Print PageSpecies may respond to ongoing environmental modifications either through the shift of their distribution, or through genetic adaptation to new environmental conditions. Quantitative genetics are useful to estimate phenotypic changes arising within few generations. Several quantitative genetics models have addressed the evolution of species distribution in a changing environment, but none of them jointly considered spatial heterogeneity in environmental conditions, and the complexity arising from multivariate genetic and selective constraints.
We developed a model describing the population dynamics of a species distributed along a continuous linear habitat, in which individuals migrate by diffusion. Individual fitness is determined by the matching of multiple traits to phenotypic optima linearly varying in space and time. We jointly analyzed the dynamics of the species’ demography and adaptation in space, to determine (i) when genetic or selective correlations between traits limit a species’ response to environmental change, (ii) what is the critical rate of environmental change that a species may sustain.
Results/Conclusions
Our model predicts that the species can track its phenotypic optimum with a constant lag, while all traits develop linear clines. As dispersal increases, the distributional range of the species expands and the population growth rate increases, while adaptation is prevented because of genetic swamping. When most genetic variance occurs in a direction parallel to the selection gradient generated by the shifting optima, and when the nonlinear selection pressures (stabilizing and correlational selection) are stronger in that same direction, the distributional range is wider, with a higher population growth rate, and better adaptation.
Extinction occurs whenever the optima shift at a speed higher than a critical threshold, which decreases when dispersal abilities are low, and when the leading directions of genetic variance, of the nonlinear selection pressures, and of the selection gradient strongly differ.
We derive analytical approximations for the spatial dynamics of demography and trait adaptation, and for the sustainable rate of environmental changes. These approximations closely match results obtained through simulations, as long as nonlinear selection and genetic variance are weak. These expressions can be used to assess whether a given species or population is at strong risk of rapid extinction due to global warming.
