Leslie Matrices:
Leslie Matrices are used to model growth (and decline) of age-structured populations. In the model named after Patrick H. Leslie (1945), we have \(N\) age classes, and record how many individuals are in each. Each time period, individuals either age into the next class, or die. The survival rate describes the proportion that moves on to the next age class, and the birth rate, or fecundity, describes the rate per capita of births arising from each age category.
Given these parameters, we model one time step with
\[ {\mathbf n}_{t+1} = L {\mathbf n}_t, \]where \({\mathbf n}_t\) is the vector of age-class populations at time \(t\), and \(L\) is the Leslie matrix.
Examples:
You can click on one of the links below to see an example, or use the table to set the parameters yourself.
Choose matrix parameters:
Fill in the fields below. All values must be non-negative, and survival rates must be at most 1. The model uses up to seven age classes. The survival value in the last active column is ignored, because there is no higher age class to move into.
| Leslie Model Parameters | Age Class 0 | Age Class 1 | Age Class 2 | Age Class 3 | Age Class 4 | Age Class 5 | Age Class 6 |
|---|---|---|---|---|---|---|---|
| Initial Population | |||||||
| Birth Rate | |||||||
| Survival Rate |
