Population Growth

Birth, death, immigration, and emigration rates factor into the growth rate of a population. Two simple models of population growth are the exponential model and the logistical model.


The growth pattern for a population with unlimited resources is exponential and represented by a "J" shaped growth curve. A population that is growing exponentially increases in a geometric pattern (for example, 2, 4, 8, 16, 32, etc.). In the formula dN/dt = riN, dN/dt is the rate of change in the number of individuals at any instant in time and ri represents the innate capacity for growth of the population (biotic potential) when in an unlimited environment. Populations that are introduced to a new environment or are recovering from a catastrophic event (such as a fire) usually exhibit "J" shaped growth curves.

Population growth eventually reaches a limit imposed by factors such as light, space, nutrients, or water. Carrying capacity (K) is the maximum number of individuals a particular habitat can support. Growth in a logistical model slows as it approaches the carrying capacity of the environment and forms an "S" shaped growth curve. In reality, populations sometimes will overshoot K, followed by a rapid decline, until conditions for growth are restored.

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References

Campbell, N. E., & Reece, J. B. (2002). Biology (6th ed.). San Francisco: Benjamin Cummings.
Raven, P. H., & Johnson, G. B. (2002). Biology (6th ed.). McGraw-Hill.