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Lets say that by studying individuals of a rare species, you have determined that species gestation period, age of sexual maturity, average time between pregnancies, maximum lifespan, and average number of individuals born per pregnancy. However, you have never had enough specimens at the same time to establish a breeding population.

How can you calculate the maximum rate of growth of a population from just the information already gathered? If not, what other information would be needed?

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  • The breeding lifespan of an individual is (maximum life span $L$ - age of sexual maturity $M$).
  • Call the time between pregnancies $\tau$ and the gestation period $g$. Then the average number of pregnancies per (female) individual is then $(L-M)/(\tau+g)$.
  • If the average number of individuals per pregnancy is $N$, then each reproducing individual produces $N(L-M)/(\tau+g)$ offspring in their lifetime.

If this species has males and females (gonochoric/dioecious), and a 50/50 sex ratio, then the number of females per female is $N(L-M)/(2(\tau+g))$.

This is a growth rate per generation: the generation time is approximately (mean time between birth of mother and birth of offspring) = $(M+(L-M)/2)$ (it's a little more complicated than this); the growth rate per unit time would be approximately equal to the ratio (growth rate per generation)/(generation time).

Other things you might need to take into account: survival of juveniles up to $M$; menopause (unusual).

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