Mathematical Demography pp 173-182 | Cite as

# On the Reproduction of Organisms with Overlapping Generations

Chapter

## Abstract

We omit the final section of Thompson’s paper, in which he shows the effects on population size of (a) lengthening the pre-reproductive interval, (b) lengthening the period of reproduction, (c) increasing the number of offspring produced per day, and (d) compacting the reproductive period while leaving the number of offspring constant. The effects can be summarized in the approximate equality, due to Lotka (1939, pp. 70–71) where

$$r = \frac{{\mu - \sqrt {\mu ^2 - 2\sigma ^2 \ln R_0 } }}{{\sigma ^2 }} = \frac{{\ln R_0 }}{{\mu - \frac{{\sigma ^2 r}}{2}}}$$

*r*is the intrinsic rate of growth,*R*_{0}the net reproduction rate, and σ_{2}and σ1 the mean and variance of the net maternity function. Where the net maternity function takes the form of a normal distribution the equalities are exact.## Keywords

Successive Generation Resultant Birth Reproductive Period Total Birth Original Ancestor
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