Species persistence under climate change: a geographical scale coexistence problem.

Forecasting the impacts of climate change on biological diversity requires better ways to incorporate competitive interactions into predictions of species' range dynamics and persistence. This problem has been studied extensively in a different context by theoreticians evaluating the coexistence of species in spatially heterogeneous environments. Here, we show how spatial coexistence theory can be adapted to provide a mathematical framework for understanding species persistence in competitive communities under climate change. We first show how the spatial low-density growth rate provides the relevant metric of species persistence along a climate gradient. We then analyse a model of multiple migrating competitors to show how mechanisms contributing to low-density growth rates quantify the effect of different competitive processes on persistence, and how these processes change in strength with species' asynchronous migration under climate change. Finally, we outline the empirical utility of the framework, showing how the theory can scale up from local measurements of species performance and competitive interactions to range-scale metrics of persistence. Treating species' range dynamics as a geographical-scale coexistence problem presents its own set of challenges, but building from a well-established body of theory may greatly improve the predictability of species persistence in competitive communities under climate change.