The evolution of cooperation and altruism

12 Pages·2006·0.52 MB·English

doi:10.1111/j.1420-9101.2006.01119.x
TTAARRGGEETT RREEVVIIEEWW
The evolution of cooperation and altruism – a general framework
and a classification of models
L. LEHMANN*(cid:2) & L. KELLER*
*DepartmentofEcologyandEvolution,UniversityofLausanne,Biophore,Lausanne,Switzerland
(cid:2)DepartmentofGenetics,UniversityofCambridge,DowningStreet,Cambridge,UK
Keywords: Abstract
altruism; Oneoftheenduringpuzzlesinbiologyandthesocialsciencesistheoriginand
cooperation; persistence of intraspecific cooperation and altruism in humans and other
kinselection; species.Hundredsoftheoreticalmodelshavebeenproposedandthereismuch
groupselection; confusion about the relationship between these models. To clarify the
punishment; situation, we developed a synthetic conceptual framework that delineates
strongreciprocity. the conditions necessary for the evolution of altruism and cooperation. We
show that at least one of the four following conditions needs to be fulfilled:
direct benefits to the focal individual performing a cooperative act; direct or
indirect information allowing a better than random guess about whether a
givenindividualwillbehavecooperativelyinrepeatedreciprocalinteractions;
preferential interactions between related individuals; and genetic correlation
betweengenescodingforaltruismandphenotypictraitsthatcanbeidentified.
When one or more of these conditions are met, altruism or cooperation can
evolve if the cost-to-benefit ratio of altruistic and cooperative acts is greater
than a threshold value. The cost-to-benefit ratio can be altered by coercion,
punishment and policing which therefore act as mechanisms facilitating the
evolution of altruism and cooperation. All the models proposed so far are
explicitlyorimplicitlybuiltonthesegeneralprinciples,allowingustoclassify
them intofour general categories.
Sachs etal. (2004) proposed a useful hierarchical
Introduction
framework to compare models, but they did not clearly
When interacting individuals are related, the evolution distinguish between helping behaviours that result in
of intraspecific cooperation and altruism (collectively positive effects on the direct fitness of the actor from
referred to as helping, see later for a more formal those that result in negative effects on the direct fitness
definition) is generally studied within the framework of of the actor. For instance, it remains unclear in their
kin selection (Hamilton, 1964; Grafen, 1984; Taylor, discussion whether the investment into helping of an
1992a; Frank, 1998; West etal., 2002). By contrast, individual under direct reciprocation actually increases
numerous theoretical models have been proposed to or decreases its fitness (Sachs et al., 2004, p. 139). Here
account for how helping can evolve when individuals we argue that such a distinction is useful because it
are unrelated. In most cases the similarities and forces one to analyse the selective forces responsible for
differences between these models and their relationship the evolution of helping in terms of the two funda-
with kin selection models is obscure. In a recent paper mental components of selection, i.e. direct and indirect
selection (Hamilton, 1964; Grafen, 1984). This is
illustrated by developing a simple conceptual frame-
Correspondence:LaurentLehmann,DepartmentofEcologyandEvolution,
work based on the analysis of a model, which allows
UniversityofLausanne,Biophore,1015Lausanne,Switzerland.
us to delineate the prerequisites necessary for the
Tel.:[phone];fax:[phone];
e-mail:[email protected] evolution of intraspecific altruism and cooperation.
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1366 L. LEHMANN AND L. KELLER
The model is framed within the direct fitness (see alsosupplementarymaterial,eqn 8).Inthiseqn,1
approach (Taylor & Frank, 1996; Frank, 1998; Rousset designates the relative baseline fecundity of an individ-
& Billiard, 2000; Rousset, 2004). In the supplementary ual,I (t)thelevelofinvestmentoftheFIintohelpingat
•,j
material we further develop this model to explicit the roundtwhenplayingagainstanindividualofclassj(i.e.
connections with classical approaches. Using this a member of the class of closely related individuals or a
framework, we clarify the relationships between avail- randommemberofthepopulation)andI (t)thelevelof
j,•
able models and categorize them into a few broad investments into helping of its partner at that round.
categories. Taking the average of the fecundities over the different
classes of individuals determines the expected fecundity
of the FI and the fitness of the FI is then defined as the
The model
expected number of offspring reaching adulthood
In our model we first consider a large (infinite) and (Hamilton, 1964):
unstructured (panmictic) population where individuals
xF þð1(cid:3)xÞF
interact in successive rounds of pair-wise interactions w¼ (cid:2);d (cid:2);0: ð2Þ
F
(see supplementary material section for other demo- 0
graphic situations such as geographically structured This is the expected fecundity of the FI relative to the
populations). We assume that the number of rounds of expected fecundity (F0) of an individual randomly sam-
interaction (1, 2, 3, …) for each individual follows a pled from the population. In the fitness function, F•,d
Geometric distribution with parameter x, which desig- designatesthefecundityoftheFIwheninteractingwitha
nates the probability that an individual interacts again closely related individual and F•,0 is its fecundity when
with a partner after a round of interaction took place interactingwitharandomindividualinthepopulation.
