Predicting success of cooperators across arbitrary heterogeneous environmental landscapes

Abstract

Cooperation is central to the organization of complex biological and social systems. Most theoretical models assume homogeneous environments; in reality, populations inhabit spatially varying landscapes in which the payoffs of cooperation differ across space. Here, we introduce a general framework for the evolution of cooperation in complex, heterogeneous environments where the benefit of cooperation depends on local environmental quality. Cooperators in environmentally rich sites confer greater benefits than those on poor sites. We show that whether heterogeneity promotes or suppresses cooperation is determined primarily by the spatial organization of environmental states. Across arbitrary environmental landscapes, a single quantity, the spatial correlation index (SCI), predicts the fixation probability of cooperators. Under weak selection, segregated environments enhance cooperation, whereas highly intermixed, checkerboard-like landscapes suppress it. Beyond fixation probabilities, environmental organization also controls evolutionary timescales: segregated landscapes generate long-lived metastable coexistence, whereas intermixed landscapes lead to faster but less successful fixation of cooperators. Together, these results provide a unifying description of how spatial environmental heterogeneity shapes the evolution of cooperation and suggest measurable predictors of cooperative success in biological and social settings.