The observation that no population can grow indefinitely and that most populations persist on ecological timescales implies that mechanisms of population regulation exist. Feedback mechanisms include competition for limited resources, cannibalism, and predation rates that vary with density. Density dependence occurs when per capita birth or death rates depend on population density. Density dependence is compensatory when the population growth rate decreases with population density and depensatory when it increases. The logistic model incorporates density dependence as a simple linear function. A population exhibiting logistic growth will reach a stable population size. Non-linear density-dependent terms can give rise to multiple equilibria. With discrete time models or time delays in density-dependent regulation, the approach to equilibrium may not be smooth—complex dynamical behavior is possible. Density-dependent feedback processes can compensate, up to a point, for natural and anthropogenic disturbances; beyond this point a population will collapse.
Peer Review #1 of "A white-box model of S-shaped and double S-shaped single-species population growth (v0.1)"