(definitions of the symbols are given in Table1). We To study the dynamics of investment in helping, we
also assume that a focal individual (FI) can interact assumethattheinvestmentlevelintohelpingatagiven
with two classes of individuals. The first class, defined round depends linearly on the partner’s investment at
as related, consists of those individuals that have a theprecedinground(Wahl&Nowak,1999a;Killingback
positive probability of bearing genes identical in state & Doebeli, 2002). Hence, the investment depends on
with those of the FI. The second class consists of those three traits: the investment on the first round s, the
individuals that have a lower probability of bearing response slope b on the partner’s investment for the
such genes. The probability of interacting nonrandomly preceding round and the memory m (varying between
with an individual of the related class is denoted by x. zero and one) of the partner’s investment at the
With complementary probability 1)x interactions preceding round. The variable m can be interpreted as
occur randomly with any member of the population. the probability of not making an assignment error by
All repeated rounds of interactions take place with the mistakenlyconsideringthatapartnerhasnotcooperated
same partner (see supplementary material for other in the previous move when in fact he has (Ohtsuki,
situations such as indirect reciprocity). During each 2004). The two first traits (s and b) can evolve and the
round of interaction the FI invests I into helping with dynamics of investment of the FI engaged in repeated
•
I varying between 0 and 1. This investment incurs a reciprocalinteractionswithapartnerofclassjthenreads
•
cost CI to the FI and generates a benefit BI . A fraction
• • I ðtþ1Þ¼mb I ðtÞandI ðtþ1Þ¼mbI ðtÞ; ð3Þ
f of the benefit generated by helping directly returns to (cid:2);j (cid:2) j;(cid:2) j;(cid:2) j (cid:2);j
the FI and the complementary fraction 1)f goes to where the investments at the first round are given by
the partner. Both the costs and the benefits are I (1) ¼ s and I (1)¼ s.
•,j • j,• j
measured in terms of offspring produced. Accordingly, Solving the equations of the dynamics of investments
helping may have divergent effects on the fecundity of (see supplementary material) and substituting into the
the FI and its partner. The effect on the FI’s fecundity fitness function w (eqn 2) allows us to determine the
can be either positive or negative depending on the inclusive fitness effect(Hamilton, 1964)and to establish
value of fBI )CI while the effect on the partner’s the direction of selection on the two evolving traits s
• •
fecundity (1) f)BI is always positive unless the FI gets and b. In the direct fitness approach, the inclusive
•
all the benefits of its helping act (i.e. f¼ 1) or does not fitness effect is calculated by considering the effects of
invest into helping (i.e. I ¼ 0). all ‘actors’ in the population (including the FI himself)
•
As the FI can interact with two classes of individuals on the fitness w of the FI (Taylor & Frank, 1996;
whomayinvestdifferentlyintohelping,thefecundityof Rousset, 2004). Accordingly, one counts the increment
theFIdependsontheclassofindividualswithwhichhe (or decrement) in the FI’s fitness stemming from the
interacts. The relative fecundity of the FI when inter- expression of the behaviour of all its relatives in
acting witha class-jindividual isgivenby the population. Then, the inclusive fitness effect of the
initial move s reads as (see supplementary material
X
F ¼1þ xt(cid:3)1ðBðfI ðtÞþð1(cid:3)fÞI ðtÞÞ(cid:3)CI ðtÞÞ ð1Þ eqns 4, 13 and 14).
(cid:2);j (cid:2);j j;(cid:2) (cid:2);j
t
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Theevolutionofcooperationandaltruism 1367
Table1 Listofsymbols.
