The question of adaptation to environmental change at long time scales remains an important area of theoretical investigation, but has been treated mainly in the context of single environments. However, organisms almost always deal with multiple environments and trade offs arising from them, in addition to the possibility of long term change. Here we combine the idea of repeated variation, heterogeneity, like seasonal shifts, with long term and directional dynamics. To address this complex situation, we extend the framework of fitness sets and study how the optimal phenotype in this situation can itself change with long term shifts. We consider selection from two distinct environments. We find that the behavior of a population under such a system is qualitatively different and more complex than that of a population responding to long term change in a single environment. The chance of survival or extinction depends crucially on the relative frequency of the two environments, the strength and asymmetry of their selection pressure in addition to population size, phenotypic diversity, fecundity and the rate of change of the environment. We study characteristics of the population under selection such as its phenotypic lag behind the optimal phenotype and the mean time to extinction.
Evolution of Populations in Heterogeneous and Dynamic Environments