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.
size at maturity
Queen conch (Lobatus gigas) is an important food source and export product for Belize, where extraction is regulated by shell length (SL) and market clean weight (MCW) limits. However, lip thickness (LT) limits are used to manage juvenile mortality and reduce risk of growth overfishing in other countries. Empirical studies suggest relationships between LT and sexual maturity vary spatially and need to be determined locally. This study was conducted to determine the most reliable, easily measurable proxy indicator(s) of maturity and associated target size limits in L. gigas that can effectively restrict harvest of juveniles. Morphological measures (SL, LT, lip width, unprocessed meat weight, MCW, operculum dimensions), gonadosomatic index (GSI) and histological evaluations were recorded from L. gigas collected in PHMR before, during, and after the L. gigas closed season. Upon determining Period 2 (during closed season) as the peak reproductive period, relationships between these variables in Period 2 were examined. No relationship was found in males between SL and maturity, and was weak in females, whereas there were significant curvilinear relationships between LT and GSI for both sexes, suggesting urgent need to base size limits on LT not SL. LT at which 50% of the population was mature (LT50) was 15.51 mm for females and 12.33 mm for males, therefore a 16 mm LT limit is recommended. MCW of female L. gigas was also significantly related to GSI, indicating MCW may be an appropriate management tool in conjunction with LT as it can be measured at landing sites whereas shells are usually discarded at sea. However, MCW at which 50% of females were mature (MCW50) was 199 g and many individuals exceeding LT50 had MCW <199 g, suggesting the current 85 g MCW limit is too low to protect juveniles yet 199 g MCW limit would be too high to substitute the recommended LT limit at landing sites. To minimize short-term impacts yet maximize long-term benefits to fishers’ livelihoods, multi-stage adaptive management is recommended that integrates initial catch reductions, followed by introduction of size limits of 16 mm LT, and 150 g MCW. Adjustable LT and MCW limits determined by fishery simulation could later be introduced.