Application ofvon Bertalanffy's equation to Nile tilapia Oreochromis niloticus growth in aquaculture experiments.

Abstract

Growth equations have not been widely applied in aquaculture, but optimum length of a growth cycle is determined by considering the difference between rate of growth and cost. An asymptotic growth model, such as von Bertalanffy's, is useful for this purpose. The initial value solution of von Bertalanffy's equation which uses fish size stocked as a starting value and does not require an estimate of fish age at stocking, is easier to fit to growth data compared to the traditional solution which uses a theoretical fish age at zero size. The initial value solutions for growth in both length and weight fit O. niloticus growth data well in terms of residual plots. For growth in length, average mean square error was 0.723 (range 0.062-3.026). A multivariate analysis of variance model was applied to experiments in Thailand and Honduras to examine season and fertilization treatment effects on growth described by asymptotic fish size (L$\sb{\rm inf}$, W$\sb{\rm inf}$), the growth coefficient (K), maximum rate of growth in weight (Max(t)) and time at this maximum (I(t)). The effect of dry season compared to wet season was to increase L$\sb{\rm inf}$, W$\sb{\rm inf}$, and I(t), and to decrease K and Max(t). In Thailand, the effect of organic compared to inorganic fertilization was to increase L$\sb{\rm inf}$ and W$\sb{\rm inf}$, and decrease K, with no effect on I(t) or Max(t). In Honduras, the effect of increasing organic fertilization was to increase L$\sb{\rm inf}$, W$\sb{\rm inf}$ and Max(t), with no effect on K or I(t). Precision of growth parameter estimates increases rapidly with number of fish sampled, sampling frequency and number of ponds sampled; however, precision is higher for the traditional solution than for the initial value solution. Precision of growth parameter estimates was more sensitive to changes in the growth coefficient variation than to changes in asymptotic length variation; this result may not depend on correlation between L$\sb{\rm inf}$ and K or the growth model. A variable growth rate modification of the initial value solution was developed to explain growth rate oscillations observed in several experiments. The modified model gave a better fit than the initial value solution. For growth in length, mean square error values decreased from 0.33 (range.248-.467) to 0.27 (range 0.17-3.04). The variable growth rate model provides the best growth parameter estimates for aquaculture.