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http://www.nature.com/scitable/knowledge/library/allee-effects-19699394
Allee Effects
By: John M. Drake & Andrew M. Kramer (Odum School of Ecology, University of Georgia,
Athens) © 2011 Nature Education
Citation: Drake, J. M. & Kramer, A. M. (2011) Allee Effects. Nature Education
Knowledge 3(10):2
© Creative
Commons Eistreter via Wikimedia Commons Some rights reserved.
History and Definition
Allee effects occur in small or sparse populations and, although rarely detected, are widely believed to be
common in nature. Population growth of populations subject to Allee effects is reduced at low density. The
originator and namesake of the phenomenon was Warder Clyde Allee (1885–1955), a University of Chicago
zoologist and animal ecologist, whose special interest was group behavior in animals.
Charles Darwin observed that large population size is an important hedge against extinction in the presence of
predators or other natural enemies (Darwin 1872, quoted in Stephens et al. 1999). Nevertheless, early
twentieth century biologists typically accepted as given both the Malthusian principle — that intra-specific
competition does not decrease with population size — and its mathematical expression in the logistic model for
population growth (Gause 1934).
Allee, an astute observer of animal behavior, noticed that in many species it was undercrowding, not
competition, that limited population growth. He observed, for instance, that aggregation had positive effects on
the survival of land isopods, which were subject to rapid desiccation when isolated (Allee 1927). His empirical
examples of the benefits of aggregation seemed to contradict both the Malthusian paradigm and the logistic
model. Much of Allee's early work focused on documenting this phenomenon in animal populations (Allee
1931).
In modern biology, Allee effects are considered to have two manifestations:
1. component Allee effects are exhibited by a population in which there is a positive association
between some fitness component (e.g., viability, juvenile survivorship, fecundity; Orr 2009) and
population size;
2. demographic Allee effects that occur when these component Allee effects produce a positive
association between per capita population growth and population size.
Keeping in mind that competition, for instance for resources or space, will limit a population's size, and noting
that per capita growth rate of a population at small size equals average absolute individual fitness (Lande et al.
2003), both kinds of Allee effects may be captured by the following general definition.
An Allee effect is a positive association between absolute average individual fitness and population size over
some finite interval.
Such a positive association may (but does not necessarily) give rise to a critical population size below which
the population cannot persist (Stephens et al. 1999). Allee effects that cause critical population sizes are called
strong, while Allee effects that do not result in critical sizes are called weak. Other names for the Allee effect
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are positive density dependence (in contrast to classical negative density dependence) and depensatory
dynamics (in contrast to classical compensatory dynamics).
Mechanisms That Cause Allee Effects
A positive relationship between fitness and population size can be caused by a variety of mechanisms that
affect reproduction and survival. A well established example, mate limitation, may result in undercrowding in
species that reproduce sexually, because sexual reproduction requires contact between male and female
gametes. Mate limitation reduces reproduction when plants or animals release gametes into the environment
or when males and females have difficulty locating each other. When behaviors such as breeding, feeding, and
defense are cooperative, they become more efficient or successful in larger social groups, resulting in
increased reproductive success or survivorship (Courchamp et al. 1999). Although cooperative behaviors are
most obvious in social vertebrates, such as prairie dogs, ungulates or birds, Allee effects resulting from group
feeding or defense can also arise in insects, such as bark beetles, and aquatic organisms, such as cichlid fish
(Friedenberg et al. 2007, Balshine et al. 2001).
Other mechanisms do not require cooperation in the behavioral sense, but merely the presence of conspecific
individuals. For example, the per capita risk of predation is smaller in large prey populations than small prey
populations (Dennis 1989, Gascoigne and Lipcius 2004). It is also known that the presence of multiple
individuals can alter environmental or biotic conditions in favorable ways. Examples of such niche construction
include reducing physical damage in intertidal zones (Bertness and Grosholz 1985) or exclusion of competitors
via allelopathy (Cappuccino 2004).
