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

Darwin viewed species range limits as chiefly determined by an interplay between the abiotic environment and interspecific interactions. Haldane argued that species' ranges could be set intraspecifically when gene flow from a species' populous center overwhelms local adaptation at the periphery. Recently, Kirkpatrick and Barton have modeled Haldane's process with a quantitative genetic model that combines density-dependent local population growth with dispersal and gene flow across a linear environmental gradient in optimum phenotype. To address Darwin's ideas, we have extended the Kirkpatrick and Barton model to include interspecific competition and the frequency-dependent selection that it generates, as well as stabilizing selection on a quantitative character. Our model includes local population growth, movements 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 be produced with sufficiently steep environmental gradients and strong dispersal. Further, in the absence of environmental gradients or barriers to dispersal, interspecific competition will not limit species ranges at evolutionary equilibrium. However, interspecific competition can interact with environmental 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 competition that results from this displacement does nor necessarily allow the two species to become sympatric everywhere. When species meet, competition reduces population densities in the region of overlap, which, in turn, intensifies the asymmetry in gene flow from center to margin. This reduces the ability of each species to adapt to local physical conditions at their range limits. If environmental gradients are monotonic but not linear, the transition zone between species at coevolutionary equilibrium occurs where the environmental gradient is steepest. If productivity gradients are also introduced into the model, then patterns similar to Rapoport's rule emerge. Interacting species respond to climate change, as it affects the optimal phenotype over space, by a combination of range shifts and local evolution in mean phenotype, while solitary species respond solely by range shifts. Finally, we compare empirical estimates for intrinsic growth rates and diffusion coefficients for several species to those needed by the single-species model to produce a stable limited range. These empirical values are generally insufficient to produce limited ranges in the model suggesting a role for interspecific interactions.