Estimation of size at sexual maturity: an evaluation of analytical and resampling procedures
Size at 50% maturity is commonly evaluated for wild popula- tions, but the uncertainty involved in such computation has been frequently overlooked in the application to marine fisheries. Here we evaluate three pro- cedures to obtain a confidence interval for size at 50% maturity, and in gen- eral for P% maturity: Fieller ’s analyti- cal method, nonparametric bootstrap, and a Monte Carlo algorithm. The three methods are compared in estimating size at 50% maturity (l50%) 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 indi- viduals. 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 l50%, 3) length and 4) shape of the confidence interval around l50%. Judging from cri- teria 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 Pleuron- codes 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 cen- tral Chile to test the hypothesis that they differed in size at 50% maturity and concluded that they were not sta- tistically different.