Modeling allometric variation: lessons from the metabolic allometry of black carp (Mylopharyngodon piceus)

Abstract

I used linear and nonlinear regression to re-examine published data on the scaling of metabolic rate vs. body mass in an ontogenetic series of black carp (Mylopharyngodon piceus (Richardson, 1846)). My objective was to expose shortcomings of the conventional procedure for fitting statistical models to bivariate observations (i.e., the procedure that is widely attributed to J.S. Huxley) and simultaneously to outline a more general and utilitarian protocol for analyzing bivariate data in studies of allometry. Authors of the original study on carp reported exponents of 0.83 and 0.78 for two-parameter power functions fitted to observations for resting metabolism and maximum metabolism, respectively. However, metabolic scaling in these fishes actually is described best by straight lines having positive intercepts with the Y axis. The allometric exponent is 1 for a straight line, so interpretations from the current analyses differ substantially from those reached in the original investigation. Contemporary theories for the evolution of optimal body size (e.g., the Metabolic Theory of Ecology) are based on patterns of metabolic allometry that have been estimated by the conventional analytical method. Thus, the current investigation raises questions about generally accepted patterns of metabolic allometry and theoretical models based upon them.