Finally, demographic and genetic mechanisms may give rise to Allee effects. In animals, active dispersal away
from low-density populations can result in decreased rates of population growth (Bonte et al. 2004). For many
organisms, when population size is small, inbreeding depression can cause an Allee effect by reducing
average fitness as population size declines (Fischer et al. 2003). While these phenomena differ in form, in the
way they affect fitness, and in which species are affected, they all result in the same general pattern: small
populations suffer from reduced average individual fitness.
Evidence of Allee Effects
Evidence for Component Allee Effects
There is evidence from natural populations for component Allee effects due to all of these mechanisms (see
references above, Courchamp et al 2008, Kramer et al. 2009; Figure 1). The most commonly observed
mechanism is mate limitation, which causes Allee effects in both animals and plants (in the form of pollen
limitation). Positive density dependence in survivorship due to either cooperative defense or predator satiation
is also found across taxonomic groups. Indeed, because the tendency of predators to become satiated and
stop increasing consumption depends on the predator rather than the prey, predator satiation has the potential
to affect any population fed upon by a predator that does not numerically track the abundance of the small prey
population, such as when a generalist predator feeds on multiple species (Kramer & Drake 2010). Evidence for
the other mechanisms described above is less abundant, but each has been found in multiple taxonomic
groups, and some studies have detected positive density dependence in reproduction or survival without
identifying the mechanism (Kramer et al. 2009), making it likely that there are other mechanisms that lead to
component Allee effects. The population level impacts of these mechanisms are less clear.
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Figure 1: The number of studies which attributed the Allee
effect in a species to a given mechanism, according to
taxonomy
Taxonomic groups for which there is evidence of Allee effects are
terrestrial arthropods, aquatic invertebrates, mammals, birds, fish,
and plants. Species were included if the mechanism was detected
empirically in natural populations. Single studies can be
represented by multiple evidence types and mechanisms. The area
of the circle represents the relative number of species exhibiting
each mechanism (smallest circle = 1 species, largest = 20 species).
Question marks indicate combinations where evidence is currently
lacking.
© 2011 Nature
Education Modified from Kramer et al.
2009 All rights reserved.
Evidence for Demographic Allee Effects
Demographic Allee effects have been harder to demonstrate. Two reasons for this include:
1. Allee effects in one component of fitness may be offset at low density by increases in other
components of fitness, such as decreased competition for resources;
2. Natural populations at low density are often difficult to detect and the high variance that results from
small sample sizes obscures statistical analysis.
For these reasons, unusual cases of population growth are important to the ongoing study of Allee effects. In
particular, monitoring data from invasive species provides an opportunity for improving understanding of Allee
effects. Some likely effects of positive density dependence are easier to observe, extinction, for instance, but it
is difficult to confirm that an Allee effect was to blame.
Dynamics of Populations with Allee Effects
The most dramatic consequences of Allee effects are associated with strong Allee effects, although weak Allee
effects are also predicted to give rise to measurable dynamical differences. The difference between Allee
effects and the classical (Malthusian) logistic theory is seen most clearly in the correlation between per capita
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growth rate and population size. This correlation can be generated using :
where x is the population size, a is the critical point, and k represents the force of competition and is known as
the carrying capacity (Figure 2a).
Figure 2: Allee effects are distinguished from other forms of density dependence by a positive association between
average absolute individual fitness and population size over a finite interval.
