Allee effect is a phenomenon in biology characterized by a
correlation between population size or density and the mean individual
fitness (often measured as per capita population growth rate) of a
population or species.
1 History and background
2.1 Component vs. demographic Allee effects
2.2 Strong vs. weak Allee effects
3.1 Ecological mechanism
3.2 Human induced
3.3 Genetic mechanisms
3.4 Demographic stochasticity
4 Effects on range-expanding populations
5 Mathematical models
6 Allee principles of aggregation
7.1 Further reading
8 External links
History and background
Main article: Warder Clyde Allee
Although the concept of
Allee effect had no title at the time, it was
first described in the 1930s by its namesake, Warder Clyde Allee.
Through experimental studies, Allee was able to demonstrate that
goldfish grow more rapidly when there are more individuals within the
tank. This led him to conclude that aggregation can improve the
survival rate of individuals, and that cooperation may be crucial in
the overall evolution of social structure. The term "Allee principle"
was introduced in the 1950s, a time when the field of ecology was
heavily focused on the role of competition among and within
species. The classical view of population dynamics stated that
due to competition for resources, a population will experience a
reduced overall growth rate at higher density and increased growth
rate at lower density. In other words, individuals in a population
would be better off when there are fewer individuals around due to a
limited amount of resources (see logistic growth). However, the
concept of the
Allee effect introduced the idea that the reverse holds
true when the population density is low. Individuals within a species
often require the assistance of another individual for more than
simple reproductive reasons in order to persist. The most obvious
example of this is observed in animals that hunt for prey or defend
against predators as a group.
The generally accepted definition of
Allee effect is positive density
dependence, or the positive correlation between population density and
individual fitness. It is sometimes referred to as "undercrowding" and
it is analogous (or even considered synonymous by some) to
"depensation" in the field of fishery sciences. Listed below are
a few significant subcategories of the
Allee effect used in the
Component vs. demographic Allee effects
Allee effect is the positive relationship between any
measurable component of individual fitness and population density. The
Allee effect is the positive relationship between the
overall individual fitness and population density.
The distinction between the two terms lies on the scale of the Allee
effect: the presence of a demographic
Allee effect suggests the
presence of at least one component Allee effect, while the presence of
Allee effect does not necessarily result in a demographic
Allee effect. For example, cooperative hunting and the ability to more
easily find mates, both influenced by population density, are
component Allee effects, as they influence individual fitness of the
population. At low population density, these component Allee effects
would add up to produce an overall demographic
Allee effect (increased
fitness with higher population density). When population density
reaches a high number, negative density dependence often offsets the
component Allee effects through resource competition, thus erasing the
demographic Allee effect. It is important to note that Allee
effects might occur even at high population density for some
Strong vs. weak Allee effects
Allee effects are classified by the nature of density dependence at
low densities. If the population shrinks for low densities, there is a
strong Allee effect. If the proliferation rate is positive and
increasing then there is a weak Allee effect. The null hypothesis is
that proliferation rates are positive but decreasing at low densities.
Allee effect is a demographic
Allee effect with a critical
population size or density. The weak
Allee effect is a demographic
Allee effect without a critical population size or density.
The distinction between the two terms is based on whether or not the
population in question exhibits a critical population size or density.
A population exhibiting a weak
Allee effect will possess a reduced per
capita growth rate (directly related to individual fitness of the
population) at lower population density or size. However, even at this
low population size or density, the population will always exhibit a
positive per capita growth rate. Meanwhile, a population exhibiting a
Allee effect will have a critical population size or density
under which the population growth rate becomes negative. Therefore,
when the population density or size hits a number below this
threshold, the population will be destined for extinction without any
further aid. A strong
Allee effect is often easier to demonstrate
empirically using time series data, as one can pinpoint the population
size or density at which per capita growth rate becomes negative.
Due to its definition as the positive correlation between population
density and average fitness, the mechanisms for which an Allee effect
arises are therefore inherently tied to survival and reproduction. In
Allee effect mechanisms arise from cooperation or
facilitation among individuals in the species. Examples of such
cooperative behaviors include better mate finding, environmental
conditioning, and group defense against predators. As these mechanisms
are more easily observable in the field, they tend to be more commonly
associated with the
Allee effect concept. Nevertheless, mechanisms of
Allee effect that are less conspicuous such as inbreeding depression
and sex ratio bias should be considered as well.
