A nonautonomous size-dependent model of fish population dynamics

The purpose of this work is to develop a model which describes the dynamics of a fish population in terms of biological processes. A first order partial differential equation which relates birth, growth, and mortality to size and the number of individuals present is developed to model a single species. This equation is then solved for size- and time-dependent growth and mortality functions.

The single species model is extended to model a two species system. Competitive, mutualistic, and predator-prey systems are all considered, and conditions are found under which the model has a unique solution. The numerical solution is discussed, along with several possible simplifications of the model. The contraction mapping method of solving this system can be extended to a system of n species. Although the model was originally developed to model fish populations. it may also be used, without modification; to model the population dynamics of radically different species.