Reproductive value (population genetics)

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Fisher's reproductive value was defined by R. A. Fisher in his 1930 book The Genetical Theory of Natural Selection as the expected reproduction of an individual from their current age onward, given that they have survived to their current age. It is used in describing populations with age structure.

Definition[edit]

Consider a species with a life history table with survival and reproductive parameters given by \ell_x and m_x, where

\ell_x = probability of surviving from age 0 to age x

and

m_x = average number of offspring produced by an individual of age x.

Depending on whether the breeding is discrete or continuous, Fisher's reproductive value is calculated as

v_x = \mbox{either }\frac{\sum_{y=x}^\infty \ell_y m_y}{R}\mbox{ or }\frac{\int_{y=x}^\infty \ell_y m_y\,dy}{R}

where

R = \mbox{ either }\sum_{y=0}^\infty \ell_y m_y\mbox{ or } \int_0^\infty \ell_x m_x\,dx,

the net reproductive rate of the population.

The average age of a reproducing adult is the generation time and is

T = \mbox{either }\sum_{y=0}^\infty \ell_y v_y\mbox{ or } \int_0^\infty \ell_x v_x\,dx.

See also[edit]

References[edit]

Fisher, R. A. (1930) The Genetical Theory of Natural Selection. Oxford University Press, Oxford.