Although numerous ecological mechanisms for Allee effects exist, the
list of most commonly cited facilitative behaviors that contribute to
Allee effects in the literature include: mate limitation, cooperative
defense, cooperative feeding, and environmental conditioning. While
these behaviors are classified in separate categories, note that they
can overlap and tend to be context dependent (will operate only under
certain conditions – for example, cooperative defense will only be
useful when there are predators or competitors present).
Mate limitation refers to the difficulty of finding a compatible and
receptive mate for sexual reproduction at lower population size or
density. This is generally a problem encountered by species that
utilize passive reproduction and possess low mobility, such as
plankton, plants and sessile invertebrates. For example,
wind-pollinated plants would have a lower fitness in sparse
populations due to the lower likelihood of pollen successfully landing
on a conspecific.
Another possible benefit of aggregation is to protect against
predation by group anti-predator behavior. Many species exhibit higher
rates of predator vigilance behavior per individual at lower density.
This increased vigilance might result in less time and energy spent on
foraging, thus reducing the fitness of an individual living in smaller
groups. One striking example of such shared vigilance is exhibited
by meerkats. Meanwhile, other species move in synchrony to confuse
and avoid predators such as schools of sardines and flocks of
starlings. The confusion effect that this herding behavior would have
on predators will be more effective when more individuals are
Certain species also require group foraging in order to survive. As an
example, species that hunt in packs, such as the African wild dogs,
would not be able to locate and capture prey as efficiently in smaller
Environmental conditioning / habitat alteration
Environmental conditioning generally refers to the mechanism in which
individuals work together in order to improve their immediate or
future environment for the benefit of the species. This alteration
could involve changes in both abiotic (temperature, turbulence, etc.)
or biotic (toxins, hormones, etc.) environmental factors. Pacific
salmon presents a unique case of such component Allee effects, where
the density of spawning individuals can affect the survivability of
the following generations. Spawning salmon carry marine nutrients they
acquired from the ocean as they migrate to freshwater streams to
reproduce, which in turn fertilize the surrounding habitat when they
die, thus creating a more suitable habitat for the juveniles that
would hatch in the following months.
Classic economic theory predicts that human exploitation of a
population is unlikely to result in species extinction because the
escalating costs to find the last few individuals will exceed the
fixed price one achieves by selling the individuals on the market.
However, when rare species are more desirable than common species,
prices for rare species can exceed high harvest costs. This phenomenon
can create an "anthropogenic"
Allee effect where rare species go
extinct but common species are sustainably harvested. The
Allee effect has become a standard approach for
conceptualizing the threat of economic markets on endangered
species. However, the original theory was posited using a one
dimensional analysis of a two dimensional model. It turns out
that a two dimensional analysis yields an Allee curve in human
exploiter and biological population space and that this curve
separating species destined to extinction vs persistence can be
complicated. Even very high population sizes can potentially pass
through the originally proposed Allee thresholds on predestined paths
Declines in population size can result in a loss of genetic diversity,
and owing to genetic variation's role in the evolutionary potential of
a species, this could in turn result in an observable Allee effect. As
a species' population becomes smaller, its gene pool will be reduced
in size as well. One possible outcome from this genetic bottleneck is
a reduction in fitness of the species through the process of genetic
drift, as well as inbreeding depression. This overall fitness
decrease of a species is caused by an accumulation of deleterious
mutations throughout the population. Genetic variation within a
species could range from beneficial to detrimental. Nevertheless, in a
smaller sized gene pool, there is a higher chance of a stochastic
event in which deleterious alleles become fixed (genetic drift). While
evolutionary theory states that expressed deleterious alleles should
be purged through natural selection, purging would be most efficient
only at eliminating alleles that are highly detrimental or harmful.
Mildly deleterious alleles such as those that act later in life would
be less likely to be removed by natural selection, and conversely,
newly acquired beneficial mutations are more likely to be lost by
random chance in smaller genetic pools than larger ones.
Although the long-term population persistence of several species with
low genetic variation has recently prompted debate on the generality
of inbreeding depression, there are various empirical evidences for
genetic Allee effects. One such case was observed in the
Florida panther (Puma concolor coryi). The Florida panther
experienced a genetic bottleneck in the early 1990s where the
population was reduced to ~ 25 adult individuals. This reduction in
genetic diversity was correlated with defects that include lower sperm
quality, abnormal testosterone levels, cowlicks, and kinked tails.
