Allee effect
Encyclopedia
The Allee effect is a phenomenon in biology
characterized by a positive correlation between population density and the per capita
population growth rate in very small populations.
. The theory states that, for very small populations, the reproduction and survival rates of individuals increases with population density. This contrasts with large populations in which increasing population density reduces the growth rate of the population. An Allee effect is synonymous with the concept of dispensation used in some economics literature.
A simple mathematical example of an Allee effect is give by the cubic growth model
where the population has a negative growth rate for
, and
a positive growth rate for
(assuming 
).
This is a departure from the logistic growth equation
where
After dividing both sides of the equation by the population size N, in the logistic growth the left hand side of the equation represents the per capita population growth rate, which is dependent on the population size N, and decreases with increasing N throughout the entire range of population sizes. In contrast, when there is an Allee effect the per-capita growth rate increases with increasing N over some range of population sizes [0, N].
When a population is made up of small sub-populations additional factors to the Allee effect arise.
If the sub-populations are subject to different environmental variations (i.e. separated enough that a disaster could occur at one sub-population site without affecting the other sub-populations) but still allow individuals to travel between sub-populations, then the individual sub-populations are more likely to go extinct than the total population. In the case of a catastrophic event decreasing numbers at a sub-population, individuals from another sub-population site may be able to repopulate the area.
If all sub-populations are subject to the same environmental variations (i.e. if a disaster affected one, it would affect them all) then fragmentation
of the population is detrimental to the population and increases extinction risk for the total population. In this case, the species receives none of the benefits of a small sub-population (loss of the sub-population is not catastrophic to the species as a whole) and all of the disadvantages (inbreeding
depression, loss of genetic diversity
and increased vulnerability to environmental instability) and the population would survive better unfragmented.
Biology
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...
characterized by a positive correlation between population density and the per capita
Per capita
Per capita is a Latin prepositional phrase: per and capita . The phrase thus means "by heads" or "for each head", i.e. per individual or per person...
population growth rate in very small populations.
Description
The Allee effect was described by its namesake Warder Clyde AlleeWarder Clyde Allee
Warder Clyde Allee was an American zoologist and ecologist who taught animal ecology. He is best known for his research on animal behavior, protocooperation, and for identifying the Allee effect.-University career:...
. The theory states that, for very small populations, the reproduction and survival rates of individuals increases with population density. This contrasts with large populations in which increasing population density reduces the growth rate of the population. An Allee effect is synonymous with the concept of dispensation used in some economics literature.
A simple mathematical example of an Allee effect is give by the cubic growth model
where the population has a negative growth rate for
, anda positive growth rate for
(assuming ).This is a departure from the logistic growth equation
Logistic function
A logistic function or logistic curve is a common sigmoid curve, given its name in 1844 or 1845 by Pierre François Verhulst who studied it in relation to population growth. It can model the "S-shaped" curve of growth of some population P...
where
- N = population size;
- r = intrinsic rate of increasePopulation dynamicsPopulation dynamics is the branch of life sciences that studies short-term and long-term changes in the size and age composition of populations, and the biological and environmental processes influencing those changes...
; - K = carrying capacityCarrying capacityThe carrying capacity of a biological species in an environment is the maximum population size of the species that the environment can sustain indefinitely, given the food, habitat, water and other necessities available in the environment...
; and - dN/dt = rate of increase of the population
After dividing both sides of the equation by the population size N, in the logistic growth the left hand side of the equation represents the per capita population growth rate, which is dependent on the population size N, and decreases with increasing N throughout the entire range of population sizes. In contrast, when there is an Allee effect the per-capita growth rate increases with increasing N over some range of population sizes [0, N].
When a population is made up of small sub-populations additional factors to the Allee effect arise.
If the sub-populations are subject to different environmental variations (i.e. separated enough that a disaster could occur at one sub-population site without affecting the other sub-populations) but still allow individuals to travel between sub-populations, then the individual sub-populations are more likely to go extinct than the total population. In the case of a catastrophic event decreasing numbers at a sub-population, individuals from another sub-population site may be able to repopulate the area.
If all sub-populations are subject to the same environmental variations (i.e. if a disaster affected one, it would affect them all) then fragmentation
Fragmentation
-In biology:* Fragmentation , a form of asexual reproduction* Fragmentation * Habitat fragmentation* Population fragmentation-Music:* Fragmented , the debut album from the Filipino independent band Up Dharma Down-Other:...
of the population is detrimental to the population and increases extinction risk for the total population. In this case, the species receives none of the benefits of a small sub-population (loss of the sub-population is not catastrophic to the species as a whole) and all of the disadvantages (inbreeding
Inbreeding
Inbreeding is the reproduction from the mating of two genetically related parents. Inbreeding results in increased homozygosity, which can increase the chances of offspring being affected by recessive or deleterious traits. This generally leads to a decreased fitness of a population, which is...
depression, loss of genetic diversity
Genetic diversity
Genetic diversity, the level of biodiversity, refers to the total number of genetic characteristics in the genetic makeup of a species. It is distinguished from genetic variability, which describes the tendency of genetic characteristics to vary....
and increased vulnerability to environmental instability) and the population would survive better unfragmented.
Strong vs. weak Allee effect
A distinction is made between a "strong Allee effect", where a population exhibits a "critical size or density", below which the population declines on average, and above which it increases on average, and a "weak Allee effect", where a population lacks a "critical density", but where, at lower densities, the population growth rate rises with increasing density.External links
- Berryman, AA (1997). Underpopulation (Allee) effects, EntomologyEntomologyEntomology is the scientific study of insects, a branch of arthropodology...
Department, Washington State UniversityWashington State UniversityWashington State University is a public research university based in Pullman, Washington, in the Palouse region of the Pacific Northwest. Founded in 1890, WSU is the state's original and largest land-grant university...
. Retrieved 19 May 2008. - Allee effect, Warner College of Natural Resources, Colorado State UniversityColorado State UniversityColorado State University is a public research university located in Fort Collins, Colorado. The university is the state's land grant university, and the flagship university of the Colorado State University System.The enrollment is approximately 29,932 students, including resident and...
. Retrieved 19 May 2008. - Stephens, PA, Sutherland, WJ and Freckleton, RP (1999). "What is the Allee effect?" (summary), OikosOikos (journal)Oikos is an international scientific journal published monthly by the Nordic Society Oikos in the field of ecology. It was previously known as Acta Oecologica Scandinavica....
, 87, 185-90, at Evolutionary Biology Group, Department of ZoologyZoologyZoology |zoölogy]]), is the branch of biology that relates to the animal kingdom, including the structure, embryology, evolution, classification, habits, and distribution of all animals, both living and extinct...
, University of OxfordUniversity of OxfordThe University of Oxford is a university located in Oxford, United Kingdom. It is the second-oldest surviving university in the world and the oldest in the English-speaking world. Although its exact date of foundation is unclear, there is evidence of teaching as far back as 1096...
. Updated 22 November 2005. Retrieved 19 May 2008 - Classics: the Allee effect