# How do you determine carrying capacity?

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21
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:

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

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6
Dec 14, 2016

Carrying Capacity is determined when the overall population does not increase and the ecosystem REACHES its maximum ability to support the population therein.

#### Explanation:

When a jungle does not grow food fast enough species that live there cannot grow in population because their habitat does not provide enough support to keep them growing and producing anymore. Hope this helps!

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