Generation time

In population biology and demography, generation time is the average time between two consecutive generations in the lineages of a population, being linked to biological life cycles. In human populations, generation time typically has ranged from 20 to 30 years, with wide variation based on gender and society. 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:

Time for a population to grow by a factor of its net reproductive rate

The net reproductive rate

R

0

{\displaystyle \textstyle R_{0}}

is the number of offspring an individual is expected to produce during its lifetime:

R

0

=

1

{\displaystyle \textstyle R_{0}=1}

means demographic equilibrium. One may then define the generation time

T

{\displaystyle T}

as the time it takes for the population to increase by a factor of

R

0

{\displaystyle \textstyle R_{0}}

. For example, in microbiology, a population of cells undergoing exponential growth by mitosis replaces each cell by two daughter cells, so that

R

0

=

2

{\displaystyle \textstyle R_{0}=2}

and

T

{\displaystyle T}

is the population doubling time.

If the population grows with exponential growth rate

r

{\displaystyle \textstyle r}

, so the population size at time

t

{\displaystyle t}

is given by

n

(

t

)

=

α

e

r

t

{\displaystyle n(t)=\alpha \,e^{rt}}

,

then generation time is given by

T

=

ln

⁡

R

0

r

{\displaystyle T={\frac {\ln R_{0}}{r}}}

.

That is,

T

{\displaystyle \textstyle T}

is such that

n

(

t

+

T

)

=

R

0

n

(

t

)

{\displaystyle n(t+T)=R_{0}\,n(t)}

, i.e.

e

r

T

=

R

0

{\displaystyle e^{rT}=R_{0}}

.