MEPS 282:237-244 (2004)  -  doi:10.3354/meps282237

Growth of fishes, crustaceans and molluscs: estimation of the von Bertalanffy, Logistic, Gompertz and Richards curves and a new growth model

Alfredo Hernandez-Llamas1,*, David A. Ratkowsky2

1Centro de Investigaciones Biológicas del Noroeste (CIBNOR), Apdo. Postal 128, La Paz, B.C.S. 23000, Mexico 2School of Agricultural Science, University of Tasmania, Private Bag 54, Hobart, Tasmania 7001, Australia

ABSTRACT: A total of 16 data sets on wild and cultivated fishes, crustaceans and molluscs were used to test and compare conventional growth curves (von Bertalanffy, Logistic, Gompertz and Richards) and a new growth model. Statistical properties for estimation of the models were evaluated and compared to determine suitability. The absolute value of the Hougaard measure of skewness of parameter estimates (h) was used as the criterion to evaluate statistical behavior of the models. For conventional curves, the cases where the estimates were severely skewed or contained considerable nonlinearity (h > 0.15) were: von Bertalanffy (93.5%), Logistic (87.5%), Gompertz (85.1%) and Richards (97.6%). Depending on the parameterization used in the new model, 87.5 to 91.6% had negligible skewness (h ≤ 0.1), indicating desirable close-to-linear behavior and better performance than conventional growth curves. The poor statistical properties for estimation of conventional growth curves call for a critical reconsideration of their indiscriminate use to model growth of fishes, crustaceans and molluscs. The new model can be reliably used to analyze growth of organisms under a wide variety of situations and to derive statistical inferences of possible relations of its parameters with ecological or management variables.


KEY WORDS: Growth modeling · von Bertalanffy · Logistic · Gompertz · Richards


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