Fitting growth with the von Bertalanffy growth function: a comparison of three approaches of multivariate analysis of fish growth in aquaculture experiments

Abstract

Three approaches for multivariate analysis of ¢sh growth in aquaculture experiments with Nile tilapia (Oreochromis niloticus niloticus L.) based on the von Bertalan¡y growth curve are presented and compared. The approaches are: an extended Gullandand-Holt (GH) plot, a forced extended GH plot and a multilinear regression analysis for the growth parameter K. All three models provide valuable insight into the major environmental factors in£uencing the daily growth rate and explain 28^46% of the variance of the observed daily growth rate of the used data set. For all three methods, the modelled parameter is sig-ni¢cantly related to the net yield of Nile tilapia and can, therefore, be used for the predictive modelling of management scenarios. The extended GH plot loads the in£uence of environmental parameters upon L 1 , while the forced extended GH plot and Direct ¢tting of K load the in£uence on the growth parameter K. The latter is more in the tradition of aquaculture research. But the forced extended GH plot and Direct ¢tting of K can only be applied if L 1 of the cultured species is known, as the selected L 1 in£uences the variance in the regression variables.

Determining Individual Variation in Growth and Its Implication for Life-History and Population Processes Using the Empirical Bayes Method

“…At the population or group level, the correlation between and k obtained from the Hessian estimated at maximum likelihood estimates of the parameters is usually negative. This correlation does not offer any biological insights, since it occurs because different combinations of and k can basically provide the same fit to the data, in particular when the range of ages is limited [58] , [82] , [83] . In other words, by slightly increasing or decreasing and k in opposite directions, the same likelihood is obtained.…”

Effects of dietary protein levels on the long-term growth response and fitting growth models of gibel carp (Carassius auratus gibelio)

“…Growth curves describe the regular changes in live weight or in a particular body part of an animal with increasing age ( Ricker, 1979 , Pauly, 1981 , He and Stewart, 2002 ). In animals, growth curves are generally S-shaped and based on long-term growth datasets ( De Graaf and Prein, 2005 , Ersoy et al., 2006 , Yang et al., 2006 ). Gompertz, logistic, Richards and von Bertalanffy models are often used to fit growth curves of fish, especially for the time-growth response estimation, which much better than ANOVA or broken-line models ( Jiang and Qin, 1996 , Gamito, 1997 , Gamito, 1998 , He and Stewart, 2002 , Hernandez-Llamas and Ratkowsky, 2004 , Ersoy et al., 2006 , Russo et al., 2009 ).…”

“…Studies on long-term growth curves of animals are of major importance for dynamically understanding the process of growth and responses on dietary nutrient density as well. The resulting information can be easily used to guide feeding and management programs ( De Graaf and Prein, 2005 , Yang et al., 2006 , Russo et al., 2009 ).…”

Using Observed Residual Error Structure Yields the Best Estimates of Individual Growth Parameters

“…Stock biomass is related to individual growth, and fish grow in response to seasonal and local environmental conditions in timing or location [1,2]. The importance is reflected in the large amount of scientific literature on individual growth in fisheries, aquaculture, and ecological studies [3][4][5][6].…”