When Allee effects are strong, a critical size occurs where the growth function dx/dt=f(x) intersects the horizontal line at zero
(panel a, red arrow). This is an unstable equilibrium. Populations with abundance greater than this value will increase to
carrying capacity (panel a, black arrow). Populations with abundance less than this value will decline to extinction. While
carrying capacity is a stable equilibrium for both strong and weak Allee effects, and for logistic growth, extinction is stable only
for strong Allee effects and unstable for weak Allee effects and logistic growth. Both kinds of Allee effects may be diagnosed by
the positive association between per capita population growth rate and small population sizes, shown here to reach an
intermediate maximum for weak Allee effects and for strong Allee effects (panel b). Strong and weak Allee effects may be
distinguished by whether the y-intercept of the per capita growth rate is less than zero (indicating strong Allee effect, red arrow
in panel b) or greater than zero (indicating weak Allee effect, blue arrow in panel b). Trajectories of populations with weak Allee
effects are delayed compared with logistic growth, but qualitatively similar: populations initialized at any size will grow smoothly
to carrying capacity (panel c). By contrast, the bistability of strong Allee effects means that eventual limit population size is
determined by the initial condition (panel c). In panel c, the dashed lines for each population are for trajectories with initial size
N =21 and the solid lines for trajectories with initial size N =19. From this plot, it is evident that the effects of small changes in
0
0
initial population size are virtually indistinguishable for populations with logistic growth or weak Allee effects, but may be crucial
for populations with strong Allee effects. Further, the delay between the trajectories for populations with weak Allee effects or
logistic growth and the dashed red line for a population with a strong Allee effect initialized just greater than the critical
population size at N =21, shows the very slow population takeoff caused by strong Allee effects, even when growth is positive.
0
© 2011 Nature
Education All rights reserved.
Dividing both sides by the population size (x) yields the per capita population growth rate:
The classical logistic theory predicts that per capita growth rate will not increase with population size (Figure
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2b). By the definition above, a population with an Allee
effect will exhibit an increase over some interval of
population size (Figure 2b). This distinction between
Allee and non-Allee populations is the same regardless
of whether the y-axis depicts per capita intrinsic rate of
increase, the reproductive multiplier, λ, or lifetime
reproductive output. Strong and weak Allee effects are
distinguished according to whether the y-intercept falls
below or above the replacement value (1/x dx/dt = 0 or
λ = 1), respectively (Figure 2b). These plots do not
distinguish whether the Allee effect is endogenous to
the dynamics of the population, such as result from
mate limitation, or due to interactions with other
species, such as the predator-induced Allee effect
exhibited by the crown-of-thorns starfish Acanthaster
planci (Dulvy et al. 2004; Figure. 3).
Other dynamical consequences of strong Allee effects
include:
Figure 3: The relationship between per capita growth rate and
starfish density show that the crown-of-thorns starfish
(Acanthaster planci) is subject to a strong Allee effect.
In this case, the Allee effect is due to escape from fish predation at
high density.
© 2011 Nature Education Adapted from Dulvy et al. 2004
All rights reserved.
1. A sigmoidal relationship between the probability
of rapid extinction and the initial population size
(Dennis 1989), a pattern which contrasts with the
concave shape predicted by the classical logistic theory (Dennis 2002) (Figure 4a);
2. A critical area that the population must occupy for it to persist (Lewis & Kareiva 1993, Vercken et al.
2011) (Figure 4b);
3. A bimodal stationary distribution of population size (Dennis 1989, Drake & Lodge 2006) (Figure 4c).
Figure 4: Three signatures of the Allee effect
A sigmoidal probability of rapid extinction results from an inflection point corresponding to the critical population size (panel a).
A critical area (panel b) results from the race between population growth at the center of a patch (where the population density
exceeds the critical value) and dispersal at the periphery (where population density is below the replacement level). The critical
area may be characterized by a radius r that the population must exceed for the patch to persist. The solid line in panel b
c
illustrates the critical area. The dashed (dotted) lines represent the areas subsequently occupied by populations that initially
occupy the area just larger (smaller) than the critical area. The critical point in the growth dynamics also gives rise to a trough in
the stationary distribution of population sizes once they have equilibrated (panel c). This trough causes the density to be
bimodal with a lower mode in the vicinity of extinction and an upper mode at carrying capacity.
© 2011 Nature
Education All rights reserved.
