Nordic Society Oikos
What Is the Allee Effect?
Author(s): P. A. Stephens, W. J. Sutherland, R. P. Freckleton
Source: Oikos, Vol. 87, No. 1 (Oct., 1999), pp. 185-190
Published by: Blackwell Publishing on behalf of Nordic Society Oikos
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FORUM
FORUM
FORUM
FORUMis intendedfor new ideasor newwaysof interpreting
It
existinginformation.
currentthinkingon
providesa chancefor suggestinghypothesesand for challenging
Formal
ecologicalissues.A lighterprose,designedto attractreaders,will be permitted.
shouldbe concise
research
andall contributions
reports,albeitshort,willnot be accepted,
witha relatively
A summary
is not required.
shortlist of references.
What is the Allee effect?
P. A. Stephens, W. J. Sutherlandand R. P. Freckleton,School of Biological Sciences, Univ. of East Anglia,
Norwich,UK NR4 7TJ ([email protected]).
W. C. Allee broughtattentionto the possibilityof a positive
relationshipbetweenaspectsof fitnessand populationsize over
fifty years ago. This phenomenon,
frequentlytermedthe Allee
effect,has beenthe focusof increasedinterestoverthe past two
decades in the light of concernsover conservationand the
problemsof rarity.Use of the termsuffersfromthe absenceof
a clear definitionhowever,withthe resultthat Allee effectsare
frequentlythoughtto involveonly a narrowrangeof phenomena
andare oftenoverlookedaltogether.We proposea definitionfor
the effectandattemptto resolvethe majorissuesunderlying
the
confusionsurrounding
this term.
It is recognisedthat individualsof many species may
benefit from the presence of conspecifics(Fig. 1), a
conceptbroadlyreferredto as the Allee effect afterthe
pioneeringwork of W. C. Allee (Allee 1931, 1938,Allee
et al. 1949). Unfortunately,however,the concept suffers from widespreadconfusionand misuse.It has been
interpretedsolely as the difficultyin findingmates at
low densities(Myerset al. 1995,Amarasekare1998),is
explained variously as a reduction in fitness at low
populationsize (McCarthy1997, Fischerand Matthies
1998) or at low population density (Gruntfestet al.
1997, Kindvallet al. 1998,Kuussaariet al. 1998,Wells
et al. 1998), and has even been erroneouslydefinedas
negativedensitydependence(Levitanet al. 1992).Other
authorshave demonstrateddecreasesin aspectsof survival or breedingoutput at low numbersor densities,
but have not termedthese Allee effects (Carboneet al.
1997,Green 1997,Macedo and Bianchi1997,Storeret
al. 1997).
We believe that inconsistentuse of the term results
from the absence of a single clear definition.In this
articlewe aim: (1) to investigatethe originsof the term
and to developa much-neededdefinition;(2) to explore
the distinctionbetweenthe componentAllee effect, of
particular interest to behaviourists,and the demoOIKOS 87:1 (1999)
graphicAllee effect, of overridingconcernto conservationists;and (3) to clarify two of the centralareas of
confusionwithin the definition-those regardingissues
of scale and demographicstochasticity.
In order to clarifythe meaningand use of the term
Allee effect, we focus attentionon a limitednumberof
examplesof mechanismsof this effect. For those unfamiliarwith the rangeof mechanismswhichmay lead to
Allee effects,thesehave been reviewedmoreextensively
elsewhere (Dennis 1989, Fowler and Baker 1991,
Stephens and Sutherlandin press). In brief, these
benefits of conspecificpresence may include one or
more of: predatordilution or saturation;antipredator
vigilance or aggression;cooperativepredation or resourcedefence;socialthermoregulation;
collectivemodificationor ameliorationof the environment;increased
availabilityof mates;increasedpollinationor fertilisation success;conspecificenhancementof reproduction;
and reductionof inbreeding,genetic drift, or loss of
integrityby hybridisation.
Originsof the term
Allee was initially stimulated by an example only
loosely linkedto the currentinterpretationof the Allee
effect: he showed that goldfish grew faster in water
which had previouslycontainedother goldfish,than in
water that had not (Allee 1931). Furtherexperiments
with a rangeof speciesshowedthat largergroupsize or
some degreeof crowdingmay stimulatereproduction,
prolong survivalin adverseconditions (throughresistance to desiccationor by social thermoregulation)
and
enhance protection from toxic reagents (Allee 1931,
1938).Allee saw these phenomenaas 'automaticcooperation',believingthat the beneficialeffectsof numbers
of animalspresentin a populationrepresenteda funda185
mental biologicalprinciple(Allee 1938).By 1953 E. P.
