Density-Dependent Leslie Matrix Modeling for Logistic Populations With Steady-Stae Distribution Control
Grade Level at Time of Presentation
Junior
Major
Mathematics and Physics
Minor
-
Institution
Western Kentucky University
KY House District #
61
KY Senate District #
17
Faculty Advisor/ Mentor
Bruce Kessler, PhD
Department
Dept. of Mathematics
Abstract
The Leslie matrix model allows for the discrete modeling of population age-groups whose total population grows exponentially. Many attempts have been made to adapt this model to a logistic model with a carrying capacity, with mixed results. This poster describes a new model for logistic populations that tracks age-group populations with repeated multiplication of a density-dependent matrix constructed from an original Leslie matrix, the chosen carrying capacity of the model, and a chosen steady-state age-group distribution. The total populations from the model converge to a discrete logistic model with the same initial population and carrying capacity, and growth rate equal to the dominant eigenvalue of the Leslie matrix minus 1.
Density-Dependent Leslie Matrix Modeling for Logistic Populations With Steady-Stae Distribution Control
The Leslie matrix model allows for the discrete modeling of population age-groups whose total population grows exponentially. Many attempts have been made to adapt this model to a logistic model with a carrying capacity, with mixed results. This poster describes a new model for logistic populations that tracks age-group populations with repeated multiplication of a density-dependent matrix constructed from an original Leslie matrix, the chosen carrying capacity of the model, and a chosen steady-state age-group distribution. The total populations from the model converge to a discrete logistic model with the same initial population and carrying capacity, and growth rate equal to the dominant eigenvalue of the Leslie matrix minus 1.