Abstract
In many species, like the Cape Rock Lobster (Jasus lalandii), the life cycles of males and females differ. This may motivate the use of two-sex models in a stock-assessment analysis. It is also true for this resource, that juveniles do not reach sexual maturity immediately. Therefore a delay-difference model is appropriate. In this study we follow a bio-economic approach and use a two-sex delay-difference model to determine a maximum economic yield strategy. Thus we determine an economic optimum steady state solution at which to harvest this resource subject to the biological constraints of the species.
Highlights
In our attempts to model the population structure of species it is often necessary to include the entire life history of the population, as some events do have an immediate and homogeneous long term impact
A natural way to model these long term effects on the population dynamics is by using delay difference equations
Sexual dimorphism in fish species is of significance in population dynamics, as for instance the growth rate of the two sexes may differ
Summary
In our attempts to model the population structure of species it is often necessary to include the entire life history of the population, as some events do have an immediate and homogeneous long term impact. A natural way to model these long term effects on the population dynamics is by using delay difference equations. The use of such discrete time population models is popular in fishery management strategies as is the case, for example, with the Pacific salmon fishery [5]. As discussed by Caswell and Weeks (1986) the male mortality of humans almost always exceeds female mortality They addressed some other significant differences among sexes in nature. Sexual dimorphism in fish species is of significance in population dynamics, as for instance the growth rate of the two sexes may differ. As is the case for the monoecious species (not shown here) periodic solutions result for specific parameter values.
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