Odumwas referringto 'Allee'sprinciple'as the concept
that "undercrowding(or lack of aggregation)may be
limiting" (Odum 1953: 154). Perhaps inevitably, we
discovered that similar observationshad been made
previouslyby Darwinwho noted that, "in many cases,
a large stock of individualsof the same species, relatively to the numberof its enemies,is absolutelynecessary for its preservation"(Darwin 1872:86). Reduction
in fitness or populationgrowth at low abundancehas
receivedconsiderableattentionin conservationgenetics,
under such guises as the '50/500 rule' (Soule and
Wilcox 1980), and is also widely debated in fisheries
science, where it is usually referredto as depensation
(Myers et al. 1995, Liermannand Hilborn 1997). Depensationis principallya populationlevelphenomenon,
whichmay or may not arisefrom changesin individual
fitness,and thus need not be directlyanalogousto the
Allee effect.
(a)
(c)
(b)
(d)
Flock size
Fig. 2. ComponentAllee effects and demographicAllee effects.A mechanismsuchas vigilanceamonga groupmay give
rise to a componentAllee effect (shortdashes).Whetherthis
results in a demographicAllee effect will depend on the
strengthof negativedensity dependenteffects (long dashes),
suchas interferenceand depletion.Overallfitness(solidline)is
shown for (a) strong,(b) intermediate,and (c) weak negative
densitydependence.(d) A sigmoidcomponentAlleeeffectmay
lead to demographicAllee effects at intermediatepopulation
sizes.
effect as: a positive relationshipbetween any component of individualfitnessand eithernumbersor density
Definition
of conspecifics.
In the spirit of Allee's original observations,this
the
Allee
effect
is
Although
reasonablywell known,the
definition
requiresthat some measurablecomponentof
a
has
of
not
all
of
which
are
concept
range meanings,
acknowledgedby contemporaryuse. Allee did not the fitnessof an organism(e.g. probabilityof dying or
providea definitionbut he clearlyconsidered"certain reproducing)is higher in a large population.Whether
aspects of survival values" (Allee et al. 1949: 396) all componentsof mean fitnesscombineto producean
rather than total fitness and we thus define the Allee overallincreaseor decreasewith increasingabundance
will dependon the relativestrengthof negativedensity
dependence.We suggest that it is thereforeimportant
(a)
to differentiate between component Allee effects (Allee
(c)
effects manifestedby a componentof fitness)and de-
0
mographic Allee effects (Allee effects which manifest at
(b)
+
(d)
+
dn
\C
0On
toincreases
kn-
*s^
I~wardsk
d-n -s
n increases towards U
U
0
ndt
/1/
decli nes
dcraes
~k ^/ to extinction
~owards
-
n decreases
I
towardsUI
Abundance
Fig. 1. Negativedensitydependenceand the Allee effect. (a)
As populationsgrow there will often be reductionsin the
fitnessof individuals,for examplefromincreasingcompetition
and depletionof resources,resultingin decreasednatalityand
survival.(b) Populationgrowthrate will declinelinearlywith
increasingabundance,as illustratedby the logistic equation,
giving a single, stable equilibrium(k). (c) For many species
however, there are benefitsassociatedwith the presenceof
conspecifics.At low numbersor densities,the benefitsfromthe
additionof each successiveindividualoutweighthe costs, such
that there is a net gain in individualfitness, and fitness is
highestat intermediatenumbersor densities.(d) In this case,
population growth rate may also be low at low levels of
abundance,as shown by the adjustedlogistic equation. If
growthbecomesnegativeat low numbers,two equilibriawill
result:a lower,unstableequilibrium(C) and an upper,stable
equilibrium(U).
186
the level of total fitness).As an illustration,largerbird
flocks are (up to a point) more likely to detect predators early, thus reducingtheirmortalityrate (Kenward
1978). There are also likely to be negative effects of
increasingnumbers,such as interferenceand depletion
of food resources,and a variety of relationshipsbetween these componentsof fitness and flock size are
possible (Fig. 2). Although the positive effect of increasingflock size on vigilanceis consistent,only where
negativedensity dependenteffects are weak is there a
positive relationshipbetweentotal fitness and number
at any stage. Thus, componentAllee effectsare seen in
all Figs 2a-d, whilstdemographicAllee effectsare seen
only in Figs 2c and d. The overallrelationshipbetween
fitness and abundancemay be seen as the cumulative
effects of all componentAllee effects and all negative
densitydependenteffects,or as Allee himselftermedit,
all terms of cooperationand disoperation(Odumand
Allee 1954).
