Modeling the Oxygen Consumption Rates in Pacific Salmon and Steelhead: Model Development

Abstract

We derived a series of models for estimating the standard metabolic rates, swimming costs, and total metabolic rates for sockeye salmon Oncorhynchus nerka and steelhead O. mykiss. The performance of these models was compared statistically and used to predict optimal cruising speeds. These predictions were tested with independent estimates of swimming speed obtained under field conditions. Standard metabolic rates were correlated with body mass and temperature. Swimming costs were correlated with body mass and swimming speed, whereas total metabolic rates were correlated with body mass, water temperature, and swimming speed. Swimming costs were also correlated with temperature and salinity in steelhead but not in sockeye salmon. Regression models accounted for 94–99% of the variance in standard metabolic rates, swimming costs, and total metabolic rates. The oxygen consumption rate models we derived for sockeye salmon were inadequate for describing oxygen consumption in other species of Pacific salmon, Oncorhynchus spp., indicating that the practice of borrowing parameters from closely related species can induce serious biases in model predictions. The models derived in this study also produced realistic estimates of swimming speed in sockeye salmon but not in steelhead. The models derived in this study appear to be useful in estimating swimming speed and total metabolic rates of sockeye salmon in the field but are not appropriate predictors for other species of Pacific salmon.

Notes

¹ The Arrhenius and Boltzmann equations are essentially the same, as the−E/k term of equation (1.2) is replaced by −E_a /R in the Arrhenius equation, where E_a is also an activation energy (although not equal to E) and R is the gas constant. The gas constant is equal to k · N_a , where N_a is the Avogadro number. Hence, E = E_a /N_a . Both equations also predict that the Q ₁₀ is a decreasing function of water temperature