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P3

is the Leslie matrix. Figure 10.6 illustrates an example of the dynamics of the stickleback population.

Leslie matrices always have the form of (10.16), where the top row of the matrix is the effective fecundity of individuals of each age class, and all other rows contain one element p,. With age-structure, all individuals must pass through each class in succession, and assuming that time is measured in terms of the age classes, an individual must move on to the next class every time step. Thus, the survival probabilities p, enter the matrix in the cells immediately below the diagonal. The elements of Leslie matrices are often referred to as the life-history parameters of the model.

10.6.2 Analysis of Age-Structured Models

The special form of Leslie matrices allows us to write its characteristic polynomial in a pleasingly simple form (Box 10.3):

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