Carrying Capacity

All living things tend to over-reproduce; they have more offspring than will probably survive to adulthood. Just how many they have in a given year is the birth rate. At the same time, nature is a dangerous place, and individuals are always dying (death rate). In a stable environment where the population size stays the same, the birth rate equals the death rate. Such a population is said to be at its Carrying Capacity - the maximum average population size that an area can support over time.

Birth rate is generally determined by the species' life history
Death rate is determined by Limiting Factors
Immigration (moving in) and Emigration (moving out) also affect population size
Every population fluctuates a little bit, the carrying capacity is the average within that change

Take it to the Limit

Limiting factors keep populations from getting too big - they limit the size of the population. They can be anything that keeps individuals from growing, reproducing, or living at all. They are two general categories of limiting factors:

Density Dependent Factors - become more of an issue when populations are dense (many individuals in a limited space)
- Starvation - food becomes scarce when many individuals are trying to eat
- Predation - the more prey there are, the more likely predators will find a meal
- Disease - pathogens spread more easily when individuals are in close contact
- Competition - when populations are dense, it becomes harder to find the best shelter, territory, mates, etc.
Density Independent Factors - these limit a population no matter how dense; they are often environmental factors
- Climate - some species cannot tolerate colder/hotter temperatures, or the lack of rain in the desert
- Soil - some soil is too sandy, some is too dense; it doesn't matter how many plants are trying to live there, if they don't have the right nutrients, none will survive.

Carrying Capacity (K) is the sweet spot where the limiting factors of an environment are pretty much equal to the birth rate (and immigration) of a species. This causes a population graph to level off for many years at a time.

Carrying Capacity makes either an "S shaped" curve, or it is a horizontal line when graphed

Growing, Growing, Gone

Without any limiting factors, populations experience exponential growth in which the population grows at an increasing larger rate. This can't go on forever, so it ends in one of two ways.

Exponential growth forms a "J shaped" curve - it gets steeper as time goes on
Some populations will start to increase less and less as they approach the carrying capacity of the environment and then level off
Other populations will "Boom and Bust." They increase so much that they destroy their environment, reduce the carrying capacity to almost zero, and die off or move on.
- Ex: Humans killed most of the predators on the Kaibab Game Preserve in Arizona. Deer increased from 4000 to 100,000, ate all the plants, and starvation caused a decreased back to 10,000 within a few years.