Evolution
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The negative effects of low density, such as difficulty finding mates or increased vulnerability to predators, is
expected to often result in strong selection for traits that reduce the influence of these mechanisms. For
instance, rare species, which are typically at low density, often have adaptations that allow positive growth at
low density, or they will become extinct. However, aggregation and sociality are not adaptations that eliminate
Allee effects per se. Rather, they increase population densities so that the densities at which Allee effects are
manifest are avoided (Stephens and Sutherland 1999). Other traits may be the result of selection on
low-density populations. For example, displays, calls, and pheromones all widen the area over which males
and females perceive mates, thus reducing mate limitation. These adaptations can also increase fitness in
other ways, however, such as signaling mate quality, so it is difficult to assign causality (Courchamp et al.
2008). Similarly, sperm storage, hermaphroditism, and parthenogenesis are all favored when chances of
encountering mates are low, but may provide fitness benefits in other contexts as well, such as accelerated
local adaptation (Cousyn et al. 2001). It is reasonable to conclude that species most likely to suffer Allee
effects are those that usually have large populations but have suffered a recent reduction in size, such as due
to habitat fragmentation or catastrophic natural events. Such populations will be more likely to suffer from
mechanisms that reduce fitness at low density, especially if traits conferring fitness at low density incur a cost
at high density. Finding such a trade-off may provide the best indication that a trait is an evolutionary response
to persistence at low density (Courchamp et al. 2008).
Environmental applications
When the size of populations subject to strong Allee effects is low, then these populations tend towards
extinction. This fact argues for a thorough understanding of Allee effects and their mechanisms in order to
develop sound management practices for a number of environmental issues. An obvious case is the
conservation of rare species. It has been shown, for instance, that small patches of the flowering herb Clarkia
concinna concinna attract pollinating insects in fewer numbers than do large patches. As a result, small
patches are more prone to extinction (Groom 1998). In general, persistence of species subject to strong Allee
effects requires that a minimum population size — specific to each population — be distributed over a
population-specific minimal area. This conclusion also applies to efforts to restore extirpated populations
through captive breeding and reintroduction.
Another environmental issue that involves the Allee effect is the management of invasive species. Population
biologists have long wondered why only a small fraction of introduced species ultimately persist in their
introduced locations (Williamson & Fitter 1996). A partial answer to this question is that many introductions are
below the critical size associated with Allee effects (Grevstad 1999). It follows that risk management for
invasive species could be improved by a better understanding of the comparative biology of Allee effects (i.e.,
the relative frequency and strength of Allee effects across species) (Drake et al. 2004), coupled with a
quantitative understanding of the rates at which introductions occur, a concept referred to as propagule
pressure (Leung et al. 2004, Lockwood et al. 2005).
Even populations with weak Allee effects may require consideration of Allee effects for effective management.
For instance, the invasive smooth cordgrass, Spartina alterniflora, is known to exhibit Allee effects due to
pollination limitation. As a result, new patches of cordgrass initially grow quite slowly. An observer of such an
invasion might wrongly conclude that this species' potential for spread is low. However, once the incipient
colony grows to a certain size its potential to spread increases dramatically (Taylor 2004).
Conclusion
Allee effects are a small population phenomenon in which population growth rate is reduced by undercrowding.
Although Allee effects are widely believed to be common and are important to environmental management,
clear documentation of demographic Allee effects in nature has mostly proved elusive.
References and Recommended Reading
Allee, W. C. Animal aggregations. The
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———. Animal
Aggregations. A Study in General Sociology. Chicago, IL: University of Chicago Press, 1931.
Balshine, S. et
al. Correlates of group size in a cooperatively breeding cichlid fish (Neolamprologus pulcher). Behavioral Ecology
and Sociobiology 50 134–140 (2001).
Bertness, M. D. & Grosholz, E. Population dynamics of the ribbed mussel, Geukensia demissa: The costs and benefits of an aggregated distribution.
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