Modelling the effect of temperature on species coexistence.

Abstract

Temperature alters organismal performance and species interactions, yet it remains unclear how generic unimodal thermal responses translate into changes in competitive coexistence. Most existing models emphasize temperatures below the thermal optimum or rely on particular thermal-response formulations. We develop a density-dependent generalized Lotka-Volterra framework for pairwise exploitative competition in which temperature modifies competition through relative resource consumption. Coexistence is quantified using a normalized structural feasibility measure that captures the range of environmental conditions compatible with positive equilibria. The framework yields one structural prediction: pairwise coexistence is maximized when temperature balances the effective competitive asymmetry between competitors. Under symmetric resource overlap, this balance occurs when the two consumption curves intersect. This result is independent of the particular unimodal thermal response function used. We then use representative left-skewed, symmetric and right-skewed unimodal responses to illustrate how thermal response shape influences coexistence. Whereas the analytical balance condition is invariant, stronger ecological patterns-including asymmetries between warming and cooling and the location of the coexistence maximum for species with different thermal optima-depend on the assumed response shape. A qualitative comparison with classic pairwise Drosophila competition experiments at $19$ and ${25}^{\circ }C$ is consistent with one illustrative left-skewed parameter regime, but is not intended as a quantitative parameter fit. By separating structural predictions from illustrative thermal response effects, our framework provides a transparent way to connect organismal thermal biology with pairwise competitive coexistence while avoiding reliance on any single thermal performance model.