Optimal fishery policy for size-specific,density-dependent population models

Optimal harvest policy is derived for a size-specific population model based on the continuity equation. In this model both growth and recruitment rates can depend on either the number of individuals of specific sizes in the population or the level of food available. Necessary conditions for values of fishing pressure and size limit that maximize the present value of the resource are obtained and are interpreted in economic terms. The general solution obtained here reduces to solutions obtained previously for some special cases: the single age-class model, and the linear age-dependent model. Solutions involving constant fishery policy are sought for several different, specific versions of the general model. In each of these versions a constant policy solution is not optimal. This implies that for a general, realistic model the policy that maximizes present value is a time-varying or pulse fishing policy. The theoretical and practical implications of the results are discussed in the light of existing results.