Mathematical Demography pp 161-166 | Cite as

# The Fundamental Theorem of Natural Selection

Chapter

## Abstract

The total reproductive value, due to Fisher, is of great importance in stable population theory. It is defined as where

$$\text{V} = \int\limits_0^\infty {P(x)v(x)dx}\\ = \int\limits_{t = 0}^\beta {\int\limits_{x = 0}^{\beta - t} {e^{ - rt} } } P(x)\frac{{l(t + x)}}{{l(x)}}m(t + x)dx dt,$$

*P*(*x*) is the observed population between ages*x*and*x*+*dx*at time 0,*v*(*x*) is the reproductive value, and standard notation*r*,*m*(*x*) is used in place of Fisher’s m and b_{ x }for the intrinsic growth rate and probability of giving birth in the age interval*x*to*x*+*dx*, respectively. The fraction*l*(*t*+*x*)/*l*(*x*) is the probability that an individual age*x*at time 0 survives*t*years to his (*t*+*x*)th birthday. In words,*V*is the backward projection of fertility accruing to an observed population to find the size of a birth cohort that would be reproductively equivalent to it. Its application is shown in Feller (1941, paper 16 above).## Keywords

Birth Cohort Reproduction Rate Reproductive Rate Intrinsic Growth Rate Compound Interest
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin · Heidelberg 1977