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

Analytic models for how species will respond to climate change can highlight key parameter dependencies. By mapping equations for population dynamics onto corresponding well-studied problems from quantum mechanics 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. Conservation measures to support range-shifting populations may have most benefit near their environmental optimum or where the environmental dependence is shallow, irrespective of whether this is the ‘leading’ or ‘trailing’ edge. A metapopulation simulation corroborates our results. ### Competing Interest Statement The authors have declared no competing interest.