#### Poster Title

Density-Dependent Leslie Matrix Modeling for Logistic Populations With Steady-Stae Distribution Control

#### Grade Level at Time of Presentation

Junior

#### 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.