A generalized, nonlinear regression approach to the length-weight relationship of European perch (Perca fluviatilis L.) from the Polish coast of the southern Baltic Sea

Length-weight relationships in fish are important tools in fisheries management. The aim of this study was to estimate the growth curve W=aL^b for European perch, Perca fluviatilis L., from the Polish coast of the southern Baltic Sea (ICES Subdivision 25). The data set comprised the total weights and total lengths of 827 specimens caught during the 2011-2013 period. The mean total length (TL) was 169.4 mm (range 100.0-310.0 mm), and the mean total weight was 83.9 g (range 11.3-553.2 g). First, a multiplicative error term and a linear regression approach to loglog-transformed data was considered. The following estimated values for the parameters were obtained: a = exp(-12.5323), b=3.25, s=0.07862. This approach was not successful in solving the common heterogeneity problem of the length-weight data. A generalized nonlinear regression approach to the original data was more suitable in our case. The estimated model was W = 3.83×10^-6×L^3.238 + ε, with ε~norm(0,0.0281×E[W|L]^2×1.242). The estimated 95% confidence interval for b was (3.218, 3.259), and the growth was allometric. The perch from the coastal waters of the Baltic Sea (ICES Subdivision 25) was characterized by slightly better condition than that caught in inland waters and estuaries.