Environmental "Knees" and "Wiggles" as Strong Stabilizers of Species' Range Limits Set by Interspecific Competition

Abstract

Whether interspecific competition is a major contributing factor to setting species range limits has been debated for a long time. Theoretical studies using evolutionary models have proposed that the interaction between interspecific competition and disruptive gene flow along an environmental gradient can halt range expansion of ecologically related species where they meet. However, the stability of such range limits has not been well addressed. We use a deterministic PDE model of adaptive range evolution over a continuous habitat to show that the range limits set by interspecific competition between two closely related species are unlikely to be evolutionarily stable if the environmental optima for fitness-related traits vary linearly in space. That is, in a (almost) linear environment without a dispersal barrier or a third (or more) related species, the range limits formed at the interface of two competing species constantly move towards the weaker species. Through extensive numerical computations, we then demonstrate that environmental nonlinearities such as "knees" and "wiggles"--wherein an isolated sharp change or a step-like change occurs in the steepness of a trait optimum--can strongly stabilize competitively formed range limits. The stabilization mechanism relies on the contrast that such nonlinearities create in the level of disruptive gene flow to the peripheral population of each species. We show that the stability of the range limits established at these nonlinearities, which are likely prevalent in nature, is robust against moderate environmental disturbances. Whether or not strong disturbances such as rapid high-amplitude changes in climate can destabilize such range limits depends on how the competitive dominance of the competing species changes across the environmental nonlinearity. Therefore, our results identify habitat regions where species ranges are fairly insensitive to climate change, and highlight the importance of measuring the competitive ability of species when predicting their response to climate change.