A sex-structured delayed recruitment model

A delay-difference model for a sex-structured population with delayed recruitment is presented. Constant-effort harvesting is introduced for examining the model's sensitivity to harvesting. Linear analyses about the steady states are performed under various parameter choices. The effects of the delay period, the survival parameter, and the harvesting effort on population stability are examined. It is shown that differences in the male and female delays to recruitment can give rise to very different stability diagrams. Our analyses indicate, for example, that a population with equal male and female delays to recruitment is the most robust to recruitment failures. Possible forms that the male and female recruitment functions could take are suggested and evaluated. Finally, the very encouraging result is obtained that maximum sustainable yield is attained at a stable steady-state population level.