Reproductive value (population genetics)

Consider a species with a life history table with survival and reproductive parameters given by ${\displaystyle \ell _{x}}$ and ${\displaystyle m_{x}}$, where

${\displaystyle \ell _{x}}$ = probability of surviving from age 0 to age ${\displaystyle x}$

and

${\displaystyle m_{x}}$ = average number of offspring produced by an individual of age ${\displaystyle x.}$

In a population with a discrete set of age classes, Fisher's reproductive value is calculated as

${\displaystyle v_{x}=\sum _{y=x}^{\infty }\lambda ^{-(y-x+1)}{\frac {\ell _{y}}{\ell _{x}}}m_{y}}$

where ${\displaystyle \lambda }$ is the long-term population growth rate given by the dominant eigenvalue of the Leslie matrix. When age classes are continuous,

${\displaystyle v(x)=\int _{x}^{\infty }e^{-r(y-x)}{\frac {\ell (y)}{\ell (x)}}m(y)dy}$

where ${\displaystyle r}$ is the intrinsic rate of increase or Malthusian growth rate.

• Population dynamics
• Euler–Lotka equation
• Leslie matrix
• Senescence

• Fisher, R. A. 1930. The Genetical Theory of Natural Selection. Oxford University Press, Oxford.
• Keyfitz, N. and Caswell, H. 2005. Applied Mathematical Demography. Springer, New York. 3rd edition. doi:10.1007/b139042