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Zur Mathematik des tierischen Wachstums
On the mathematics of animal growth. III. Testing the Gompertz function as growth formula usingSiliqua patula andThunnus thynnus (Pisces)
III. Testung der Gompertz-Funktion als Wachstumsformel am Beispiel vonSiliqua patula (Bivalvia) undThunnus thynnus (Pisces)
Helgoländer wissenschaftliche Meeresuntersuchungen volume 31, pages 499–526 (1978)
Abstract
The parameters of the Gompertz function, the Bertalanffy function, and the reciprocal function (Krüger, 1962) are calculated for comparison using growth data obtained by Weymouth et al. (1930, 1931) for the razor clam from ten localities and the tuna fish. An new method is employed for the determination of growth parameters under the conditions of linear relations between the power ofe and the linear values of size in the Bertalanffy function and its natural logarithm in the Gompertz function. Both equations may therefore be solved by the well known method of linear regressions analysis. The method delivering optimal parameters for the Bertalanffy and the Gompertz function is described in a methodological chapter. Compared to the other functions the Gompertz delivers the best results for the growth curves of the arctic mussels including an inflection point. For curves without inflection points less good results are obtained. Deviations in the numeration of age are compensated in the Gompertz function by the parameterB. This parameter represents the difference between the natural logarithms of the upper limit size and the size at the age zero (normally corresponding to the size at birth). The parameterC includes the description of the curvature of the growth curve. A disadvantage of the Gompertz function is, that the upper limit of the equation is very near to the highest numbers evaluated and may be exceeded by real observations. A disadvantage of the reciprocal function is that the calculated inflection point does not correspond to the real inflection point. The result obtained for the relationship between length and weight of tuna fish show that the Gompertz function is exactly compatible with the allometric formula. It delivers for the summing up of the allometric formula the same solution as that reached by the reciprocal function. The three formulas employed are of the same structure, differing only in the use of linear numbers, logarithms or powers ofe. They deliver good approximations of growth data, but cannot be regarded as exact solutions for the mathematica description of growth curves.
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Krüger, F. Zur Mathematik des tierischen Wachstums. Helgolander Wiss. Meeresunters 31, 499–526 (1978). https://doi.org/10.1007/BF02189497
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DOI: https://doi.org/10.1007/BF02189497