Allee effect

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.^{[citation needed]}

Description

The Allee effect was described by its namesake, Warder Clyde Allee. 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

$\frac{dN}{dt} = r N \left( \frac{N}{A} - 1 \right) \left( 1 - \frac{N}{K} \right),$

where the population has a negative growth rate for $0< N < A$, and a positive growth rate for $A < N < K$ (assuming $0 < A < K$). This is a departure from the logistic growth equation

$\frac{dN}{dt} = r N \left( 1- \frac{N}{K} \right)$

where

N = population size;

r = intrinsic rate of increase;

K = carrying capacity; 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 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.

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.

References

• Allee, WC, Emerson, AE, Park, O, Park, T and Schmidt, KP (1949). Principles of animal ecology.
• Leviton DA and McGovern TM (2005) "The Allee Effect in the Sea" in Marine conservation biology: the science of maintaining the sea's biodiversity, Eds: Norse EA and Crowder LB. ISBN 978-1-55963-662-9
• Stephens, PA, Sutherland, WJ and Freckleton, RP (1999). "What is the Allee effect?", Oikos, 87, 185-90.

External links

• Berryman, AA (1997). Underpopulation (Allee) effects, Entomology Department, Washington State University. Retrieved 19 May 2008.
• Allee effect, Warner College of Natural Resources, Colorado State University. Retrieved 19 May 2008.
• Stephens, PA, Sutherland, WJ and Freckleton, RP (1999). "What is the Allee effect?" (summary), Oikos, 87, 185-90, at Evolutionary Biology Group, Department of Zoology, University of Oxford. Updated 22 November 2005. Retrieved 19 May 2008
• Classics: the Allee effect