On the dynamics of reproductive values and phenotypic traits in class-structured populations

Abstract

In natural populations, individuals of a given genotype may belong to different classes. Such classes can for instance 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 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 densitydependence, ecological feedbacks and arbitrary distributions of the trait. I discuss the role of reproductive values for prospective and retrospective analyses of the dynamics of phenotypic traits.\n\nNote on this versionCompared to the previous version of the manuscript, some changes have been made to improve the readability and structure of the text, and to clarify the connections with the existing literature. One reviewer pointed out inconsistencies in some of the numerical simulations, and in the mutation term in appendix A2, which have now been fixed. When checking the calculations, I have also identified a missing term in the equation for the dynamics of individual reproductive values. The new equation makes much more sense. Additional results are also presented, in particular for discrete-time models and populations with a continuous age structure, for which Fishers original definition of reproductive value can be recovered.