Generation time
In population biology and demography, the generation time is the average time between two consecutive generations in the lineages of a population. In human populations, the generation typically ranges from 20 to 30 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 the generation time fall into two categories: those that treat the 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:[1]
- The time it takes for the population to grow by a factor of its net reproductive rate:
The net reproductive rate is
the number of offspring an individual is expected to produce during its
lifetime (a net reproductive rate of 1 means that the population is at its
demographic equilibrium). This definition envisions the generation time as a
renewal time of the population. It justifies the very simple definition used
in microbiology ("the time it takes for the population to double", or doubling time) 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 (the mother cell and the daughter cell).
If the population dynamic is exponential with a growth rate
(i.e.
,
where
is the size of the population at time
), then this measure of the generation time is
given by:
.
Indeed, is such that
, i.e.
.
- The average difference in age between parents and offsprings when the population is at the stable age distribution:
This definition is a measure of the distance between generations rather than a renewal time of the population. Since many demographic models are female-based (that is, they only take females into account), this definition is often expressed as a mother-daughter distance (the "average age of mothers at birth of their daughters"). However, it is also possible to define a father-son distance (average age of fathers at the age of their sons) or not to take sex into account at all in the definition. In age-structured population models, an expression is given by:[2]
,
where is the growth rate of the
population,
is the survivorship function
(probability that an individual survives to age
) and
the maternity function (or birth function, or
age-specific fertility). For matrix population models, there is a more simple
and general formula:[3]
,
where is the discrete-time growth rate of
the population,
is its fertility
matrix,
its reproductive value (row-vector)
and
its stable stage distribution (column-vector);
the
are the
elasticities of
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 provide more information about the generation time in the population. This measure is given by:[2]
.
Indeed, the numerator is the sum of the ages at which a member of the cohort
reproduces, and the denominator is , the average
number of offspring it produces.
References
- ↑ Coale, A.J. (1972). The Growth and Structure of Human Populations. Princeton University Press.
- ↑ 2.0 2.1 Charlesworth, Brian (1994). Evolution in Age-structured Populations. Cambridge: University of Cambridge Press. pp. 28–30. ISBN 0-521-45967-2.
- ↑ Bienvenu, F.; Demetrius, L.; Legendre, S. (2013). "arXiv:1307.6692".