On the exponent in the von Bertalanffy growth model

Bertalanffy proposed the differential equation m´ ( t ) = p × m ( t ) a – q × m ( t ) for the description of the mass growth of animals as a function m ( t ) of time t . He suggested that the solution using the metabolic scaling exponent a = 2/3 (von Bertalanffy growth function VBGF) would be universal for vertebrates. Several authors questioned universality, as for certain species other models would provide a better fit. This paper reconsiders this question. Using the Akaike information criterion it proposes a testable definition of ‘weak universality’ for a taxonomic group of species. (It roughly means that a model has an acceptable fit to most data sets of that group.) This definition was applied to 60 data sets from literature (37 about fish and 23 about non-fish species) and for each dataset an optimal metabolic scaling exponent 0 ≤ a opt < 1 was identified, where the model function m ( t ) achieved the best fit to the data. Although in general this optimal exponent differed widely from a = 2/3 of the VBGF, the VBGF was weakly universal for fish, but not for non-fish. This observation supported the conjecture that the pattern of growth for fish may be distinct. The paper discusses this conjecture.