A method to identify bimodal weight–length relations: Possible ontogenetic diet and/or metabolism shift effects in Anguilla anguilla (actinopterygii: Anguilliformes: Anguillidae)

Background. The power function W = a.L-b is commonly used to describe the weight-length (W-L) relation (WLR) of fish. Smaller/younger specimens may present different WLR from larger/older ones, introducing errors in the derivation of WLR of the total population. This difference appears through a breakpoint in the log-log plot of W-L data and can be justified due to biological factors or due to errors in the sampling procedure. The aim of the study is to propose a bilinear model (LinBiExp) that identifies the specific coordinates of the breakpoint in the log-transformed W-L measurements.Materials and methods. The analysis was performed using 2627 W-L measurements of European eel, Anguilla anguilla (Linnaeus, 1758), from the Comacchio Lagoon (Italy). The bilinearity produced by LinBiExp model was verified through comparison of slopes and intercepts (ANOVA) of the two linear segments and through the 95% intervals of the highest posterior density (HPD) distribution of breakpoint coordinates estimated by bootstrap regression of LinBiExp. Additionally, gut content analysis was performed in order to detect any diet shift in order to justify the existence of the breakpoint.Results. The LinBiExp function identified the breakpoint coordinates (L-t, W-t) = (28.9 cm, 35.9 g). The ANOVA showed that there was a statistically significant difference between the slopes and between the intercepts of the two linear segments at 99.9% confidence level. The 95% HPD intervals of L-t and W-t were 28.4-29.4 cm and 34.5-38.0 g, respectively, based on 10 000 bootstrap estimates. The gut content analysis showed inclusion of other fish preys in the diet of eels when their weight and length exceeded the coordinates of the breakpoint in W-L data.Conclusion. The estimated breakpoint for the specific dataset was justified by the possible interrelation of ontogenetic diet shift with other metabolic processes (e.g., beginning of sexual maturation). The study showed that the LinBiExp function can be a valuable tool for detecting the absolute coordinates of a breakpoint in log-transformed W-L data, while the presented methodology can increase the robustness of weight-length analysis of fishes using the typical power function.