Evolutionary Adaptation in Heterogeneous and Changing Environments

Organisms that are adapting to long term environmental change almost always deal with mul- tiple environments and trade-offs that affect their optimal phenotypic strategy. Here we combine the idea of repeated variation or heterogeneity, like seasonal shifts, with long-term directional dy- namics. Using the framework of fitness sets, we determine the dynamics of the optimal phenotype in two competing environments encountered with different frequencies, one of which changes with time. When such an optimal strategy is selected for in simulations of evolving populations, we observe rich behavior that is qualitatively different from and more complex than adaptation to long-term change in a single environment. The probability of survival and the critical rate of environmental change above which populations go extinct depend crucially on the relative fre- quency of the two environments and the strength and asymmetry of their selection pressures. We identify a critical frequency for the stationary environment, above which populations can escape the pressure to constantly evolve by adapting to the stationary optimum. In the neighborhood of this critical frequency, we also find the counter-intuitive possibility of a lower bound on the rate of environmental change, below which populations go extinct, and above which a process of evolutionary rescue is possible.