# Derivation

## Modelling density dependent population growth (logistic growth)

Let’s derive some more population growth functions! The logistic population growth function In a previous post we derived a function for population growth based on the vital rates of reproduction and mortality. We assumed that the growth rate was constant with respect to the number of individuals in the population or (\frac{dt}{dN} = rN). This led to the unrealistic prediction that populations will grow indefinitely. Of course, populations will eventually run into resource problems (e.

## Unconstrained population growth

Let’s derive some population growth functions! How to grow Populations grow. They grow positively, if rates of reproduction > mortality, or negatively, if reproduction < mortality. For an unconstrained population of size (N) this diffence in per capita reproduction and mortality is referred to as the intrinsic growth rate, (r) and has the units individuals per individual per time (N.N^{-1}.t^{-1}) . The value of (r) is a constant if the age-distribution is constant (e.