Modeling framework for establishing the power law between length and weight of fishes and a meta-analysis for validation of LWRs for six commercially important marine fishes from the northwestern Bay of Bengal

Accurate and unbiased modeling of length-weight relationship (LWR) is essential for precise estimation of biomass from length-based abundance data for aquatic ecosystem modeling and developing resource management strategies for the sustainable utilization of aquatic living resources. The present study was conducted to develop the best modeling method for establishing the relationship between the length and weight of the fish, giving adequate priority to the variance distribution structure, which is often overlooked. Three modeling methods viz. (1) NLM: nonlinear model with additive homogeneous variance structure, (2) wNLM: weighted nonlinear model with additive heterogeneous power variance structure and (3) LM: log-transformed linear model with multiplicative heterogeneous variance structure in untransformed scale were evaluated for their performance in accurately estimating the model parameters and their confidence intervals. As variance in fish weight increases with the increase in fish size, usually, a multiplicative heterogeneous variance structure is assumed while explaining the relationship between length and weight, which was evidenced from the residual plot of NLM. As the data did not follow the additive homogenous variance assumption of NLM, the worst performance (highest AIC and BIC) was obtained when NLM was used. The variance distribution structure could be homogenized and normalized in three out of six fishes (i.e., Plicofollis layardi, Cynoglossus arel, Otolithes ruber) investigated in the study using LM, resulting in superior performance (lowest AIC and BIC) among the three models. For two out of three remaining species (i.e., Nemipterus japonicus and Parastromateus niger) for which the variance distribution cannot be normalized by log transformation (LM), the residuals could be homogenized and normalized by the wNLM which was evidenced by the lowest AIC and BIC for the model. Even for the species (i.e., Pampus argenteus), where the residuals could not be normalized by any of the models, better performance was obtained from wNLM. A meta-analysis was performed to validate the hitherto available information on the LWRs of these six species by regressing the regression parameters [log(a) vs. b] of the available LWRs and by computing the form factors. The erroneous LWRs were identified as doubtful reports by carefully scrutinizing the outliers obtained from Cook’s distance method and subsequently validating them by observing their dispersion from modeled prediction intervals (PI) and interquartile range (IQR) based outlier detection methods using the form factor analysis. The study presents the decision support framework for an appropriate modeling approach while dealing with certain assumptions such as variance normality and homoscedasticity. The study also describes a combined approach for the validation of derived LWRs by a comprehensive meta-analysis.