The Fundamental Theorem of Natural Selection

  • R. A. Fisher
Part of the Biomathematics book series (BIOMATHEMATICS, volume 6)


The total reproductive value, due to Fisher, is of great importance in stable population theory. It is defined as
$$\text{V} = \int\limits_0^\infty {P(x)v(x)dx}\\ = \int\limits_{t = 0}^\beta {\int\limits_{x = 0}^{\beta - t} {e^{ - rt} } } P(x)\frac{{l(t + x)}}{{l(x)}}m(t + x)dx dt,$$
where 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).


Birth Cohort Reproduction Rate Reproductive Rate Intrinsic Growth Rate Compound Interest 
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© Springer-Verlag Berlin · Heidelberg 1977

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  • R. A. Fisher

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