@article{10.7287/peerj.preprints.3303v1,
title = {On the exponent in the von Bertalanffy growth model},
author = {Renner-Martin, Katharina and Brunner, Norbert and Kühleitner, Manfred and Nowak, Georg and Scheicher, Klaus},
year = 2017,
month = sep,
keywords = {multi-model inference, von Bertalanffy growth function (VBGF), metabolic scaling exponent, Akaike’s information criteria (AIC), weak universality},
abstract = {
Bertalanffy proposed the differential equation \textit{m´}(\textit{t}) = \textit{p} × \textit{ m } (\textit{t})\textit{\textsuperscript{ a }}–\textit{q} × \textit{ m } (\textit{t}) for the description of the mass growth of animals as a function \textit{m}(\textit{t}) of time \textit{t}. He suggested that the solution using the metabolic scaling exponent \textit{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 ≤ \textit{a\textsubscript{ opt }} < 1 was identified, where the model function \textit{m}(\textit{t}) achieved the best fit to the data. Although in general this optimal exponent differed widely from \textit{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.
},
volume = 5,
pages = {e3303v1},
journal = {PeerJ Preprints},
issn = {2167-9843},
url = {https://doi.org/10.7287/peerj.preprints.3303v1},
doi = {10.7287/peerj.preprints.3303v1}
}