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

Abstract

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

ACKNOWLEDGMENTS

We thank K. Aydin and S. John for providing excellent feedback on manuscript drafts. Publication of this work was partially funded by the Joint Institute for the Study of the Atmosphere and Ocean under National Oceanic and Atmospheric Administration (NOAA) Cooperative Agreement NA10OAR4320148 and by the National Aeronautics and Space Administration's Applied Sciences Award NNX08AK72G. In-kind support for the project also came from the NOAA Alaska Fisheries Science Center and the NOAA Integrated Ecosystem Assessment Program. The findings and conclusions in the paper are those of the authors and do not necessarily represent the views of the NOAA National Marine Fisheries Service. Reference to trade names does not imply endorsement by the NOAA National Marine Fisheries Service.