The geometry of coexistence

Understanding the processes that maintain diversity has been the focus of e xtensive study, yet there is much that has not been integrated into a cohes ive framework. First, there is a separation of perspective. Ecological and evolutionary approaches to diversity have progessed in largely parallel dir ections. Second, there is a separation of emphasis. In both ecology and pop ulation genetics, classical theories favour local explanations with emphasi s on population dynamics and selection within populations, while contempora ry theories favour spatial explanations, with emphasis on population struct ure and interactions among populations. What is lacking is a comparative ap proach that evaluates the relative importance of local and spatial processe s in maintaining genetic and ecological diversity. I present a framework fo r diversity maintenance that emphasizes the comparative approach. I use a w ell-known but little-used mathematical approach, the perturbation theorem f or dynamical systems, to identify key points of contact between ecological and population genetic theories of coexistence. These connections provide f or a synthesis of several important concepts: population structure (source- sink versus extinction-colonization), spatial heterogeneity (intrinsic vers us extrinsic) in fitness and competitive ability, and temporal scales over which local and spatial processes influence diversity. This framework ties together a large and diverse body of theory and data from ecology and popul ation genetics. It yields comparative predictions that can serve as guideli nes in biodiversity management. (C) 2000 The Linnean Society of London.