Adaptation of thermal reaction norms in constant and fluctuating environments

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Thermal reaction norms depict how temperature influences biological performances, thus also known as thermal performance curves (TPCs). Arguably, the interplay of the thermal environment and the TPC can shape the strength of natural selection, thereby driving the long-term evolution of the TPC. We develop a Lotka-Volterra model, using adaptive dynamics (AD), to investigate how constant versus periodically fluctuating environmental temperatures drive the TPC adaptation. To formulate invasion fitness under fluctuating selection, we assume that the intrinsic rate of growth and carrying capacity to be temperature dependent, and also that the competition coefficient from one individual to another is proportional to the ratio of their beta-distribution-shaped thermal performances at the current environmental temperature. Results show that, under a constant temperature, the optimal temperature of the TPC evolves to align perfectly with the environmental temperature, with the TPC breadth shrinking to zero, reflecting local adaptation to complete thermal specialisation. In fluctuating thermal environments, adaptation produces broader TPCs, with their optimal temperature potentially mismatching the average environmental temperature. When the TPC’s optimal temperature matches the average temperature, large temperature fluctuations lead to broad TPCs (thermal generalisation). Our model also shows the emergence of bimodal TPCs under rapid and large temperature fluctuations, indicating adaptation to extreme temperatures and potentially a divergence of thermal strategies within the population. Our theoretical model has demonstrated that adaptation of TPCs in periodic thermal regimes promotes the evolution of thermal generalists and possible character divergence, compared to complete thermal specialisation in constant environments.