In age-structured models of populations, age classes or "cohorts" are introduced to distinguish individuals at different life stages. For

, where

is the number of different age classes, let

denote the number of individuals that are in cohort

at the discrete time (generation)

and assume an initial age distribution at

, here chosen as {0, 50%, 50%, 0, 0, 0}. In the population model put forward by P. H. Leslie ("On the Use of Matrices in Certain Population Mathematics,"

*Biometrika*,

**33**(3), 1945 pp. 183–212), the evolution from the given initial age distribution is determined by the recursion

for the distribution vector

and the "Leslie matrix"

. The parameters in

embody the survival rates yielding the fraction of the

class at time

that enter into the

class at time

, and the "fertility" or "fecundity" coefficients giving the average number of newborns to a member of the respective cohort. The age distributions displayed are computed as

, where

is the total population size at time

. It can be shown (by invoking the Perron–Frobenius theorem) that if

is regular then there exists an eigenvector with strictly positive components; this eigenvector yields the ''equilibrium" age distribution to which the evolution converges upon time

growing to infinity.