Numerical Integration of Temperature‐Dependent Functions in Bioenergetics Models to Avoid Overestimation of Fish Growth

The Wisconsin bioenergetics model is widely used to evaluate the effects of environmental conditions, trophic interactions, and human‐mediated alterations to physical and trophodynamic processes on the growth and survival of individual fish species. In particular, bioenergetics models are increasingly applied to evaluate conditions that vary on subdaily time steps, such as vertical migrations that influence thermal experience and fluvial alterations that increase diurnal temperature variability. However, because the algorithms that describe the relationship between temperature and physiological rates are often nonlinear, using inputs of daily mean temperatures can result in underestimation or overestimation of growth and energetic demand. We used simulations of daily and subdaily models of Chinook Salmon Oncorhynchus tshawytscha as an example to demonstrate that the nonlinear, temperature‐dependent algorithms for consumption and respiration induce large differences in growth between constant‐ and fluctuating‐temperature conditions (despite the same mean daily temperature); these differences increase with high diurnal variability and as temperatures approach the thermal optimum for the species. To correct for model bias in growth, we propose an integrated temperature‐scaling algorithm that allows application of the daily model to systems where daily temperatures exhibit considerable subdaily variation. This approach can also be used for any bioenergetics model that includes nonlinear, temperature‐dependent algorithms and should be considered when modeled temperatures approach inflection points in nonlinear relationships. Received February 11, 2015; accepted September 8, 2015