Estimating fish length and age at 50% maturity using a logistic type model

We propose a two-parameter logistic type model for estimating fish length and age at 50% maturity using the nonlinear least-squares method. The independent and dependent variables in the model are length (or age) and the corresponding arcsin-square-root transformed proportion of mature fish (P_i). The two parameters in the model are length (or age) at 50% maturity (L50 or A50) and instantaneous rate of maturation (K). A simulation study was conducted to examine the statistical behaviour of the proposed model in estimating L50 and K. The L50 was well estimated with a small bias (<1%) using the proposed model in all simulation cases. The K was well estimated (bias < 1%) when its true value and the variance in P_i were small. The proposed model was found to have relatively smaller bias than the probit and Lysack's methods in estimating L50 (or A50). To examine whether there are significant differences in maturation patterns between different groups of fish, we propose fitting the maturation data to the proposed model, and then conducting an analysis of residuals sum of squares to test whether there are significant differences in the fitted models.