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...

Full description

Saved in:
Bibliographic Details
Published in:Bulletin of mathematical biology 2019-10, Vol.81 (10), p.3732-3753
Main Authors: Callahan, Jason, Eager, Eric, Rebarber, Richard, Strawbridge, Eva, Yuan, Shenglan
Format: Article
Language:English
Subjects:
Animals
Bass - growth & development
Bass - physiology
Biomass
Cell Biology
Computer Simulation
Density
Female
Fertility
Fish
Fish populations
Fishes - growth & development
Fishes - physiology
Introduced Species - statistics & numerical data
Life Sciences
Male
Mathematical analysis
Mathematical and Computational Biology
Mathematical Concepts
Mathematical models
Mathematics
Mathematics and Statistics
Matrix methods
Models, Biological
Morone americana
Nonlinear Dynamics
Original Article
Population
Population Density
Population Dynamics - statistics & numerical data
Population Growth
Structured matrices
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0092-8240
1522-9602
DOI:10.1007/s11538-019-00648-3