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Gill size and temperature as governing factors in fish growth : A generalization of von Bertalanffy’s growth formula (2nd edition)

Pauly, D. (Daniel)

In von Bertalanffy's theory, growth is defined as the net result of two processes with opposite tendencies, one synthesizing native protein (anabolism), the other degrading the protein (catabolism). Both food and oxygen supply are needed for anabolism, and this investigation presents evidence suggesting that, in fishes, it is primarily oxygen, rather than food supply, which limits anabolism and growth performance. This is due chiefly to the fact that the respiratory area of fishes (the gills) do not grow, with increasing size, as fast as body weight, and to the fact that fish can store only very small amounts of oxygen. It is demonstrated that, as a rule, fishes able to reach a large size (e.g. tuna) tend to have gills growing in proportion to a power of weight close to unity9F 10, while small fishes (e.g. guppy) have gills growing in proportion to a power of weight close to 2/3. The von Bertalanffy growth formula (VBGF), whose derivation rests on the assumption of the universal validity of the ‘2/3 rule,’ is therefore considered to be a special case of a generalized formula (‘generalized VBGF’) which is derived here, and whose properties and applications are discussed. Various properties of the VBGF's parameters are discussed in detail, particularly the relationship between the values of K and estimates of mean environmental temperature, where a clear, regular pattern could be demonstrated, which is closely allied to Krogh's normal curve (of metabolism against temperature). Also, a close relationship between K and the asymptotic size of a large number of stocks is demonstrated, which further emphasizes the uniformity of growth patterns in fishes and which can be used to estimate growth parameters in certain stocks and assess the inter- relationships between various species, particularly through the use of a newly developed ‘auximetric grid.’ Potential applications for these theoretical considerations are discussed, particularly as the demonstrated uniformity of fish growth patterns and the established relationships allow for the estimation, in the field, of the growth parameters of tropical and other little-investigated fish stocks.

Text

2024-07-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/88603

Pauly, D. 2024. Gill size and temperature as governing factors in fish growth: A generalization of von Bertalanffy’s growth formula (2nd edition). Fisheries Centre Research Reports 32(2). 105 pp.

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