FI Abbreviationforfocalindividual
w Fitnessofafocalindividualdefinedasitsexpectednumberofoffspringreachingadulthood.Itisthefecundityofthe
focalindividualrelativetotheaveragefecundityinthepopulation
I Levelofinvestmentintohelping(varyingbetween0and1)
I (t) Levelofinvestmentintohelpingatroundtofanindividualofclassiengagedinrepeatedinteractionswithanindividualofclassj
i,j
I•,j(t) Levelofinvestmentintohelpingatroundtofthefocalindividualengagedinrepeatedinteractionswithanindividualofclassj
C Fecunditycostperunitinvestmentintohelping
B Fecunditybenefitperunitinvestmentintohelping
)c Effectofthebehaviourofthefocalindividualonitsfitness
b Canbeinterpretedintwoways,eitherastheeffectofthebehaviourofthefocalindividualonthefitnessofitsrelatedpartneror
astheeffectofthepartnerwhenbearingthesamegeneastheFIonthefitnessoftheFI
F Totalrelativefecundityofanindividualresultingfromtherepeatedreciprocalinteractionswithitspartners
s Evolvinglevelofinvestmentintohelping(varyingbetween0and1)onthefirstround
b Evolvingresponseslope(varyingbetween0and1)onthepartner’sinvestmentatthepreviousround
a Evolvingresponseslope(varyingbetween0and1)onthepartner’simagescore
z Genericdesignationofanevolvingphenotype,heres,bora
zj Averagephenotypeofanindividualsofcategoryj
z Phenotypeofthefocalindividual
•
z Averagephenotypeofanindividualsofthe‘related’class
d
z Averagephenotypeofanindividualrandomlysampledfromthepopulationinarandomlymixingpopulationor
0
fromthefocalgroupinageographicallystructuredpopulation
V Proportionofthebenefitsgeneratedbyahelpingactthatdirectlyreturntothefocalindividual
x Probabilitythatanindividualinteractsagainwithapartneronceaninteractiontookplace
m Probabilitythatanindividualknowstheinvestmentintohelpingofitspartneratthepreviousmove
q Probabilitythatanindividualknowstheimagescoreofitspartner
x Probabilitythatanindividualinteractsnonrandomlywithanindividualoftherelatedclass
a Probabilitythataindividualinteractsnonrandomlywithanotherindividualthatbearsthesamegenesatthealtruisticlocus
Qj Probabilityofgeneticidentitybetweenpairsofhomologousgenes,onesampledfromtheFIandtheotherfromacategoryjmember
Q• ProbabilityofgeneticidentitybetweentworandomlysampledhomologousgenesintheFI.InhaploidorganismsQ•¼1
Q ProbabilityofgeneticidentitybetweenonegenesampledintheFIandanotheronesampledfromtherelatedclassofindividuals
d
Q ProbabilityofgeneticidentitybetweenonegenesampledintheFIandanotheronerandomlysampledinthepopulationbutexcludingtheFI
0
r ¼ Qd(cid:3)Q0 Coefficientofrelatedness,whichisaratioofdifferenceofprobabilitiesofgeneticidentity
rb)Qc(cid:2)(cid:3)>Q00 Hamilton’srule
N Groupsize
nd Numberofgroups(demes)inthepopulation
ddi0 DPrisopbearbsialitlyporofbsatabyiliintygaintdthisetannactealipatch(cid:3)d0 ¼ 1(cid:3)nPd(cid:3)1di(cid:4)
i¼1
s Survivalprobabilityofanadulttothenextgeneration
k ¼ NNhl Relativepopulationsize,whereNlisthenumberofindividualsinademeoflowdensityandNhisthenumberofindividuals
inademeofhighdensity
fBþð1(cid:3)fÞxmbB(cid:3)C Rousset’s terminology, we categorize as cooperation
DW ¼
IF ð1þðB(cid:3)CÞ(cid:3)xmbÞð1þxmbÞ those cases where the act of helping is associated with
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} an increase in the FI’s direct fitness (i.e. when )c> 0)
(cid:3)c
and as altruism cases where helping is associated with a
x½ð1(cid:3)fÞBþxmbðfB(cid:3)CÞ(cid:4)
þr : ð4Þ decreaseintheFI’sdirectfitness(i.e.)c<0).Asweshall
ð1þðB(cid:3)CÞ(cid:3)xmbÞð1þxmbÞ
see later, using cooperation and altruism as originally
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
b defined by Hamilton is important because the different
As in Hamilton’s (1964) framework, the inclusive conditions are required for the evolution of helping
fitness effect is broken down into the fitness cost of when it results in positive vs. negative effects on the
helping for the FI ()c) and the fitness benefits (b) direct fitness of theFI.
providedtopartnersoftherelatedclassmultipliedbythe Because the inclusive fitness effect of the response
coefficientofrelatedness(r)betweentheFIandindivid- slope is proportional to eqn (4) (see supplementary
uals of that class. The trait spreads when the inclusive material eqns 13–14 and eqns 15–16) the same condi-
fitness effect is positive, that is when Hamilton’s tionsmustbesatisfiedfortheinclusivefitnesseffectofs
rule rb )c>0 is satisfied. Following Hamilton’s and and btobe positive,i.e.
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1368 L. LEHMANN AND L. KELLER
Table2 Classificationofselectivepressurespromotinghelping.
