Density-dependent Population Growth
To represent an environment that is not unlimited, models incorporate a carrying capacity ("logistic growth models"). When the population is far from carrying capacity ("K"), density effects are minor. As the population approaches carrying capacity, using the continuous time model, per capita population growth rate decreases towards zero. When the population is greater than carrying capacity, per capita population growth is negative. This causes populations to approach carrying capacity smoothly.
Although per capita population growth rate is highest when the population is small, overall population growth rate is highest at half of carrying capacity ("maximum sustained yield"). At low population sizes, per capita growth is high but few individuals are able to contribute to population growth. At population sizes close to K, per capita growth is close to zero.
Complex dynamics can occur when there is a delay in the response of populations in relation to their densities. Delays between population growth and population density may be caused by fat storage, gestation or incubation, seed banks, or litter build-up. Discrete time models treat time as occurring in clear steps. As population growth rate increases, populations first overshoot carrying capacity but eventually reach carrying capacity. With increasingly high population growth rates, populations may cycle (boom and bust cycles). Populations with extremely high growth rates have chaotic dynamics. Models with reproduction occurring only at certain times (discrete models) show the same progression of dynamic behaviors as the time delay models.
- Alstad, D. (2001). Basic populus models of ecology. Upper Saddle River, NJ: Prentice Hall.
Young, M. (2004). Density-dependent population growth model. Center For Educational Outreach. Houston, TX: Baylor College of Medicine.
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