In practice,distinguishingbetweencomponentAllee
effectsand demographicAllee effectsmay enableAllee
effectsto be describedwith greatercertaintyin the field.
The instabilityof the lower equilibrium(see Fig. Id)
OIKOS 87:1 (1999)
means that natural populations subject to a demographic Allee effect are unlikely to persist in the range
of population sizes where that effect is manifest. It has
been observed that empirical data on Allee effects are
sparse (Dennis 1989, Kuussaari et al. 1998). Establishing whether an observed component Allee effect will
lead to a demographic Allee effect is further complicated by the effects of environmental variability on the
strength of negative density dependence, and by a
potential lag between component and demographic
Allee effects. For example, in colonial breeding birds,
higher fledging success due to increased colony size
could be negated due to greater over-winter mortality
of young, perhaps as a result of increased competition
for food and hence decreased fat reserves before winter.
The component Allee effect of increased fledging success would not be translated into a demographic Allee
effect, due to the seasonal nature of negative density
dependence. Thus it is interesting to note that whilst
theoreticians are principally concerned with demographic Allee effects, empiricists, by the very nature of
their work, are usually constrained to the quantification
of component Allee effects. In practice, the importance
of identifying component Allee effects is usually that
their existence indicates the potential for the existence
of a demographic Allee effect, which is far less easily
demonstrated.
a)
b)
Number, density and issues of scale
Widespread confusion over the use of the term Allee
effect surrounds the contrast between Allee effects that
result from low population sizes and those that result
from low population densities. Allee himself did not
confront this issue directly but clearly his examples
included effects of both number, for example, improved
social thermoregulation in larger litters of mice, Mus
sp., and of density, for example, increased per capita
reproduction among higher densities of flour beetles,
Triboliumconfusum (Allee 1938). However, for the majority of mechanisms which lead to Allee effects, the
distinction between number and density is complex,
depending largely on the spatial resolution at which the
system is studied. To the field ecologist, working within
a fixed study area, any drop in number will be inseparable from a corresponding reduction in density. Local
density may be a more useful measure but still may be
difficult to interpret.
A useful thought experiment to distinguish between
number and density as the basis for a given mechanism
is to consider isolated, closed systems, and then compare the consequences of a change in density with those
of a concomitant increase in number and area. This
approach may be used to distinguish a mechanism such
as maintenance of balanced sex ratios that is dependent
on numbers of individuals present, from a mechanism
C)
Fig. 3. Allee effects,populationsize and populationdensity.Determiningwhetheran Allee effectresultsfrom low numbers(n)
or low densities(6) of individualsmay be thoughtof in termsof isolatedpatchesor islandsof habitat.The threediagramsshow
a) n = 4, 6 = 2, b) n = 16, 6 = 2, and c) n = 4, 6 = 4. Consider a mechanism such as the maintenance of balanced sex ratios. Such
a mechanismmay fail as a speciesbecomesrarer,reducingaverageindividualfitnessand causingan Allee effect. In patch (a),
thereis a high chancethat both individualsmay be of one sex and that matingmay not take place at all. Highernumbersof
individualsin patch (b) reducethe probabilityof such a biasedsex ratio, demonstratingthat increasingnumbersmay alleviate
the Allee effect, without an increasein density.Indeed,a highly skewedsex ratio is less likely in patch (b) than in patch (c),
despitethe fact that individualsin patch(c) are at the higherdensity.Thus Allee effectsarisingfrom sex ratio skewsresultfrom
low numbersof individuals,or small populationsizes. By contrast,considera mechanismsuch as the modificationof soil
a phenomenonby whichplantsmay improvelocal conditionsfor growth.Assumingthat an individualplantmay
characteristics,
have a giveneffecton, say, the pH of a givenvolumeof soil, then plantsin patches(a) and (b) will be equallywell off, and only
an increasein density(as in patch (c)) will lead to an increasein individualfitness.
OIKOS 87:1 (1999)
187
such as modificationof soil propertiesthat is dependent
on densityof individualspresent(Fig. 3).
Translationof Allee effects from one temporal or
spatialscale to anotheris also dependenton the mechanism involved. Temporalchanges in aggregativebehaviourmay indicatetemporalchangesin the strength
of Allee effects.A strikingexampleis that of the mara
(Dolichotispatagonum)(Taber and Macdonald 1992).
