## Definition of Generation Time

The famous Euler-Lotka polynomial equation, allows us to calculate the asymptotic population growth rate A if the survival function lx, which gives the probability of being alive from age 1 to age x, as well as the fecundity rate at age x, mx, are known. This equation has ! roots, that is, equal to the maximum number of age classes, which can be obtained numerically. The generation time is then given by

Many species have demographic rates that are almost constant or independent of age. If a is the age of first reproduction, and assuming ! = 1, we get a simplified expression for the generation time T = a + s/(A - s), where s is the adult survival rate. We see that in general, T decreases with A and increases with the net reproductive rate.

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