Analysis of a Length-Structured Density-Dependent Model for Fish

We present a length-structured matrix model for fish populations in which the probability that a fish grows into the next length class is a decreasing nonlinear function of the total biomass of the population. We present mathematical results classifying the dynamics that this density-dependent model predicts. We illustrate these results with numerical simulations for an invasive white perch population and show how the mathematical results can be used to predict the persistence and/or boundedness of the population as well as an equilibrium structure that is dominated by small fish. We illustrate the results with management recommendations for an invasive white perch population.