Evolving integral projection models: evolutionary demography meets eco-evolutionary dynamics

Patterns of survival and reproduction determine fitness, and there is a rich body of theory linking demography with evolution. For example, selection analysis can be used to predict changes in trait values, and by approximating selection, equations describing trait dynamics derived and evolutionary endpoints predicted. Here, we provide an overview of how these methods can be used to understand evolutionary dynamics and selection in a structured population modelled by an integral projection model (IPM). General expressions for selection are given, and we show how these can be approximated using eigenvalue sensitivities. Approximations for the dynamics of both the trait mean and variance are presented and compared to simulation results (IPMs and individual-based models) for monocarpic perennials. We describe how selection can be decomposed into components related to survival and reproduction and into components resulting from changes in demography versus changes in population structure. We show that, in an empirically based IPM, effects of changes in population structure can be a major component of the overall selection pressure. Most studies of selection in natural populations have focused entirely on selection due to changes in demography, so our results may help explain why directional selection is often predicted but no evolutionary response is observed. The endpoints of evolution, what we expect to see in nature, are explored using ideas from adaptive dynamics theory. The key methods are based on evolutionarily stable strategies (ESS) and convergence stability. Efficient methods for finding an ESS are described. We then extend these ideas to function-valued traits, where it is assumed that an entire function can evolve, rather than a few parameters defining it. By combining theory for IPMs with ideas from several different fields, we show how the dynamics of ecologically complex, evolving systems can be understood.