A Density-dependent Function for Fishing Mortality Rate and a Method for Determining Elements of a Leslie Matrix with Density-dependent Parameters

Abstract

Abstract A density-dependent function for the instantaneous fishing mortality rate is presented. It is shown that this function may be readily incorporated into the age-specific probability of survival in a Leslie-matrix population model. A method is presented for indirectly determining the probability of survival for age-class 0 of a fish population using a density-dependent Leslie matrix. The method involves the two constraints that the population be at equilibrium and that the index of absolute population size in the density-dependent function be assigned a value. In addition, given the probability of survival for age-class 0, it is shown that the probability of survival through a selected life stage within age-class 0 can be indirectly determined. Three problems in modeling a fish population using a Leslie model are discussed in light of the difficulties involved in modeling density dependence due to insufficient information and lack of understanding concerning density-dependent phenomena.