Interspecific competition, environmental gradients, gene flow, and the coevolution of species' borders

Darwin viewed species range limits as chiefly determined by an interplay be tween the abiotic environment and interspecific interactions. Haldane argue d that species' ranges could be set intraspecifically when gene flow from a species' populous center overwhelms local adaptation at the periphery. Rec ently, Kirkpatrick and Barton have modeled Haldane's process with a quantit ative genetic model that combines density-dependent local population growth with dispersal and gene flow across a linear environmental gradient in opt imum phenotype. To address Darwin's ideas, we have extended the Kirkpatrick and Barton model to include interspecific competition and the frequency-de pendent selection that it generates, as well as stabilizing selection on a quantitative character. Our model includes local population growth, movemen ts over space, natural selection, and gene now. It simultaneously addresses the evolution of character displacement and species borders. It reproduces the Kirkpatrick and Barton single-species result that limited ranges can b e produced with sufficiently steep environmental gradients and strong dispe rsal. Further, in the absence of environmental gradients or barriers to dis persal, interspecific competition will not limit species ranges at evolutio nary equilibrium. However, interspecific competition can interact with envi ronmental gradients and gene flow to generate limited ranges with much less extreme gradient and dispersal parameters than in the single-species case. Species display character displacement in sympatry, yet the reduction in c ompetition that results from this displacement does nor necessarily allow t he two species to become sympatric everywhere. When species meet, competiti on reduces population densities in the region of overlap, which, in turn, i ntensifies the asymmetry in gene flow from center to margin. This reduces t he ability of each species to adapt to local physical conditions at their r ange limits. If environmental gradients are monotonic but not linear, the t ransition zone between species at coevolutionary equilibrium occurs where t he environmental gradient is steepest. If productivity gradients are also i ntroduced into the model, then patterns similar to Rapoport's rule emerge. Interacting species respond to climate change, as it affects the optimal ph enotype over space, by a combination of range shifts and local evolution in mean phenotype, while solitary species respond solely by range shifts. Fin ally, we compare empirical estimates for intrinsic growth rates and diffusi on coefficients for several species to those needed by the single-species m odel to produce a stable limited range. These empirical values are generall y insufficient to produce limited ranges in the model suggesting a role for interspecific interactions.