Schrödinger’s range-shifting cat: analytic predictions for the effect of asymmetric environmental performance on climate change responses

Abstract

Analytic models for how species will respond to climate change can highlight key parameter dependencies. By mapping equations for population dynamics onto corresponding problems from quantum mechanics with known solutions we derive analytical results for the frequently observed case of asymmetric environmental response curves. We derive expressions in terms of parameters representing climate velocity, dispersal rate, maximum growth rate, niche width, high-frequency climate variability and environmental performance curve skew for three key responses: 1) population persistence, 2) lag between range displacement and climate displacement, 3) location of maximum population sensitivity. Surprisingly, under our model assumptions, the direction of performance curve asymmetry does not strongly contribute to either persistence or lags. A simple metapopulation simulation corroborated this result. Measures to support range-shifting populations may have most benefit where the environmental dependence is shallow, irrespective of whether this is the 'leading' or 'trailing' edge. Our results introduce new tools to ecology and illustrate the continued role of analytic theory.