The Ultimate - Sustainable - Yield Problem in Nonlinear Age - Structured Populations

The Beverton-Holt theory of harvesting a multicohort fishery subject to constant recruitment, and the Leslie matrix harvesting model modified to include a nonlinear stock-recruitment relationship, are extended and shown to be related through the ultimate-sustainable-yield problem for an age-structured population. The well-known result that the optimal harvesting policy for the Leslie matrix model is bimodal is shown to hold for the Leslie matrix model modified to include an arbitrary stock-recruitment relationship, This conclusion extends a recent result of Reed (1979), who proved biomodality of the optimal harvesting strategy for the Leslie matrix model modified to include only compensatory stock-recruitment relationships. The paper concludes with a numerical example which demonstrates how the ultimate sustainable yield can be used as a standard of comparison for any sustainable-yield harvesting policy.