Beyond Thermal Performance Curves: Modeling Time-Dependent Effects of Thermal Stress on Ectotherm Growth Rates.

Thermal performance curves have been widely used to model the ecological responses of ectotherms to variable thermal environments and climate change. Such models ignore the effects of time dependence-the temporal pattern and duration of temperature exposure-on performance. We developed and solved a simple mathematical model for growth rate of ectotherms, combining thermal performance curves for ingestion rate with the temporal dynamics of gene expression and protein production in response to high temperatures to predict temporal patterns of growth rate in constant and diurnally fluctuating temperatures. We used the model to explore the effects of heat shock proteins on larval growth rates of Manduca sexta. The model correctly captures two empirical patterns for larval growth rate: first, maximal growth rate and optimal temperature decline with increasing duration of temperature exposure; second, mean growth rates decline with time in diurnally fluctuating temperatures at higher mean temperatures. These qualitative results apply broadly to cases where proteins or other molecules produced in response to high temperatures reduce growth rates. We discuss some of the critical assumptions and predictions of the model and suggest potential extensions and alternatives. Incorporating time-dependent effects will be essential for making more realistic predictions about the physiological and ecological consequences of temperature fluctuations and climate change.