A general population dynamics theory for largemouth bass fisheries

Abstract

Resolution of the main issues in largemouth bass management will require the ability to predict the effects of exploitation on population structure, optimally select size limits, relate bass population structure to prey population structure, and predict the effects of fluctuations in recruitment on production and yield. A general model of population structure was developed for use in studying these problems.

The model was derived by examining the relationship between life history and population structure. Life history processes are described as mixed continuous and jump stochastic processes. The model was derived in two forms, an integro-differential equation and a stochastic integral equation, which include all of the classical continuous-time population models as special cases.

Two general results concerning the model were proven. First, the stochastic integral equation was shown to predict the same expected population structure as a deterministic model using average birth and death rates whenever the processes are uncorrelated. However, it is very unlikely that birth rate, death rate, and density will be independent, so the stochastic and deterministic models will generally diverge. Second, it was shown that with density-independence the expected population structure in the stochastic model is asymptotically stable.

Special cases of the model were used to illustrate the possible effects of exploitation on average catchability and population structure. Methods for calculation of optimal length limits and production and yield were illustrated for simple cases. Use of the full power of the model, however, must await more detailed description of factors influencing mortality and growth, especially the effect of the density and size structure of available prey.