On the exponent in the von Bertalanffy growth model
- Published
- Accepted
- Subject Areas
- Agricultural Science, Aquaculture, Fisheries and Fish Science, Computational Biology, Mathematical Biology
- Keywords
- multi-model inference, von Bertalanffy growth function (VBGF), metabolic scaling exponent, Akaike’s information criteria (AIC), weak universality
- Copyright
- © 2017 Renner-Martin et al.
- Licence
- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Preprints) and either DOI or URL of the article must be cited.
- Cite this article
- 2017. On the exponent in the von Bertalanffy growth model. PeerJ Preprints 5:e3303v1 https://doi.org/10.7287/peerj.preprints.3303v1
Abstract
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.
Author Comment
This is a submission to PeerJ for review.