Helping
rb)c>0
fBþð1(cid:3)fÞxmbB(cid:3)Cþrx½ð1(cid:3)fÞBþxmbðfB(cid:3)CÞ(cid:4)>0ðeqn8Þ
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
(cid:3)c b
Cooperation Altruism
)c>0 )c<0
Directbenefits Reciprocation Kinselection Greenbeard
x¼0andr¼0 f¼0andr¼0 x¼0andf¼0 x¼0andf¼0
fB(cid:3)C>0ðeqn6Þ Directreciprocity r xB (cid:3) C >0ðeqn8Þ aB (cid:3) C >0ðeqn9Þherer¼1
|fflfflfflffl{zfflfflfflffl} |{z} |{z} |{z} |{z}
(cid:3)c xmbB(cid:3)C > 0ðeqn7Þ b c b c
|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}
(cid:3)c
Indirectreciprocity
xqaB(cid:3)C > 0ðeqn26oftheappendixÞ
|fflfflfflfflfflffl{zfflfflfflfflfflffl}
(cid:3)c
Thevarioussituationsencapsulatedineqn 8ofthemaintextandshowninTable2arenotmutuallyexclusive,butweconsiderthem
separatelyforsimplicity.
benefitsareequallysharedbetweengroupmembers.Itis
fBþð1(cid:3)fÞxmbB(cid:3)C importanttonotethatwhenfB)C>0issatisfiedhelping
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
(cid:3)c evolves simply because the FI increases its direct fitness
þrx½ð1(cid:3)fÞBþxmbðfB(cid:3)CÞ(cid:4)>0 ð5Þ by performing such an act. This situation has also been
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} previously referred to as weak altruism (Wilson, 1979;
b
Sachs etal., 2004) or by-product mutualism (Brown,
Inequality 5 allows us to delineate the different 1983). More recently it has been discussed under the
conditionswherecooperationandaltruismarefavoured. headingof ‘snowdrift game’(Hauert, 2004).
Table2 summarizes these conditions that will now be There are several situations under which helping
discussedin detailin thenextsections. generatesdirectbenefitsfortheFI(i.e.f>0).Aclassical
case is when individuals invest in communal activities
such as nest defence, nest building and group hunting.
The evolution of cooperation
Whilethebenefitsofsuchcooperationareusuallyshared
Therearetwogeneralsituationswherehelpingcanevolve equallyamongallindividualsinthegroup,thevalueoff
andtheactiscooperative[i.e.ineqn (5)issatisfiedand will also depend on the cooperative behaviour of other
)c> 0].Thefirst iswhenthe FIgetssomedirectbenefit group members when there are synergistic effects of
(i.e. f>0) from its investment in helping. The other is cooperation (Queller, 1985). The selective pressure on
whentheFIbenefitsindirectlyfromrepeatedinteractions helpingisalsoexpectedtobehighwhenthefitnessofan
withapartnerwhoalsoinvestsinhelping(i.e.xmb>0). individualcriticallydependsonitsinvestmentincooper-
Althoughbothsituationsarenotmutuallyexclusive,we ation, for example if helping significantly increases
shallconsiderthemseparatelyforsimplicity. survival (Eshel & Shaked, 2001) or the chance of
inheriting a territory.
Directbenefits
Repeated interactions andinformation
When f> 0 helping can evolve even in the absence of
discriminationbetweenmoreandlessrelatedindividuals Whenindividualsinteractrepeatedly(i.e.x >0)helping
(x ¼ 0)andintheabsenceofrepeatedinteractions(x¼ can evolve even if the FI gets no direct benefits from its
0)when the inequality investment in helping (f¼ 0) and in the absence of
discriminationbetweenmoreandlessrelatedindividuals
fB(cid:3)C>0 ð6Þ
(x ¼ 0)when the inequality
is satisfied. Helping is cooperative because the action
resultsinincreasedfitnessforboththeFI(byfB)C)and xmbB(cid:3)C>0 ð7Þ
itspartner(by(1)f)B).Asimilarresultcanbeobtained is satisfied. In this case, helping is again cooperative
frommodels,whichconsiderasituationwhereunrelated because)c>0.Interestingly,whenrepeatedinteractions
individuals in a group equally share the benefits of a occur with certainty (x ¼1) and individuals have a
cooperativeact(Uyenoyama&Feldman,1980;Nunney, perfect memory (m ¼1), in eqn (7) reduces to the
1985). In that case f is equal to 1/N where N is the thresholdtheoremofKillingback&Doebeli(2002)when
numberofindividualsinthegroup.Clearly,smallgroup individuals do not take into account their own invest-
size facilitates the evolution of cooperation when the ment in the previous move while interacting with their
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Theevolutionofcooperationandaltruism 1369
partner. This result emphasize that cooperation can implementation of helping (i.e. m¼1). In that case the
spread only if interacting individuals have an initial initialmoveandtheslopeconvergerespectivelytowards
tendency to be cooperative (i.e. b>0). At the other s¼ 1 and b¼ 1 (Wahl & Nowak, 1999a). The optimal
extreme when x¼ 0 cooperation can never evolve. In strategyisthustobegenerousonthefirstmovebecause
orderforcooperationtoevolve,theremustbeaminimal itelicitscooperationinreturn.Whilesimulationssuggest
probability to interact again with the same partner and thatsuchastrategyisstableandimmunetotheinvasion
this probability must be greater when the ratio C/B is of cheaters (Wahl & Nowak, 1999a; Killingback &
small (Friedman, 1971; Trivers, 1971; Axelrod & Doebeli, 2002), analytical work seems to indicate that
Hamilton, 1981). this may not be the case when players interact long
Severalmechanismsmayleadtomgreaterthanzero.It enough (Lorberbaum, 1994). The second situation is
iscommonknowledgethathumanshavestrongcapacity when errors occur. While it has been suggested that
