Temporal variation can facilitate niche evolution in harsh sink environments.

We examine the impact of temporal variation on adaptive evolution in "sink" environments, where a species encounters conditions outside its niche. Sink populations persist because of recurrent immigration from sources. Prior studies have highlighted the importance of demographic constraints on adaptive evolution in sinks and revealed that adaptation is less likely in harsher sinks. We examine two complementary models of population and evolutionary dynamics in sinks: a continuous-state quantitative-genetics model and an individual-based model. In the former, genetic variance is fixed; in the latter, genetic variance varies because of mutation, drift, and sampling. In both models, a population in a constant harsh sink environment can exist in alternative states: local maladaptation (phenotype comparable to immigrants from the source) or adaptation (phenotype near the local optimum). Temporal variation permits transitions between these states. We show that moderate amounts of temporal variation can facilitate adaptive evolution in sinks, permitting niche evolution, particularly for slow or autocorrelated variation. Such patterns of temporal variation may particularly pertain to sinks caused by biotic interactions (e.g., predation). Our results are relevant to the evolutionary dynamics of species' ranges, the fate of exotic invasive species, and the evolutionary emergence of infectious diseases into novel hosts.