The mathematics of thermal sub-optimality: Nonlinear regression characterization of thermal performance of reptile metabolic rates
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Although several approaches have been suggested, there is no broadly accepted single approach for quantitative characterization of thermal performance in ectotherms. I sought to identify the most appropriate non-linear function with which to represent thermal performance of ectothermic metabolic rate, and to interrogate the biological relevance of the thermal parameters of this function. I used published data for exercise-induced metabolic rates of eight species of reptile from a broad phylogenetic base and global distribution. Using an Akaike Information Criterion, I compared 12 different models proposed to characterize thermal performance adapted from a broad range of disciplines, finding that a beta-distribution model described the reptile metabolic rate data most parsimoniously. Using the beta-distribution model, unique functions were parameterized for each species. Four parameters were extracted from each species-specific fit: the temperature coincident with the peak of the thermal performance curve, T opt ; the point at which the function intersected the x-axis, CT max ; and two points indicative of thermal breadth, T d(lower) and T d(upper) . There was a positive relationship between the species’ preferred body temperatures (T pref ) reported in the scientific literature and both T opt and T d(lower) extracted from the species-specific beta functions. While T d(lower) estimates were not different to published T pref values, T opt estimates were statistically higher than T pref . This is consistent with previous observations that the point of peak performance does not match T pref . The predicted CT max also correlated well with published values. The model in its current form was not able to estimate CT min , and this parameter was not explored here, but should be in future research. By providing a quantitative description of the thermal performance, the beta-distribution function offers a new theoretical basis for thermal optimality. I contend that T pref aligns with the mathematical threshold T d(lower) , where metabolic rate is at its maximum prior to thermal inhibition.
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