“Class structure, demography, and selection: reproductive-value weighting in non-equilibrium, polymorphic populations”
Sébastien Lion (May 2018)
Dynamical reproductive values to study the interplay of demography and selection in class-structured populations
Nearly 90 years ago, Ronald A. Fisher introduced the concept of reproductive value in his seminal book, The Genetical Theory of Natural Selection. Fisher defined reproductive value as the relative contribution of individuals of a given age to the future of the population. He further suggested that, when evaluating the consequences of natural selection, individuals should be weighted by their reproductive value. This idea proved influential and reproductive value has since become a central concept of evolutionary theory. It is routinely used when analyzing populations structured into different classes (such as age groups, developmental stages, habitats, or sexes).
In theoretical models, reproductive values are generally calculated in populations that have very simple dynamics or are at equilibrium. In this article by Sébastien Lion of the Centre National pour la Recherche Scientifique in Montpellier, new theory is developed that shows how Fisher's seminal idea can be extended to analyze populations with more complex ecological dynamics, provided each individual is weighted by a time-dependent reproductive value. With this weighting, the effect of natural selection can always be separated from the effect of demographic transitions. Indeed, to calculate the relevant reproductive values, the theory shows that we can ignore genetic variation and focus on the aggregate demographic dynamics of the population. This could prove useful for analyzing empirical data where the underlying genetic variation of a trait is unknown. At a more conceptual level, this research shows that a dynamical and demographic definition of reproductive values allows evolution to be described through a simple Price equation in which demography and selection are neatly separated.
In natural populations, individuals of a given genotype may belong to different classes. Such classes can represent different age groups, developmental stages, or habitats. Class structure has important evolutionary consequences because the fitness of individuals with the same genetic background may vary depending on their class. As a result, demographic transitions between classes can cause fluctuations in the trait mean that need to be removed when estimating selection on a trait. Intrinsic differences between classes are classically taken into account by weighting individuals by class-specific reproductive values, defined as the relative contribution of individuals in a given class to the future of the population. These reproductive values are generally constant weights calculated from a constant projection matrix. Here, I show, for large populations and clonal reproduction, that reproductive values can be defined as time-dependent weights satisfying dynamical demographic equations that only depend on the average between-class transition rates over all genotypes. Using these time-dependent demographic reproductive values yields a simple Price equation where the non-selective effects of between-class transitions are removed from the dynamics of the trait. This generalises previous theory to a large class of ecological scenarios, taking into account density-dependence, ecological feedbacks, arbitrary strength of selection and arbitrary trait distributions. I discuss the role of reproductive values for prospective and retrospective analyses of the dynamics of phenotypic traits.