Patchy habitat quality and rapid depletionlead to the
highly territorial,monogamousbehaviourof marasfor
most of the year. However, despite an abundanceof
warrens,puppingis communal,probablyas a resultof
the benefitsto pups of increasedvigilanceand improved
thermoregulationin communalcreches.
Spatialinconsistenciesin Allee effectsmay also occur.
Howlermonkeys(Alouattapalliata)on BarroColorado
Island, Panama, live in troops of 6-31 individuals
(Smith 1977). Individualswithin a group may gain
considerablebenefitsfrom the presenceof conspecifics,
includingincreasedanti-predatorbehaviour,and cultural transmissionof food-finding and anti-predator
information.Troops show considerablerange overlap.
Over a period of time, high recruitmentinto a single
smallgroupof howlermonkeysmay elevatetheirnumbers considerably.Thus at the local scale of the group,
a demographicAlleeeffectmay be seen.At a widerscale
however, such an increase in the number of howler
monkeysin one troop may cause a markedincreasein
the resourcedepletion,loweringthe averagefitness in
other groups.
fluctuationsmay be usefullyconsideredas a mechanism
of the Allee effect.
In generaltermsan Allee effect resultingfrom demographic stochasticityis proposed to arise as a consequence of an increasein the variancein the rate of
populationchangeor meanfitnessat low numbers.The
mechanism for this change in variance is directly
analogous to the familiar phenomenon of increased
samplingvarianceof the populationmean as sample
sizes become small, for example as predictedby the
centrallimit theorem.The long-termstochasticdynamics of a populationmay be predictedby transformation
of the originalpopulationsize (N) to a new scale (x),
such that x = g(N) wherethe transformationg has the
propertythat varianceabout the mean fitness is homogenisedas x varies.The most familiarexampleof this
'isotropic'transformationis the geometricmeanpopulation growth rate for population growth of discrete
generations in a stochastic environment,i.e. when
g(N) = InN (e.g. Lewontinand Cohen 1969).The key
featureof this method is that patternsof dynamicsare
predictedcorrectlyby x, but not by N. In particular,the
mean value of x, which may be termedthe 'dynamic
mean' of the population,correctlypredictspopulation
persistenceor growth.
In the particularcase of the effect of demographic
stochasticityon the variance in mean fitness, if the
variance resulting from demographicstochasticityis
given by c2N, then p(x), the mean value of the change
in x at a given value of N, is (Lande 1998):
a2g
Demographicstochasticity
Demographicstochasticityarisesas a consequenceof the
discrete rather than continuous nature of biological
populationsizes (May 1973);it leads to fluctuationsin
percapitagrowthratesthatmay threatenthe persistence
of small populations.It has been suggestedthat demographic stochasticityrepresentsa type of Allee effect
(Lande 1998) but whetherthis is the case dependson
both the definitionof the Allee effectused and the type
of demographicstochasticityconsidered.The definition
of the Allee effect that we propose above is framedin
termsof the effectsof populationsize, or density,on the
fitnessof individualsand the consequencesthat thismay
or may not have for populationchange.In this respect
we contrasttwo categoriesof demographicstochasticity:
firstwe considerthe most commonlyinvokedsourceof
demographicstochasticity- the randomvariationresultingfromdiscreteindividual(ratherthancontinuous)
birthand deathevents(May 1973,Lande 1993);second
we considersex ratio fluctuations,also commonlycited
as a form of demographicstochasticity(Caughley1994,
Lande 1998). Taking these categoriesin isolation, we
show that despitethe importantimplicationsof both for
population dynamics and persistence,only sex ratio
188
ag
a2N
p(x) = -FN m2 2
ON
ON2
(1)
In this case it is assumedthat changeis modelledby a
density independent model (AN=rtN) defined by
growthparameterr and that demographicstochasticity
is the only form of variability.For this model, the
appropriatevariance homogenisingtransformationis
x = 2/N.
Eq. 1 thereforebecomes:
(2
(X) = ,
4-- 4/N=
rx
22
c2
2x
2x
(2)
The varianceresultingfrom demographicstochasticity
reducesthe mean rate of changeof x to below r/2, its
maximumvaluein the absenceof demographicstochasticity. The strengthof this reductionis proportionalto
the reciprocalof x, i.e. the effect becomesmore important as x becomessmaller,leadingto the proposalthat
there is an Allee effect.
