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Resource are often not uniformly distributed within a population. Spatialvariations of concentration of a resource, change the fitness of competingstrategies locally. The notion of fitness varying with respect to both genotypeand environment is important in modeling cancer initiation, microbial evolutionand evolution of drug resistance. Environmental interactions can be asymmetric,that is, they affect the fitness of one type more than the other. The questionis how local environmental variations in network population structures changethe selection dynamics in a finite population setting. We considerone-dimensional lattice population structures with spatial fitnessdistributions with a periodic pattern. Heterogeneity is determined by standarddeviation of fitnesses and period. The model covers biologically relevantlimits of two-habitat subdivided populations and randomly-distributed resourcesin high- and low-periods. We numerically calculate fixation probability andfixation times for a constant population birth-death process as fitnessheterogeneity and period vary. We identify levels of heterogeneity for which apreviously deleterious mutant, in a uniform environment, becomes beneficial. Inother regimes of the problem we observe unexpected behavior where the fixationprobability of both types are larger than their neutral value at the same time.This coincides with an exponential increase in time to fixation as a functionof population size, which points to significant slow-down in selection processand the potential for coexistence between types in realistic time scales. Wealso discuss `fitness shift' model where the fitness function of one type isidentical to the other up to a constant spatial shift. This leads tosignificant increase (or decrease) in the fixation probability of the mutantdepending the value of the shift.

Counterintuitive properties of fixation probability and fixation time in population structures with spatially periodic resource distribution