phenotype that is associated with the males pre- and post-copulatory reproductive success, using an inclusive-fitness based analysis applied to group-structured populations. We show that: (i) the sex-specific timing of the dispersal phase of the life cycle can drive the evolution of sexual conflict; (ii) the inclusive fitness of a female in this conflict is determined solely by direct (i.e. personal) effects on its own competitive ability. Our analysis is supported by results from individual-based simulations of multi-level selection. Our results support the suggestion that kin selection can influence the evolution of sexual conflict, but reveal that such a role might be more complex than previously appreciated when sex-specific life histories are taken into consideration. We discuss the implications of our results for sexual conflict in various species of insects, but focus primarily on dipteran flies of the family Sepsidae.
A spatially explicit model of sex ratio evolution in response to sex-biased dispersal
2011, Theoretical Population Biology
Citation Excerpt :
The DDM model, where both sexes disperse before mating, fits the life cycle of many animals, whereas the DMD model, where fertilized females disperse after mating, is appropriate for higher plants. However, some animals may show patterns of dispersal similar to the one assumed in the DMD model (Taylor, 1994b; Guillon et al., 2006). In some butterflies, for example, dispersal is female biased and occurs after the first mating (Hirota, 2005).
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.
Sex allocation and dispersal in a heterogeneous two-patch environment
2006, Theoretical Population Biology
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.

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Regular ArticleSex Ratio in a Stepping-Stone Population with Sex-Specific Dispersal

Abstract

Regular Article
Sex Ratio in a Stepping-Stone Population with Sex-Specific Dispersal