# Drummond:PopGen

### From OpenWetWare

## Per-generation and instantaneous growth rates

Let *n*_{i}(*t*) be the number of organisms of type *i* at time *t*, and let *R* be the *per-capita reproductive rate* per generation. If *t* counts generations, then

Now we wish to move to the case where *t* is continuous and real-valued.
As before,

where the last simplification follows from L'Hôpital's rule. Explicitly, let ε = Δ*t*. Then

The solution to the equation

*t*. We can define the

*instantaneous rate of increase*

*r*= ln

*R*for convenience.