Reproduction value

The reproduction value is the age-dependent expected value of the number of future direct descendants of individuals, normalized with the reproduction rate of a total population. The term was coined by Ronald Fisher in his book The Genetical Theory of Natural Selection (1930).

definition

Consider a species with survival and reproductive parameters and , where ${\displaystyle \ell _{x}}$ ${\displaystyle m_{x}}$

${\displaystyle \ell _{x}}$= Probability of surviving to old age ${\displaystyle x}$

and

${\displaystyle m_{x}}$ = arithmetic mean of the offspring produced by individuals in one age group

For discrete generations, the reproduction value is introduced as a sum, which becomes an integral in the case of continuous reproduction:

${\displaystyle v_{x}={\mbox{diskret: }}{\frac {\sum _{y=x}^{\infty }\ell _{y}m_{y}}{R}}{\mbox{ kontinuierlich: }}{\frac {\int _{y=x}^{\infty }\ell _{y}m_{y}\,dy}{R}}}$

with a reproduction rate based on the total population of:

${\displaystyle R={\mbox{ diskret:}}\sum _{y=0}^{\infty }\ell _{y}m_{y}{\mbox{ kontinuierlich:}}\int _{0}^{\infty }\ell _{x}m_{x}\,dx,}$

See also

• Biogerontology
• Reproduction costs
• Life history theory

literature

• RA Fisher: The genetic theory of natural selection . Oxford University Press, Oxford 1930.
• ME Begon, JL Harper, CR Townsend: Ecology. Spectrum Akademischer Verlag, Heidelberg 1996. ISBN 3-8274-0226-3 .