Pulsed Immigration Events Can Facilitate Adaptation to Harsh Sink Environments

In nature, rates of dispersal vary greatly over time, yet most theoretical explorations of ecological and evolutionary dynamics to date have assumed constant movement rates. Here we examine how a particular pattern of temporal variation-periodic pulses of immigration-influences adaptation to a harsh environment, in which a species experiences conditions outside its niche requirements. Using both deterministic models and stochastic individual-based simulations, we show that for many ecological and genetic scenarios, temporally spacing out immigration events increases the probability that local adaptation is sufficient for persistence (i.e., niche evolution). When immigration events are too frequent, gene flow can hamper local adaptation in sexual species, but sufficiently infrequent pulses of immigration allow for repeated opportunities for adaptation with temporary escapes from gene flow during which local selection is unleashed. We develop versions of our models with and without density dependence for three different assumptions about the genetics underlying fitness (haploid, diploid, and quantitative genetic variation) so that our results may be applicable to a wide range of natural systems. Our study adds to a growing body of literature showing that temporal variation in migration rates can have significant effects on local adaptation and is among the first to show how such variation affects niche evolution.