Search results
Results From The WOW.Com Content Network
Although growth may initially be exponential, the modelled phenomena will eventually enter a region in which previously ignored negative feedback factors become significant (leading to a logistic growth model) or other underlying assumptions of the exponential growth model, such as continuity or instantaneous feedback, break down.
Biological exponential growth is the unrestricted growth of a population of organisms, occurring when resources in its habitat are unlimited. [1] Most commonly apparent in species that reproduce quickly and asexually , like bacteria , exponential growth is intuitive from the fact that each organism can divide and produce two copies of itself.
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
Exponential growth cannot continue indefinitely, however, because the medium is soon depleted of nutrients and enriched with wastes. The stationary phase is often due to a growth-limiting factor such as the depletion of an essential nutrient, and/or the formation of an inhibitory product such as an organic acid. Stationary phase results from a ...
By now, it is a widely accepted view to analogize Malthusian growth in Ecology to Newton's First Law of uniform motion in physics. [8] Malthus wrote that all life forms, including humans, have a propensity to exponential population growth when resources are abundant but that actual growth is limited by available resources:
The Limits to Growth (LTG) is a 1972 report [2] that discussed the possibility of exponential economic and population growth with finite supply of resources, studied by computer simulation. [3] The study used the World3 computer model to simulate the consequence of interactions between the Earth and human systems.
Limiting factors may be physical or biological. [4]: 417, 8 Limiting factors are not limited to the condition of the species. Some factors may be increased or reduced based on circumstances. An example of a limiting factor is sunlight in the rain forest, where growth is limited to all plants on the forest floor unless more light becomes ...
Thus r is the maximum theoretical rate of increase of a population per individual – that is, the maximum population growth rate. The concept is commonly used in insect population ecology or management to determine how environmental factors affect the rate at which pest populations increase. See also exponential population growth and logistic ...