Genotype specificity and spatial arrangement govern the direction and magnitude of selection in variable environments
Spatial environmental variation can either amplify or suppress the fixation of beneficial mutants in structured populations, yet the interplay of ecological factors and spatial structure in determining which outcome occurs remains theoretically unresolved. Here, we develop a unified framework for selection on lattice graphs with environmental heterogeneity, in which mutant and resident fitness depend on the local environmental state. Across three common classes of genotype-environment interactions and a wide range of spatial arrangements of environmental states, we identify two governing principles. Genotype specificity determines the direction of the effect: heterogeneity amplifies selection when it modulates resident fitness, but suppresses selection when it modulates mutant fitness, with genotype-symmetric modulation producing weaker amplification. Spatial arrangement determines the magnitude: intermixed versus clustered environments tune the strength of amplification or suppression without reversing the direction of the effect. Together, these principles reconcile disparate theoretical results and provide predictive criteria for adaptation in heterogeneous landscapes, from microbial communities to somatic evolution and cancer.