In response, a genetic rescue plan was put in motion and several
female pumas from Texas were introduced into the Florida population.
This action quickly led to the reduction in the prevalence of the
defects previously associated with inbreeding depression. Although the
timescale for this inbreeding depression is larger than of those more
immediate Allee effects, it has significant implications on the
long-term persistence of a species.
Demographic stochasticity refers to variability in population growth
arising from sampling random births and deaths in a population of
finite size. In small populations, demographic stochasticity will
decrease the population growth rate, causing an effect similar to the
Allee effect, which will increase the risk of population
extinction. Whether or not demographic stochasticity can be considered
a part of
Allee effect is somewhat contentious however. The most
current definition of
Allee effect considers the correlation between
population density and mean individual fitness. Therefore, random
variation resulting from birth and death events would not be
considered part of
Allee effect as the increased risk of extinction is
not a consequence of the changing fates of individuals within the
Meanwhile, when demographic stochasticity results in fluctuations of
sex ratios, it arguably reduces the mean individual fitness as
population declines. For example, a fluctuation in small population
that causes a scarcity in one sex would in turn limit the access of
mates for the opposite sex, decreasing the fitness of the individuals
within the population. This type of
Allee effect will likely be more
prevalent in monogamous species than polygynous species.
Effects on range-expanding populations
Demographic and mathematical studies demonstrate that the existence of
Allee effect can reduce the speed of range expansion of a
population and can even prevent biological
Recent results based on spatio-temporal models show that the Allee
effect can also promote genetic diversity in expanding
populations. These results counteract commonly held notions that
Allee effect possesses net adverse consequences. Reducing the
growth rate of the individuals ahead of the colonization front
simultaneously reduces the speed of colonization and enables a
diversity of genes coming from the core of the population to remain on
the front. The
Allee effect also affects the spatial distribution of
diversity. Whereas spatio-temporal models which do not include an
Allee effect lead to a vertical pattern of genetic diversity (i.e., a
strongly structured spatial distribution of genetic fractions), those
Allee effect lead to a "horizontal pattern" of genetic
diversity (i.e., an absence of genetic differentiation in space).
A simple mathematical example of an
Allee effect is given by the cubic
displaystyle frac dN dt =rNleft( frac N A -1right)left(1-
frac N K right),
where the population has a negative growth rate for
, and a positive growth rate for
). This is a departure from the logistic growth equation
displaystyle frac dN dt =rNleft(1- frac N K right)
N = population size;
r = intrinsic rate of increase;
K = carrying capacity;
A = critical point; 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].
Spatio-temporal models can take
Allee effect into account as well. A
simple example is given by the reaction-diffusion model
displaystyle frac partial N partial t =D frac partial ^ 2 N
partial x^ 2 +rNleft( frac N A -1right)left(1- frac N K
displaystyle frac partial ^ 2 partial x^ 2
= one-dimensional Laplace operator.
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
Allee principles of aggregation
Clumping results due to individuals aggregating in response to: 1)
local habitat or landscape differences, 2) daily and seasonal weather
changes, 3) reproductive processes, or 4) as the result of social
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Classics: the Allee effect
Agent-based model in biology
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Symmetry breaking of escaping ants
Swarming (honey bee)
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Ant colony optimization
Particle swarm optimization
Group size measures
Task allocation and partitioning of social insects
Ecology: Modelling ecosystems: Trophic components
List of feeding behaviours
Metabolic theory of ecology
Primary nutritional groups
Generalist and specialist species
Mesopredator release hypothesis
Optimal foraging theory
Microbial food web
North Pacific Subtropical Gyre
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Competitive exclusion principle
Energy Systems Language
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Trophic state index
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Ecology: Modelling ecosystems: Other components
Effective population size
Malthusian growth model
Maximum sustainable yield
Overpopulation in wild animals
Predator–prey (Lotka–Volterra) equations
Small population size
Ecological effects of biodiversity
Latitudinal gradients in species diversity
Minimum viable population
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Relative abundance distribution
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Ideal free distribution
Intermediate Disturbance Hypothesis
r/K selection theory
Resource selection function
Environmental niche modelling
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Liebig's law of the minimum
Marginal value theorem
Alternative stable state
Balance of nature
Biological data visualization
Ecosystem based fisheries
List of ec