tokeeptrackofthenatureoftheirpreviousinteractions direct reciprocity can then be stable (Lorberbaum etal.,
with partners as well as detecting cheating (Fehr & 2002), this seems not to be generally the case. For
Fischbacher, 2003). Experimental studies also revealed instance, in the direct reciprocity setting of Wahl &
thathumansaremorelikelytocooperatewithindividuals Nowak (1999b), discriminator cooperative strategies can
thathavebeencooperativeinpreviousinteractions(Fehr invade defectors but when discriminator cooperative
& Fischbacher, 2003). These are the required conditions strategies have reached a high frequency, nondiscrimi-
for cooperation to evolve by direct reciprocity. While native cooperative strategies may emerge. This, in turn,
direct reciprocity is certainly an important force under- enablesdefectorstoinvade,resultinginapopulationthat
lying altruism in humans, its role in other organisms cycles between cooperation and defection. The same
is highly debated and probably of low significance conclusionholdsforindirectreciprocitywhenreputation
(Hammerstein,2003;Stevens,2004).Oneofthereasons throughimagescoresisbasedonindividualspastactions
for this difference lies in the higher cognitive abilities of (Nowak & Sigmund, 1998). By contrast, sustained
humans that allows for a much higher m-value than in cooperation over time seems possible under indirect
otherorganisms.Goodmemoryisforexamplecrucialin reciprocity when specific assumptions are made on the
‘negotiation games’ where players exchange offers back distribution of the number of rounds of interactions
andforthinanegotiationphaseuntiltheyconvergetoa (Brandt & Sigmund, 2004) or when reputation is
finalpairofcontributions(Taylor&Day,2004). modelled as standing, where an individual’s standing is
In addition to the memory of a partner’s previous not negatively affected by refusing to provide help to
moves, information on whether a given individual is partners in bad standing (Panchanathan & Boyd, 2003).
likely to be cooperative may come from its reputation Itisnotclearwhythesedifferentconditionsleadtosuch
(Nowak & Sigmund, 1998). Here individuals have some contrasting results, and more generally, whether coop-
informationontheoveralllevelofcooperativetendency eration can be stable with imperfect memory and a
of individuals they randomly meet for an interaction. limited number of interactions as is the case for most
Accordingly, they can adjust their investment in natural systems.
cooperation based on the reputation of their partner
and cooperation can evolve by indirect reciprocity
The evolution of altruism
(Nowak & Sigmund, 1998). The difference between
direct and indirect reciprocity lies in the mechanism When )c <0 (i.e. helping is altruistic as it is associated
underlyingtheevaluationofthecooperativetendencyof with a decrease in the FI’s direct fitness but an in
the partner. In the supplementary material, we derive a increase in the direct fitness of individuals receiving
model for the evolution of helping in the presence of help), in eqn (4) can only be satisfied when there are
indirect reciprocity where reputation of the partner different kin classes in the population and helping is
dependsonitsimagescoreandwhereassignmenterrors preferentially directed toward individuals of the related
canoccur.Theconditionfortheevolutionofhelpingby class (i.e. x >0). In the following sections we will
image score is then similar to that in eqn(7) with the differentiate two situations that differ depending on
only difference that m describes the probability of whether the kin classes are defined on the basis of the
correctly assessing the partner’s reputation [i.e. likeli- average genetic similarity over the whole genome
hoodtoknowitssocialscore,whichisdesignatedbyqin (genetic relatedness) or similarity at particular loci
Nowak&Sigmund(1998),seeTable1andeqn 26inthe (greenbeard effect).
supplementary material]. In other words, the main
difference between direct and indirect reciprocity lies in
Preferential interactions andhelping betweenkin
thesourceofinformationratherthanadifferenceinthe
type ofselective forceinvolved. When xr >0, helping can evolve even if the FI gets no
Whether or not repeated interaction leads to stable directbenefitsfromitsinvestmentinhelping(f¼0)and
cooperation is still unclear. Two cases can be distin- whenthereisnorepeatedinteractionsbetweenindivid-
guished. The first is when no errors occur in the uals (i.e.x¼ 0)whenthe inequality
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1370 L. LEHMANN AND L. KELLER
xrB(cid:3)C>0 ð8Þ phenotypic trait used for recognition and the gene(s)
responsible for helping. Imagine the simple case of two
is satisfied. When x¼ 1 (i.e. perfect discrimination genes, one causing a specific phenotypic effect and the
between more and less related partners), the inequality other determining the level of helping and allowing its
simplifies to rB )C> 0, which is the condition for the bearers to determine whether or not other individuals
spread of helping when altruistic acts are directed only exhibit a specific phenotype expressed by the first gene.
