Estimation of size at sexual maturity: An evaluation of analytical and resampling procedures

Abstract

Size at 50% maturity is commonly evaluated for wild populations, but the uncertainty involved in such computation has been frequently overlooked in the application to marine fisheries. Here we evaluate three procedures to obtain a confidence interval for size at 50% maturity, and in general for P% maturity: Fieller's analytical method, nonparametric bootstrap, and a Monte Carlo algorithm. The three methods are compared in estimating size at 50% maturity (l(50%)) by using simulated data from an age-structured population, with von Bertalanffy growth and constant natural mortality, for sample sizes of 500 to 10,000 individuals. Performance was assessed by using four criteria: 1) the proportion of times that the confidence interval did contain the true and known size at 50% maturity, 2) bias in estimating l(50%), 3) length and 4) shape of the confidence interval around l(50%). Judging from criteria 2-4, the three methods performed equally well, but in criterion 1, the Monte Carlo method outperformed the bootstrap and Fieller methods with a frequency remaining very close to the nominal 95% at all sample sizes. The Monte Carlo method was also robust to variations in natural mortality rate (M), although with lengthier and more asymmetric confidence intervals as M increased. This method was applied to two sets of real data. First, we used data from the squat lobster Pleuroncodes monodon with several levels of proportion mature, so that a confidence interval for the whole maturity curve could be outlined. Second, we compared two samples of the anchovy Engraulis ringens from different localities in central Chile to test the hypothesis that they differed in size at 50% maturity and concluded that they were not statistically different.