The predictive power of empirical relationships describing size selectivity, with application to gadoid fish

Abstract

The use of empirical linear relationships between 50% retention length ( L 50%) and codend mesh size ( MS) of historical selectivity experiments has been suggested whenever selection data on a particular fish species are not readily available. However, when this procedure has been used in prediction, the predictive power of the fitted regression lines has been largely disregarded. Regression lines with large coefficients of determination (r 2) usually significant at α=0.05 or α=0.10, are considered appropriate, and the estimated regression coefficients are used to predict L 50% values for given mesh sizes without any consideration for prediction errors. We analyzed historical data of 689 selectivity experiments for 12 gadoid fish species and calculated an all-gadoids regression line as L 50%=−0.0831 + 0.344 MS( r 2=0.739). The predictive power of the regression was assessed by means of the ‘one item out’ cross-validation technique, and was found to be low in spite of the relatively high coefficient of determination. We investigated the effects of more homogeneous data sets on r 2 and predictive power by repeating the regression and cross-validation analyses on subsets including the results of selectivity experiments carried out on the same species, with the same experimental method (alternate-haul or covered codend) and codends of similar material. We found that (1) many simple linear models generally have low predictive powers in spite of their relatively large coefficients of determination, which reduces the value of their predictions for assessment or management purposes, and (2) linear regressions based on more homogeneous data subsets often display smaller prediction errors and larger coefficients of determination. Consequently, we suggest that the predictive power of empirical relationships describing size selectivity should be considered to select the regression line that provides more precise estimates of L 50%.