The Leslie Population Model

The Leslie Model was designed to determine the population distribution, the total population, and the long-term rate of growth for certain animal species over a specified amount of time.

The Leslie Model Set-up using matrices:

1. - The Initial Population Matrix- always a row matrix. The number of columns depends on the number of age groups described for the population. Each entry in the matrix is the number of animals/organisms in each age group initially.

2. L- The Leslie Matrix- always a square matrix, the dimensions of which are determined by the number of columns in the corresponding matrix. The first column of L is the birth rates and the super diagonal (above the main diagonal) is the survival rates. The last survival rate is not used, as it is always 0. The remaining entries in the matrix are 0’s.

3. C1- A Column of 1’s- always the transpose dimensions of Po. This matrix will be used to find population totals and growth rates.

Using the Leslie Model

  1. To find thepopulation distribution after a given amount of cycles (the amount in each age group), use: P0∙Ln,where n is the number of cycles.
  • Be careful here. If a time period is given in years, months, weeks, etc., be sure to represent it in cycles.
  1. To find the population total(the sum of all age group amounts) after a given amount of cycles, use: P0∙Ln∙C1, where n is the number of cycles.
  2. To find the rate of population growth between two cycles, find the population totals for two successive cycles, say Pn and Pn+1. Subtract the previous cycle’s total (Pn) fromthe later cycle’s total (Pn+1), divide the difference by the previous cycle’s total, and then multiply the result by 100. Use:.
  3. To find the long term rate of growth for a population, find the rate of growth between two pair of successive cycles. If the growth rates are the same, then the population’s growth has stabilized. If they differ, repeat the process for higher cycle numbers.
  • Try the rate of growth between P30 and P31 and between P31 and P32. For most populations, the rate is stable here.