The importantfeatureof eq. (2), however,is that it is
assumedthat demographicstochasticityaffectsonly the
varianceabout the mean of N, and not the mean or
expectedrateof change(F).This applies,for example,to
demographicstochasticity resulting from births and
OIKOS 87:1 (1999)
deaths.If, for example,the meanprobabilityof deathis
d, and the numberssurvivingare predictedby a binomially distributedrandomvariable,then the variancein
populationsize is given by Nd(l - d). The varianceis a
functionof N, but the probabilityof a randomlychosen
individual surviving remains constant at a value of
(1 - d). A similar argument could, for example, be
developedfor natalityor ratesof recruitment.Although
for anypopulationthismechanismwouldleadto increasingprobabilitiesof extinctionwithdecreasingpopulation
sizes, expectedindividualfitnesswould not declineconcomitantly.
The other form of demographicstochasticitythat is
commonlyproposedto lead to reducedratesof change
at low densitiesis the effect of populationsize on sex
ratios, in particularsex ratio skews at low densities.In
thiscasetheeffectof populationsizeon individualfitness
is ratherdifferent.Considera species which produces
young with, on average,an equal ratio of males(M) to
females (F), i.e. the probabilityof producingeither is
p(M) =p(F)= 0.5. At very low population sizes (e.g.
N = 2), therearethreepossiblepopulationcompositions
(allmale,MM;maleandfemale,FM; andall female,FF)
whicharisewith probabilitiesp(MM) = 0.25,p(MF) =
p(FM) = 0.25, and p(FF) = 0.25. The probabilityof a
reproductivepair is thus p(MF) +p(FM) = 0.5 and
hence the probability of any individual being in a
position to reproduceis also 0.5. As population sizes
becomehigh(N-, oo),however,the populationsex ratio
will approach1:1,and nearlyeveryindividualwithinthe
populationwillbe ableto finda mateof the oppositesex.
Hencethe probabilityof an individualbeingin a position
to reproduceapproachesunity.
The key point to emergeis that the effect of demographicstochasticitythroughbirthsand deathsarisesin
a very differentway from the effects of demographic
stochasticitythroughpopulationsexratios.In theformer
case there is no measurablecomponent of individual
fitnessthat is affectedby populationsize or interactions
with otherpopulationmembers.The fate of an individual, in termsof its probabilityof dying or reproducing,
is unaffectedby the size of the populationwithinwhich
it finds itself. In the case of demographicstochasticity
throughpopulationsex ratios, on the other hand, the
probabilityof an individualbeingableto mateis affected
by populationsize, i.e. thereis a measurablecomponent
of individualfitnessthat can be relatedto the size of the
populationand interactionsbetweenorganisms.Thefate
of the populationas a whole is affectedby its size when
demographicstochasticitythrough births and deaths
occurs.This, however,is not a consequenceof changing
fates of the individualswithinthe populationand hence
cannot be consideredas an exampleof the Allee effect.
A similarargumentcan be used to categorizeother
phenomenaarisingfrom low populationdensityor size.
Inbreedingdepression,for example,is commonlyproposedto leadto reducedfitnessat low densities.InbreedOIKOS 87:1 (1999)
ing could be consideredto generatean Allee effect since
the degreeof inbreedingdepressionto whichan individual is subjectdependson the size of the populationinto
which it is born.
Oneof the importantconclusionswe derivefromthese
distinctionsbetweencomponentand demographicAllee
effects as well as between the forms of demographic
stochasticityis that Allee effectsdo not inevitablylead
to impactson net populationgrowth, such as positive
densitydependenceandunstablelowerequilibria;neither
do the existenceof these implyunderlyingAllee effects.
An Alleeeffectat the levelof the populationimpliesthat
positive densitydependenceresultsfrom the effects of
densityon the fatesof, andinteractionsbetween,individuals within the population.
In summary,following our definitionof the Allee
effect,whichis closelybasedon Allee'soriginalwork,it
is reasonableto includestochasticsex ratio fluctuations
as a mechanismleadingto Allee effectsbut misleading
to group stochasticbirth and death processestogether
with Allee effects. Although stochasticmortality and
natality produce increasedextinction risks for small
populations,they are qualitativelydifferentfrom Allee
effectmechanismsand will occureven in the absenceof
a requirement
for conspecificinteractions.It is important
to emphasisethis differenceby retainingthesewithinthe
separateidea of demographicstochasticity,ratherthan
subsumingthem into a relaxeddefinitionof Allee effect
mechanisms.
- This work was partlyfundedby a grant
Acknowledgements
from the NaturalEnvironmentResearchCouncilto PAS.
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