On the Reproduction of Organisms with Overlapping Generations

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)

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

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.

From Bulletin of Entomological Research 22. Excerpts are from pages 147–152, 154–160, 163, 168–170.