| Abstract: | A sex-age-structured population model with density dependence in the conversion of reproductive potentials into zygotes and in first year survivorship is described. The model has two equilibria; the smallest is mathematically unstable, and the origin and the larger equilibrium are locally stable. The population can thus go extinct for certain initial states, or if the two equilibria coincide. The ratio between the two equilibria can be regarded as a measure of the risk of extinction, since it is related to the chance that detrimental environmental conditions will cause the population to enter the region of attraction of the origin. In simple monoecious models, recovery to former levels is only possible provided that the population is not driven to extinction before harvesting effort is reduced. Ratios between the two unexploited equilibria, and between the stable unexploited equilibrium and the recruitment level at which the two equilibria coincide are given solely in terms of the degree of density dependence in the model. I show that the harvesting strategy which maximizes the equilibrium yield has a four age form, involving harvesting of at most two male and two female age classes. Out of ten commercial Pacific groundfish species, knife-edge selectivity sustainable yields of eight are at least 90% of ultimate sustainable yield (USY). With no effort restrictions, the range of lengths at first capture which achieve more than 60% of USY is narrow. When one of the sexes is not harvested, sustainable yield is between 20% and 80% of USY, but lowest when females are not harvested. |
