# How do you determine carrying capacity?

Jun 15, 2016

$\frac{\mathrm{dN}}{\mathrm{dt}} = r N \left(\frac{1 - N}{K}\right)$ is the formula for determining the change in population size.

#### Explanation:

Legend for the above formula:

$\frac{\mathrm{dN}}{\mathrm{dt}}$ = change in population size, $r$= intrinsic rate of increase,

$N$ = population size; $K$ = carrying capacity.

To solve for carrying capacity, isolate for $K$:

$K = \frac{r N \left(\left(1 - N\right)\right)}{\frac{\mathrm{dN}}{\mathrm{dt}}}$

There is maximal population growth at carrying capacity thus:

$N = \frac{K}{2}$

Your formula would give you the carrying capacity:

$K = \frac{r \left(\frac{K}{2}\right) \left(1 - \frac{K}{2}\right)}{\frac{\mathrm{dN}}{\mathrm{dt}}}$