Fig 1. Predicting the impact of fluctuating temperatures on organismal performance and ecological outcomes.

(A) A stereotypical TPC fit based on measurements in constant temperature environments. As temperature increases, performance initially also increases from a lower limit, then reaches its maximum value at the optimal temperature, and finally decreases to the upper limit. In some cases, this pattern also scales up to species interactions like disease transmission, often predicted by a mathematical model parameterized with organismal traits. (B) Nonlinear averaging predicts performance in fluctuating environments by assuming that performance (or ecological outcome) follows the constant temperature TPC and performance changes instantaneously with the environment. Fluctuations reduce predicted performance if the curve is decelerating or concave down (e.g., near the optimum), because the organism spends little time at the ideal temperature. Fluctuations increase predicted performance if the curve is accelerating or concave up. (C) The impact of temperature fluctuations and the ability of nonlinear averaging to accurately predict performance or ecological outcomes may depend on the timescale or predictability of the fluctuations. Thermal fluctuations can occur over “daily” (left column) or longer (right column) timescales, and fluctuations at both timescales may be either predictable (top row) or unpredictable (bottom row). Most studies focus on just 2 combinations of timescale and predictability: (i) predictable “daily” fluctuations and (iv) unpredictable fluctuations over larger timescales. (Note: fluctuations between the daily maximum and minimum temperatures [e.g., day vs. night; left column] are commonly called “daily” or “diurnal” temperature variation, although temperature is changing at the hourly timescale).