toward relatives. Because competition occurs at random Whether or not helping may evolve will depend on the
in the population, this situation represents the family- linkagedisequilibriumbetweenthesetwogenes.Incase
structured model as originally envisioned by Hamilton of perfect linkage, the situation is that of a greanbeard
(1964). In eqn (8), xr measures the extent to which gene,aconceptinventedbyHamilton(1964)andnamed
individuals are more related in altruistic than in com- by Dawkins (1976). A greanbeard gene is defined as a
petitive interactions, in line with the view that individ- genethatcausesaphenotypiceffect(e.g.thepresenceof
uals must be more related in altruistic than in a greanbeard or any other conspicuous feature) that
competitive interactions for helping to evolve when it allows the bearer of this feature to recognize it in other
resultsinanetfecunditycost(Queller,1994).Inversely, individuals, and results in the bearer to behave differ-
when helping is provided irrespective of relatedness, entlytowardotherindividualsdependingonwhetheror
helpingcannotbeselectedforunlessitresultsinadirect not they possess the feature. If a haploid greenbearded
fecunditybenefit,aresultwhichusuallyholdswhatever individual has a probability a to correctly identify
the genetic structure of the population (Taylor, 1992b; and preferentially interact with another greenbearded
Rousset,2004)(see supplementarymaterial). individual investment into helping is selected when
Severalmechanismsmaygenerateanxgreaterthan0.
Themostcommoninnatureisprobablytheuseofspatial aB(cid:3)C>0 ð9Þ
cues with individuals expressing conditional altruism in is satisfied and one recovers the conditions described by
thenatalnestorcolony.Indeedmostoftheextremecases Hamilton(1975).Importantly,thisinequalityissimilarto
of altruism are found within families such as in social in eqn (8), the parameter a being equivalent to x. The
insects (Keller & Chapuisat, 2001). A more active and coefficientofrelatednessisequaltooneherebecausethe
refined mechanism is phenotype-matching, with indivi- probability of genetic identity at the altruistic locus is
duals being able to actively estimate their genetic one. This situation of preferential interactions between
similaritybycomparingtheirownphenotypiccharacter- individuals sharing the same altruistic gene is also
istics with those of other individuals (Reeve, 1989). As sometimes referred to as ‘assortative meeting’ models
common genealogy generates phenotypic similarity for (Eshel & Cavalli-Sforza, 1982). If recombination can
geneticallydeterminedtraits,eachtraitcanbeusedasan break down the linkage between ‘recognition’ and
independent value to estimate average genetic identity. ‘altruistic’ genes, the situation become quite different
This is a process of statistical inference with arbitrary because altruism becomes intrinsically unstable. This
phenotypictraitsbeingusedasquantitativeorqualitative is because individuals with the gene conferring the
variables. Importantly, both spatial recognition and greenbeard phenotype but without the gene coding
phenotype matching lead to uniform genetic similarity altruism will have greatest fitness and there will be a
overthewholegenome.Hamilton’sruleisthenbroadly rapid decrease in frequency of the altruism gene. In
satisfied and there is no intragenomic conflict. In other contrast, if the recognition and altruistic effects are the
words,altruismisstableandimmunetocheating(Seger, productofasinglegeneortwocompletelylinkedgenes,
1993). However, deception may occur when individuals a breakdown of the system can occur only after the
can circumvent the recognition mechanism. This may evolution of a new gene, which confers the greenbeard
occur when individuals succeed in infiltrating a foreign but not response effect. In other words, greenbeard
family.Anexcellentexampleofthisissocialparasitismin systemsshouldessentiallybeunstableoverevolutionary
ants,wherequeensenterforeignestablishedcoloniesand time, with rapid collapse if there are two genes and
securehelpfromtheresidentworkerstoraisetheirbrood recombination and significantly slower collapse when
ofreproductiveindividuals.Importantly,however,these the greenbeard and response effect are the product of a
cases of parasitism are expected to be relatively rare single geneortwo geneswithoutrecombination.
because frequency-dependent selection on the recogni-
tionsystemofthehostsshouldmaintaintherateofpara-
Cost and benefit of helping
sitismundercheck(Reeve,1989;Axelrodetal.,2004).
