Generation time

Generation time is a quantity used in population biology and demography to reflect the relative size of intervals of offspring production. Generation time usually expresses the average age of breeding females within a population. Suppose females begin breeding at age α and stop breeding (or die) at age ω, then the average age of first reproduction of a cohort of females is

$T = \frac{\sum_{x=\alpha}^{\omega} x l(x) m(x) }{\sum_{x=\alpha}^{\omega} l(x) m(x) }$

where l(x) is the hazard function and m(x) is the fecundity of females aged x .

When the population is in stable age distribution, we can express the generation time as the average age of mothers of zero-year-olds:

$T = \sum_{x=\alpha}^{\omega} x e^{-rx} l(x) m(x)$

where r is the Malthusian parameter of the population.