Selecting optimal bin size to account for growth variability in Electronic LEngth Frequency ANalysis (ELEFAN)

Electronic LEngth Frequency ANalysis (ELEFAN) is a widely used method to fit von-Bertalanffy Growth Function (VBGF) using length frequency data for data-poor fisheries. However accuracy of this method depends on diverse assumptions, among which the variability of individual growth may be particularly influential. In addition, the selection of class interval of length frequency data, defined as bin size, is also considerable source of uncertainty. However, rare guidance exists on how to account for the growth variability and to select bin size. In this study, we considered the effects of growth variability and bin size together by testing whether appropriate bin size can reduce estimating bias due to growth variability. We used a Monte Carlo simulation framework to evaluate the performances of ELEFAN under scenarios of different bin size and levels of individual growth variability for 10 fish species. The results indicated that growth variability might result in large variations and biased estimation of growth parameters if the bin size was chosen arbitrarily. On the contrary, there was an optimal bin size for each species, which led to unbiased estimates even in a substantially high level of growth variability. Summarizing the optimal bin sizes of the 10 species, we proposed a rule of thumb to select optimal bin size (OBS) for the future applications of ELEFAN according to the maximum body length (OBS = 0.23 x L-max(0.6)) and age (OBS = 1.86 x (L-max/A)(0.45)) of fish species. The improvement of accuracy of VBGF parameter estimation will help to understand the growth characteristics and reduce the uncertainty for data-limited stock assessment methods.