Estimating growth from length frequency distribution: comparison of ELEFAN and Bayesian approaches for red endeavour prawns (Metapenaeus ensis)

Using length frequency distribution data (LFD) is cost-effective for estimating somatic growth in fish or invertebrates as length data are relatively easy to obtain. The recently developed R packages TropFishR and fishboot extend classic ELEFAN (Electronic LEngth Frequency ANalysis) programs and include more powerful optimization procedures and a bootstrap method for estimating uncertainties. Yet, the fundamental functions require users to provide search conditions (e.g. upper and lower limits for each parameter, length-class size, number of length-classes for the calculation of moving average), which can significantly affect the results. In this paper, we compare the ELEFAN approach with a Bayesian approach in analysing LFD, employing both standard and seasonal von Bertalanffy growth functions. We apply both approaches to a commercially valuable but poorly studied red endeavour prawn (Metapenaeus ensis) harvested in Australia's Northern Prawn Fishery. Sensitivity tests on ELEFAN confirm that any change in search settings would affect the results. Simulation studies on Bayesian growth models show that L-inf and K can be accurately obtained even with modal progression of only one year-class and using non-informative priors. However, age information, including the theoretical age at length zero (t(0)), is difficult to estimate and requires LFD from multiple age classes and informative priors. The Bayesian models yield mean parameters of: L-inf = 36.56 mm (carapace length), K = 2.74 yr(-1), and t(0) = -0.02 yr for the males, and L-inf = 51.81 mm, K = 1.94 yr(-1), and t(0) = -0.02 yr for the females. Seasonal oscillation models fit the LFD better, but the improvement is small and the estimated season-related parameters have large variances.

Automated summary

Using length frequency distribution data (LFD) is a cost-effective way to estimate somatic growth in fish or invertebrates. This study compares the ELEFAN approach with a Bayesian approach in analyzing LFD and finds that the Bayesian method can accurately estimate L-inf and K, but estimating t(0) is more challenging.