On the Reproduction of Organisms with Overlapping Generations

  • W. R. Thompson
Part of the Biomathematics book series (BIOMATHEMATICS, volume 6)


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)
$$r = \frac{{\mu - \sqrt {\mu ^2 - 2\sigma ^2 \ln R_0 } }}{{\sigma ^2 }} = \frac{{\ln R_0 }}{{\mu - \frac{{\sigma ^2 r}}{2}}}$$
where r is the intrinsic rate of growth, R0 the net reproduction rate, and σ2 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.


Successive Generation Resultant Birth Reproductive Period Total Birth Original Ancestor 
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Copyright information

© Springer-Verlag Berlin · Heidelberg 1977

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  • W. R. Thompson

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