In population biology and demography, generation time is the average time between two consecutive generations in the lineages of a population. In human populations, generation time typically ranges from 22 to 33 years. Historians sometimes use this to date events, by converting generations into years to obtain rough estimates of time.
Definitions and corresponding formulas
The existing definitions of generation time fall into two categories: those that treat generation time as a renewal time of the population, and those that focus on the distance between individuals of one generation and the next. Below are the three most commonly used definitions:
The net reproductive rate R0 is the number of offspring an individual is expected to produce during its lifetime. This definition envisions the generation time as a renewal time of the population. It justifies the very simple definition used in microbiology since one can consider that during the exponential phase of bacterial growth mortality is very low and as a result a bacterium is expected to be replaced by two bacteria in the next generation. If the population dynamic is exponential with a growth rater ~ α.ert, where n, then this measure of the generation time is given by: Indeed, is such that n = R0n, i.e. erT = R0.
The average difference in age between parent and offspring
This definition is a measure of the distance between generations rather than a renewal time of the population. Since many demographicmodels are female-based, this definition is often expressed as a mother-daughter distance. However, it is also possible to define a father-son distance or not to take sex into account at all in the definition. In age-structured population models, an expression is given by: where r is the growth rate of the population, ℓ is the survivorship function and m the maternity function. For matrix population models, there is a general formula: where λ = er is the discrete-time growth rate of the population, F = is its fertility matrix, v its reproductive value and w its stable stage distribution ; the are the elasticities of λ to the fertilities.
The age at which members of a given cohort are expected to reproduce
This definition is very similar to the previous one but the population need not be at its stable age distribution. Moreover, it can be computed for different cohorts and thus provides more information about the generation time in the population. This measure is given by: Indeed, the numerator is the sum of the ages at which a member of the cohort reproduces, and the denominator is R0, the average number of offspring it produces.
