Zusammenfassung: In mathematics, the age-length key method is an estimating method for the ratio of each distribution in a mixture of distributions. Although the maximum likelihood method is the principle of this estimation, this model is a nonlinear model with a restrictive condition. At first, Hasselblad solved this model by using a new iteration method with a computer. Although his method was regarded as the steepest descent method or EM algorithm, it is proved to be an application of Lagrange's indeterminate multiplier method to the iteration method. Nowadays, there are other useful algorithms of optimization, especially Marquardt's method, for this estimation.

Zusammenfassung: The authors simulated length-frequency distributions for 3-, 7-, and 13-age-class exploited populations (Peprilus triacanthus, Gadus morhua, Paralichthys dentatus, Pomatomus saltatrix ) to compare the performance of Shepherd's length composition analysis (SRLCA) and MULTIFAN in resolving the distributions to age frequencies. The length distributions were characterized by von Bertalanffy growth, variable recruitment, variable mortality, partial selectivity of fishing gear for the youngest age-groups, and a length-dependent trend in the standard deviation in length at age. Comparative performance of SRLCA and MULTIFAN was assessed quantitatively by using the Kolmogorov-Smirnov cumulative distribution test to compare calculated proportions at age with the simulated values. Shepherd's analysis provided a good return for the amount of computational resources invested, with limited subjective user input. In contrast, MULTIFAN offered a much more complex but powerful estimation technique, and performed consistently better than SRLCA in matching the simulated proportions at age.

Zusammenfassung: We compared the von Bertalanffy growth function (VBGF) and five polynormial functions (PF) in modelling fish growth for 16 populations comprising six species of freshwater fishes. Ranked results of the variance explained by each growth function indicated that VBGF described growth data better than three- and four-parameter polynomial functions. Log-transforming length and age greatly improved the goodness-of-fit of the three-parameter polynomial function. Statistical comparison of growth between populations or sexes was done using a general linear model for polynomial functions. The VBGF proved to be the best growth model for all 16 populations.