Describing Populations

How Is Population Growth Affected by Carrying Capacity?

Carrying Capacity

The carrying capacityglossary term (opens in a new window) (K) of a habitat is the largest populationglossary term (opens in a new window) size that can be supported in an ecosystemglossary term (opens in a new window) over a period of time. Many factors, including water, light, nutrients, and space, influence an ecosystem’s carrying capacity. In theory, a population will grow exponentially until it is using all of its available resources. At this point, the population should stabilize at the carrying capacity. At carrying capacity, death rate equals birth rate. This rarely occurs in nature because disease, predation, and density-independent factorsglossary term (opens in a new window), such as an extremely cold winter, usually intervene.

If you know calculus, the carrying capacity can be used to determine the logistical growth curve for a population. If a population size (N) is below the carrying capacity, it will grow at a rate that is proportional to (K-N)/K. This information can be used to generate a logistic growthglossary term (opens in a new window) equation:

ΔNΔr=rmaxN(K−NK)$\frac{\Delta N}{\Delta r}=r_{\text{max}}N\left(\frac{K-N}{K}\right)$

Returning to the logistical growth curve, we can better understand this relationship. The smaller the population (N) the closer (K-N)/K will be to 1, meaning population growth will be high. When the population reaches carrying capacity (K), then (K-N)/K equals zero and growth ceases.

It is possible for a population to temporarily exceed the carrying capacity of its habitat. This, however, cannot last. Such a population causes rapid degradation of the environment. The loss of food and other resources will cause the population to crash.