In the previous sections we highlighted four situations
Greenbeard effect conducivetotheevolutionofhelping.Foreachofthese
The other possible mechanism leading to altruism is situations, the condition required for helping to be
when preferential interactions between the FI and favoured is directly dependent on the cost to benefit
related individuals at the helping loci are mediated by a ratio(C/B)ofthisbehaviour.Theimportanceofthisratio
linkage disequilibrium between the gene encoding a has been repeatedly recognized. For example, both the
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Theevolutionofcooperationandaltruism 1371
roleofecologicalfactorsandspecies-specificidiosyncratic models show that punishment should co-evolve with
characteristics, which benefit altruism are all important cooperation if the cost of being punished is sufficiently
in promoting the evolution of reproductive altruism in high to make it a better option not to behave selfishly
social insects. Thus, it has been suggested that the andifthecostofpunishmentissmallerthanthebenefit
presenceofastingandtheraisingofbroodinacomplex gained by the punisher in terms of increased group
nest are preadaptations responsible for the dispropor- productivity and survival. An important simplifying
tionate number of eusocial evolution in Hymenoptera assumption of these models is that individuals cannot
(Seger, 1993). Similarly, living in a relatively invariable develop countermeasures or retaliate to punishment. It
and warm climate coupled with low annual mortality would be of interest to determine the evolutionary
possibly predisposes certain taxonomic lineages of birds consequences of countermeasures and/or arms races
to cooperative breeding(Arnold& Owens,1999). between conflicting parties on the stability of the pun-
Another central issue that has received increased ishment andcooperation.
attention over the last decade is that the costs and Thisbriefoverviewofmodelsrevealsthatpunishment
benefits of helping are not fixed variables since other and other behaviours of that type have the potential to
groupmemberscanactivelyalterthem.Thiscanoccurby influencethecost/benefitratioofcooperativeacts.These
coercion, punishment and policing (collectively called behaviours can thus alter the social and demographic
punishment hereafter) which, in essence, imply that a conditions where cooperation may evolve. However,
fineisimposedondefectors.Asaresult,therelativecost thesemodelsarestillintheirinfancyanditremainstobe
ofdefectingbecomesgreatercomparedwiththealternate studied whether their predictions would be altered if
optionof helping. someof theircrucialassumptions werenot fulfilled.
Numerous models of coercion, punishment and poli-
cing have been developed and they can be broadly
A classification of models of helping
separatedintwoclasses.Thefirstclassmainlyconceives
punishment as a mechanism channelling the behaviour Our general model revealed that there are four general
ofdefectorstowardhigherlevelsofcooperation(Boyd& situations where helping is favoured. The first is when
Richerson, 1992; Clutton-Brock & Parker, 1995; Bowles the act of helping provides direct benefits to the FI that
&Gintis,2004).Thegeneralideaofthesemodelsisthat outweighs the cost of helping (i.e. there are direct
when individuals interact repeatedly, punishment is benefits). In that case helping simply evolves because it
selected because the ensuing cost ismorethan compen- is associated with an increase of the direct fitness of the
satedbytheshifttocooperationofthepartner.Thereare FI. The second situation is when the FI can alter the
several important assumptions in these models (Boyd & behaviourresponseofitspartnersbyhelpingandthereby
Richerson, 1992; Bowles & Gintis, 2004). First, the receives in return benefits that outweigh the cost of
punishing and cooperativetraits are frequentlyassumed helping.Inbothsituations,thehelpingactiscooperative
linked,constitutingaso-called‘strongreciprocator’gene. asitresultsinanincreaseofthefitnessofboththeFIand
However,thereisnoapriorireasontoassumethatthese its partners. A difference, however, is that in the first
traitsarelinked.Infact,itismorelikelythatthesetraits situation the increase of the FI’s fitness is because of its
willbeunlinked(Gardner&West,2004)andsimulations own behaviour while in the second situation it results
suggest that cooperation is not stable when cooperation from the behavioural change induced in its partner(s).
and punishing can co-evolve (L. Lehmann & L. Keller, ThethirdsituationconducivetoaltruismiswhentheFI
unpublisheddata).Thesecondandrelatedassumptionis interactsandprovideshelptorelatedindividuals(i.e.kin
that these models assume that ‘strong reciprocators’ can selection). In that case, Hamilton’s rule provides the
recognize and punish defectors conditionally. In other conditions when helping can evolve even when it is
words,thesemodelsareakintogreenbeardmodelswith associated with a decrease in the FI’s direct fitness (i.e.
helping behaviour being used as the ‘recognition cue’. whentheactisaltruistic).Thefourthsituationisaspecial
Accordingly, strong reciprocators are always harmful case of the third with, in this case, recognition and
towards defectors. It remains to be studied what the helping being coded by two individual loci (i.e. green-
consequences would be of allowing conditional expres- beard effect). In that case, helping can also evolve and
sion of both cooperation and punishment as well as the remain stable when the two loci are linked and the
possibility of these two traits to evolve independently conditions ofHamilton’s rule arefulfilled.
with explicitgenedynamics. In this section we shall briefly review several models
Thesecondclass ofmodels envisions punishmentas a proposed for the evolution of cooperation and altruism
mechanism suppressing selfish behaviour, which may andinvestigatewhethertheycanbeclassifiedinthefour
threaten group integrity and/or productivity (Clutton- general categories outlined above or whether there are
Brock & Parker, 1995; Frank, 1995; Reeve & Keller, other general selected forces that may select for
1997). This would, for example, be the case of a cooperation and altruism. We list in Table 3 a subset of
behaviour that would increase the relative share of an models selected on the criteria of representing to us
individual at a cost to overall group productivity. These ‘influentialororiginalmodels’.Thistablerevealsthatall
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1372 L. LEHMANN AND L. KELLER
Table3 Subsetofmodelsselectedonthe
Helping
criteriaofrepresentingtous‘influentialor
originalmodels’.
