Evaluating the most suitable nonlinear growth model for turbot (Scophthalmus maximus) in aquaculture 2 (weight application): Multi‐criteria model selection and growth prediction

Abstract

Seeking the most suitable model to describe the growth of turbot, we analysed growth data of two different turbot (Scophthalmus maximus) strains reared communally in a recirculating aquaculture system. We fitted 10 different nonlinear growth models to individual weight gain data (n = 2,010) during the grow‐out phase. Analyses were carried out for each strain, for sexes within strains and for a pooled data set containing both strains and sexes. To assess the model performance, three different criteria are used. Further, a growth‐simulation was performed to evaluate the shape of the generated curve. This way we could assess the capability of the models to predict future growth. The 3‐parametric Gompertz model achieved the best fit in 42.9% of all cases tested and the lowest Bayesian information criterion in 100% of cases. The model produced realistically shaped curves and asymptotic values matching the biological attributes of the species. In contrast, 5‐parametric functions projected unrealistically shaped curves and predicted improbable mature sizes. Our results show that increasing number of parameters do not lead to increasing goodness of fit, but tend to result in overfitting, and demonstrate the advantages of the 3‐parametric Gompertz model for describing the growth of turbot.

Determination of a predictive growth model for cultivated African catfish Clarias gariepinus (Burchell, 1882)

“…In order to be conclusive about which of the projections best fits the catfish growth data for a longer period, it is necessary to extend the experiment to a longer period. In this regard, we agree with Lugert et al (2019), who explicated that assuming a single suitable a priori model, in this case for C. gariepinus , is unlikely.…”

“…Although growth is a complex biological process, mathematical functions represent it empirically in a very precise way in terms of organism increases in size or weight gain over time, simply by relating these changes over time. Since there are a variety of models to describe growth, the best methodological route to select one of them is to compare their performance with the observed data and select the one with the best fit (Lugert et al, 2019). These models describe growth, and impreciseness can result in significant changes in the expected outcomes of the aquaculture systems.…”

“…gariepinus . Similarly, Lugert et al (2019) employed inferential statistics to determine which of 10 nonlinear models best represented the growth of farmed turbot ( Scophthalmus maximus ) and reported that the Gompertz model was the best. It is noteworthy that the parameters calculated for C .…”

“…Subsequently, according to the groups of tanks obtained from the U value (Theil's inequality coefficient), the five candidate models were fitted to the pooled data set: von Bertalanffy (Lugert et al, 2019), Gompertz (Wang & Zuidhof, 2004), Brody (1945), Richards (1959) and logistic (Bacaër, 2011; Sit & Poulin‐Costell, 1994). The growth models we compared were as follows:…”

“…These nonlinear equations present different biological interpretations related to initial conditions, growth rates and maximum body weight, all linked to economic aspects of production (Mello et al, 2015). Although the number of studies on prediction of fish size with age is skewed towards modelling the growth of fish species in natural (wild) environments, these models have equally been applied in forecasting for farmed fish, for example tilapia (Oreochromis niloticus; Ansah & Frimpong, 2015;Oliveira et al, 2013;Santos et al, 2007Santos et al, , 2013Zardin et al, 2019), common carp (Cyprinus carpio; Rosa et al, 1997), gibel carp (Carassius auratus gibelio; Yun et al, 2015), cachara (Pseudoplatystoma reticulatum) and cachapinta hybrid (P. reticulatum × P. corruscans ;Fantini et al, 2019), and turbot (Scophthalmus maximus; Baer et al, 2011;Lugert et al, 2014Lugert et al, , 2017Lugert et al, , 2019Wang & Ma, 2016), among others.…”