Natural populations often show variation in traits that can affect the strength of interspecific interactions. Interaction strengths in turn influence the fate of pairwise interacting populations and the stability of food webs. Understanding the mechanisms relating individual phenotypic variation to interaction strengths is thus central to assess how trait variation affects population and community dynamics. We incorporated nonheritable variation in attack rates and handling times into a classical consumer-resource model to investigate how variation may alter interaction strengths, population dynamics, species persistence, and invasiveness. We found that individual variation influences species persistence through its effect on interaction strengths. In many scenarios, interaction strengths decrease with variation, which in turn affects species coexistence and stability. Because environmental change alters the direction and strength of selection acting upon phenotypic traits, our results have implications for species coexistence in a context of habitat fragmentation, climate change, and the arrival of exotic species to native ecosystems.