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A partial differential equation model of changing sizes and numbers in a cohort of juvenile fish

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Numbers and lengths of young crappie were measured over a 20-week period in a Tennessee River reservoir. From these data, the average length at the swimming interval and growth rate were computed. A partial differential equation model was formulated for changes in length distribution through time. The equation was solved analytically and this solution used to predict the numbers by length class through time, given an initial known recruitment or swim-up rate. The simulated numbers agreed in considerable detail with the observations, indicating that the model accurately reflected the basic population mechanics involved. This suggests the model can be used to predict impacts to the fish population of size-dependent mortality caused by man, such as impingement on power plant intake screens.

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Authors and Affiliations

  1. Environmental Sciences Division, Oak Ridge National Laboratory (operated by Union Carbide Corporation under contract W-7405-eng-26 with the U.S. Department of Energy), 37830, Oak Ridge, Tennessee, U.S.A.

    Donald L. DeAnglis

  2. Office of Natural Resources, Tennessee Valley Authority, 37828, Norris, Tennessee, U.S.A.

    Peter A. Hackney & Jane C. Webb

Authors
  1. Donald L. DeAnglis
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  2. Peter A. Hackney
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  3. Jane C. Webb
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DeAnglis, D.L., Hackney, P.A. & Webb, J.C. A partial differential equation model of changing sizes and numbers in a cohort of juvenile fish. Environ Biol Fish 5, 261–266 (1980). https://doi.org/10.1007/BF00005361

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  • DOI: https://doi.org/10.1007/BF00005361

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