Zusammenfassung: Schaefer's model on the exploitation of a single species fish community obeying the logistic law of growth has been modified by adopting an alternative functional form for the harvest rate. The stability of the nontrivial steady state is discussed. The existence of a bionomic equilibrium is proved. The problem for optimal exploitation of the fishery is studied by using variational calculus. Some results are numerically computed to make a comparative study of Schaefer's model and the present one.

Zusammenfassung: Length-based population analyses have had a fairly long but not too successful history. These methods are required over a range of situations from when aging is impossible to when it is difficult or prohibitively expensive. There have been 3 sorts of approaches: 1) modal analysis to convert length frequencies to ages 2) age-length key enhancement and 3) imbedded growth models. The last group is what is generally known as length-based methods and the focus of this review. At the 1991 ICES Methods Working Group, 5 techniques were compared and these results are summarized. Two of these techniques, cohort slicing and length-based ADAPT, are applied to swordfish (Xiphias gladius ) data. The imbedded growth model for the former technique is the mean size at age while the latter uses the distribution of size at age. A new method is also presented which begins with cohort slicing then estimates numbers at age and enhances an inferred age-length key at each step of an iterative process.