Fisher's reproductive value was defined by R. A. Fisher (1930) 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

---

Consider a species with a life history table with survival and reproductive parameters given by $l\_x$ and $m\_x$, where

$l\_x$ = 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

$v\_x\; =\; \backslash frac\{\backslash sum\_\{y=x\}^\backslash infty\; l\_y\; m\_y\}\{l\_x\; R\}$ or $=\backslash frac\{\backslash int\_\{y=x\}^\backslash infty\; l\_y\; m\_ydy\}\{l\_x\; R\}$

where

$R\; =\; \backslash sum\_0^\backslash infty\; l\_x\; m\_x$ or $=\; \backslash int\_0^\backslash infty\; l\_x\; m\_xdx$, the net reproductive rate of the population.

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

$T\; =\; \backslash sum\_0^\backslash infty\; l\_x\; v\_x$ or $=\; \backslash int\_0^\backslash infty\; l\_x\; v\_xdx$

See also

---

Effective population size

Senescence

References

---

Fisher, R. A. (1930) The genetical theory of natural selection. Oxford University Press, Oxford.

population genetics