Abstract:聽Many theoretical models of evolution assume that all competing individuals experience the same environment. Here, we consider the more realistic scenario of evolution in heterogeneous environments.聽We introduce a novel formalism to approach any form of spatial fitness heterogeneity in an evolutionary graph. We calculate the condition for natural selection to favor the mutant type relative to the resident on a complete graph structure. Environmental heterogeneity elucidates an interesting asymmetry between the mutant and resident types. Mutant heterogeneity suppresses fixation probability, and if strong enough, it can completely offset the effects of natural selection. In contrast, resident heterogeneity can amplify a mutant鈥檚 fixation probability if population聽is small and has no effect on mutant fixation probability otherwise. Our results hold for any environmental heterogeneity and selection intensity. We address generalization of the above聽observations聽to other graph structures, as well as heterogeneous evolutionary games.聽