“Stage-structured evolutionary demography: linking life histories, population genetics, and ecological dynamics”

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Charlotte de Vries and Hal Caswell (Apr 2019)

The DOI will be https://dx.doi.org/10.1086/701857

Wouldn’t it be nice if population genetics and stage-classified demography got together? Now they have

This lesser world is all about reproduction, as you might well know. Those who cease to duplicate simply die.
     —Rawi Hage, Carnival
Eurasian Buzzard (Buteo buteo).
(Image © Jan van Arkel, IBED/University of Amsterdam)

Organisms are born and they die. These processes change the size and structure of populations as well as their genetic make-up. Demography (the rates of birth, death, aging, development, etc.) is thus crucial to evolution. Yet many of these rates have been neglected or ignored in traditional population genetics, which has generally focused on survival rates only (an assumption known as “viability selection”). A central question for genetics is whether one gene will come to dominate the population, or whether multiple genetic types will coexist in what is called a genetic polymorphism. What determines coexistence of genes when demographic processes are included? Answering this question requires a model that keeps track of individuals of different ages or sizes as well as their genetic make-up. Charlotte de Vries and Hal Caswell from the University of Amsterdam introduce such a model. It connects a powerful set of demographic methods (known as matrix population models) to basic Mendelian genetics.

The authors use their model for two purposes. First, they show how to calculate the way that population size, structure, and genetics will change over time, taking into account births, deaths, and development. Second, they derive new, and very general, conditions that lead to coexistence of genetic types in a polymorphism. The results of more traditional genetic analyses appear as special cases, but the authors’ new results are more general. These results provide a new framework for analyzing the evolution of life histories of plants, animals, and humans. As an example, the authors apply their model to a study of genetically determined color polymorphism in the common buzzard, Buteo buteo.

Eurasian Buzzard (Buteo buteo).
(Image © Jan van Arkel, IBED/University of Amsterdam)

Abstract

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 demographic component of the model may be stage-classified or age-classified, linear or nonlinear, time-invariant or time varying, deterministic or stochastic, and may include dependence on environmental resources or interactions among species. 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 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, 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.