Adaptation of a quantitative trait to a changing environment: New analytical insights on the asexual and infinitesimal sexual models.

Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits subject to stabilizing selection around an optimal phenotype, whose value is shifted continuously through time. In this context, the population fate results from the equilibrium distribution of the trait, relative to the moving optimum. Such a distribution may vary with the shape of selection, the system of reproduction, the number of loci, the mutation kernel or their interactions. Here, we develop a methodology that provides quantitative measures of population maladaptation and potential of survival directly from the entire profile of the phenotypic distribution, without any a priori on its shape. We investigate two different systems of reproduction (asexual and infinitesimal sexual models of inheritance), with various forms of selection. In particular, we recover that fitness functions such that selection weakens away from the optimum lead to evolutionary tipping points, with an abrupt collapse of the population when the speed of environmental change is too high. Our unified framework allows deciphering the mechanisms that lead to this phenomenon. More generally, it allows discussing similarities and discrepancies between the two systems of reproduction, which are ultimately explained by different constraints on the evolution of the phenotypic variance. We demonstrate that the mean fitness in the population crucially depends on the shape of the selection function in the infinitesimal sexual model, in contrast with the asexual model. In the asexual model, we also investigate the effect of the mutation kernel and we show that kernels with higher kurtosis tend to reduce maladaptation and improve fitness, especially in fast changing environments.

Optimal life-history schedule in a metapopulation with juvenile dispersal.

Previous models have predicted that when mortality increases with age, older individuals should invest more of their resources in reproduction and produce less dispersive offspring, as both their future reproductive value and their prospect of competing with their own sib decline. Those models assumed stable population sizes. We here study for the first time the evolution of age-specific reproductive effort and of age-specific offspring dispersal rate in a metapopulation with extinction-recolonization dynamics and juvenile dispersal. Our model explores the evolutionary consequences of disequilibrium in the age structure of individuals in local populations, generated by disturbances. Life-history decisions are then shaped both by changes with age in individual performances, and by changes in ecological conditions, as young and old individuals do not live on average in the same environments. Lower juvenile dispersal favours the evolution of higher reproductive effort in young adults in a metapopulation with extinction-recolonization compared with a well-mixed population. Contrary to previous predictions for stable structured populations, we find that offspring dispersal should generally increase with maternal age. This is because young individuals, who are overrepresented in recently colonized populations, should allocate more to reproduction and less to dispersal as a strategy to exploit abundant recruitment opportunities in such populations.