Abstract
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.
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17 June 2021
A Correction to this paper has been published: https://doi.org/10.1007/s11538-021-00916-1
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This work was made possible through continuation funding from the Research Experiences for Undergraduate Faculty program supported by the National Science Foundation through Division of Mathematical Sciences Grants 1620073 to the American Institute of Mathematics and 1620080 to Institute for Computational and Experimental Research in Mathematics. Richard Rebarber was partially supported by National Science Foundation Division of Mathematical Sciences Grant 1412598.
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Callahan, J., Eager, E., Rebarber, R. et al. Analysis of a Length-Structured Density-Dependent Model for Fish. Bull Math Biol 81, 3732–3753 (2019). https://doi.org/10.1007/s11538-019-00648-3
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DOI: https://doi.org/10.1007/s11538-019-00648-3