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

Sex-specific paternal age effects on offspring quality in Drosophila melanogaster

Advanced paternal age has been repeatedly shown to modulate offspring quality via male- and/or female-driven processes, and there are theoretical reasons to expect that some of these effects can be sex-specific. For example, sex allocation theory predicts that, when mated with low-condition males, mothers should invest more in their daughters compared to their sons. This is because male fitness is generally more condition-dependent and more variable than female fitness, which makes it less risky to invest in female offspring. Here, we explore whether paternal age can affect the quality and quantity of offspring in a sex-specific way using Drosophila melanogaster as a model organism. In order to understand the contribution of male-driven processes on paternal age effects, we also measured the seminal vesicle size of young and older males and explored its relationship with reproductive success and offspring quality. Older males had lower competitive reproductive success, as expected, but there was no difference between the offspring sex ratio of young and older males. However, we found that paternal age caused an increase in offspring quality (i.e., offspring weight), and that this increase was more marked in daughters than sons. We discuss different male- and female-driven processes that may explain such sex-specific paternal age effects.

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.

Mathematical Modeling of Population Dynamics Based on Recurrent Equations: Results and Prospects. Part I

Abstract

Approaches to modeling population dynamics using discrete-time models are described in this two-part review. The development of the scientific ideas of discrete time models, from the Malthus model to modern population models that take into account many factors affecting the structure and dynamics, is presented. The most important and interesting results of recurrent equation application to biological system analysis obtained by the authors are given. In the first part of this review, the population dynamic effects that result from density-dependent regulation of population, the age and sex structures, and the influence of external factors are considered.

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.

Selection in two-sex stage-structured populations: Genetics, demography, and polymorphism

The outcome of natural selection depends on the demographic processes of birth, death, and development. Here, we derive conditions for protected polymorphism in a population characterized by age- or stage-dependent demography with two sexes. We do so using a novel two-sex matrix population model including basic Mendelian genetics (one locus, two alleles, random mating). Selection may operate on survival, growth, or fertility, any or all of which may differ between the sexes. The model can therefore incorporate genes with arbitrary pleiotropic and sex-specific effects. Conditions for protected polymorphism are expressed in terms of the eigenvalues of the linearization of the model at the homozygote boundary equilibria. We show that in the absence of sexual dimorphism, polymorphism requires heterozygote superiority in the genotypic population growth rate. In the presence of sexual dimorphism, however, heterozygote superiority is not required; an inferior heterozygote may invade, reducing the population growth rate and even leading to extinction (so-called evolutionary suicide). Our model makes no assumptions about separation of time scales between ecological and evolutionary processes, and can thus be used to project sex×stage×genotype dynamics of eco-evolutionary processes. Empirical evidence that sexual dimorphism affects extinction risk is growing, yet sex differences are often ignored in evolutionary demography and in eco-evolutionary models. Our analysis highlights the importance of sexual dimorphism and suggests mechanisms by which an allele can be favored by selection, yet drive a population to extinction, as a result of the structure and interdependence of sex- and stage-specific processes.

Stage-Structured Evolutionary Demography: Linking Life Histories, Population Genetics, and Ecological Dynamics

Demographic processes and ecological interactions are central to understanding evolution and vice versa. We present a novel framework that combines basic Mendelian genetics with the powerful demographic approach of matrix population models. The ecological components of the model may be stage classified or age classified, linear or nonlinear, time invariant or time varying, and deterministic or stochastic. Genotypes may affect, in fully pleiotropic fashion, any mixture of demographic traits (viability, fertility, development) at any points in the life cycle. The dynamics of the stage × genotype structure of the population are given by a nonlinear population projection matrix. We show how to construct this matrix and use it to derive sufficient conditions for a protected genetic polymorphism for the case of linear, time-independent demography. These conditions demonstrate that genotype-specific population growth rates (λ) do not determine the outcome of selection. Except in restrictive special cases, heterozygote superiority in λ is neither necessary nor sufficient for a genetic polymorphism. As a consequence, the population growth rate does not always increase, and populations can be driven to extinction due to evolutionary suicide. We demonstrate the construction and analysis of the model using data on a color polymorphism in the common buzzard (Buteo buteo). The model exhibits a stable genetic polymorphism and declining growth rate, consistent with field data and previous models.

Mating, births, and transitions: a flexible two-sex matrix model for evolutionary demography

Models of sexually-reproducing populations that consider only a single sex cannot capture the effects of sex-specific demographic differences and mate availability. We present a new framework for two-sex demographic models that implements and extends the birth-matrix mating-rule approach of Pollak. The model is a continuous-time matrix model that explicitly includes the processes of mating (which is nonlinear but homogeneous), offspring production, and demographic transitions and survival. The resulting nonlinear model converges to exponential growth with an equilibrium population composition. The model can incorporate age- or stage-structured life histories and flexible mating functions. As an example, we apply the model to analyze the effects of mating strategies (polygamy or monogamy, and mated unions composed of males and females, of variable duration) on the response to sex-biased harvesting. The combination of demographic complexity with the interaction of the sexes can have major population dynamic effects and can change the outcome of evolution on sex-related characters.