DensityDependent Leslie Matrix Modeling for Logistic Populations With SteadyStae 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 agegroups 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 agegroup populations with repeated multiplication of a densitydependent matrix constructed from an original Leslie matrix, the chosen carrying capacity of the model, and a chosen steadystate agegroup 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.
DensityDependent Leslie Matrix Modeling for Logistic Populations With SteadyStae Distribution Control
The Leslie matrix model allows for the discrete modeling of population agegroups 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 agegroup populations with repeated multiplication of a densitydependent matrix constructed from an original Leslie matrix, the chosen carrying capacity of the model, and a chosen steadystate agegroup 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.