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

Theoretical Population Biology

2019

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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.

Section: Discussionmentioning

confidence: 99%

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

Vries

Theoretical Population Biology

2019

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“…In the literature on two-sex models, homogeneous models are often referred to as "frequency dependent" to distinguish them from density-dependent nonlinear models (Shyu and Caswell 2016). We do not follow that practice here because it causes confusion with the genetic concept of frequencydependent fitness.…”

Section: Nonlinearity and Homogeneitymentioning

confidence: 99%

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

Vries

The American Naturalist

2019

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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 (l) do not determine the outcome of selection. Except in restrictive special cases, heterozygote superiority in l 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.

“…If multiple male and female stages interbreed to form different types of unions, stage-specific mating preferences can also be integrated into this mating function (Shyu and Caswell 2016b ; see Appendix 4 ).…”

Section: Model Developmentmentioning

confidence: 99%

“…The number of these products increases dramatically when more stages, and hence more mating combinations, are included. See Shyu and Caswell ( 2016b ) and Appendix 4 for incorporation of multiple mating stages in the continuous-time model.…”

Section: A 5-stage Bmmr Matrix Modelmentioning

confidence: 99%

See 1 more Smart Citation

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

Shyu

2018

Population Ecology

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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 sexrelated characters.