Cooperation Altruism
)c>0 )c<0
References Directbenefits Reciprocation Kinselection Greenbeard
Friedman(1971) +
Hamilton(1975) + +
Cohen&Eshel(1976) +
Wilson(1977) +
Uyenoyama&Feldman(1980) + +
Axelrod&Hamilton(1981) +
Eshel&Cavalli-Sforza(1982) + +
Vehrencamp(1983) +
Nunney(1985) + +
Queller(1985) + + +
Nowak&May(1992) +
Nowak&Sigmund(1992) + +?
Dugatkinetal.(1994) + +
Frank(1995) + +
Nakamaruetal.(1997) + +
Wilson&Dugatkin(1997) + +
Nowak&Sigmund(1998) +
VanBaalen&Rand(1998) +
Michod(1998) + +
Roberts&Sherratt(1998) +
Reeveetal.(1998) + +
Killingbacketal.(1999) +
Taylor&Irwin(2000) + + +
Kokkoetal.(2001) + +
Eshel&Shaked(2001) +
Aviles(2002) +
Killingback&Doebeli(2002) +
Pepper&Smuts(2002) +
LeGalliardetal.(2003) +
Bowlesetal.(2003) + +?
Boydetal.(2003) + +?
Traulsen&Schuster(2003) +
Axelrodetal.(2004) +
Panchanathan&Boyd(2004) +
Ohtsuki&Iwasa(2004) +
Taylor&Day(2004) +
Hauert(2004) + +
Pfeifferetal.(2005) +
thesemodelsfallwithinoneofthefourgeneralcategories at the beginning of the simulation, with the effect that
at least once. Some models actually fall in several cate- altruists generally do better than defectors. In this
gories,anditisnotalwayseasytodisentangletherelative situation, altruism can be maintained as long as
rolesoftheforcespromotingaltruismorcooperation. individuals are more related in altruistic than in
Four types of models deserve special attention in that competitive interactions, which are the conditions
theyhavebeenproposedasprovidingnewprinciplesfor required for kin selection to operate (Queller, 1994).
theevolutionofcooperationandaltruism.Thefirstclass Hence, the heuristic eqn (p. 1725) of Killingback etal.
consists of ‘spatial structuring’ models (Nowak & May, (1999) exactly gives Queller’s requirements for kin
1992; Killingback etal., 1999). A close inspection of selection to be effective.
these models shows that the actual selective force Several demographic factors can sustain the spread of
operating in the system is generally kin selection. Thus, an altruistic gene under ‘spatial structuring’ when
inthe simulations of Nowak & May (1992),altruists are initially rare. Thus, overlapping generations have a
more likely to be surrounded by altruists than defectors greater effect on the kin selected benefits of altruism
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Theevolutionofcooperationandaltruism 1373
than on kin competition (Taylor & Irwin, 2000) (see system is not stable over time because the association
supplementary material). Similarly, the capacity of the between the tag and altruistic genes is bound to decay
population to expand as a consequence of helping can just as any greenbeard mechanism (Roberts & Sherratt,
facilitate the spread of altruism. This might occur when 2002). Similarly, the ‘grouping’ model leads to altruism
the population remains unsaturated through environ- because altruistic individuals are more likely to group
mental and/or demographic stochasticity (Van Baalen & and interact. This is once again a special case of a
Rand,1998;Mitteldorf&Wilson,2000;LeGalliardet al., greenbeard mechanism, which cannot be stable over
2003) or when helping increases group survival or time. Indeed, selection should favour nonaltruistic indi-
carrying capacity (see supplementarymaterial). viduals to preferentially associate with altruists. As a
Realising that the actual force promoting altruism in result, the association between the altruistgeneand the
spatially structured models in kin selection is important recognition trait (in that case grouping behaviour) will
because it helps to identify the actual demographic and decay andaltruism willdisappear.
biological processes promoting the trait. Frequently, it is Thefinalclassofmodelstobediscussedarethe‘group
claimedthatanewmechanismfavouringcooperationor selection’ models. The general idea of these models is to
altruismhasbeenidentified.However,whathasusually useamulti-levelselectionapproachtopartitionselection
been found is a new situation (e.g. demographic or into components of within group and between group
environmental stochasticity, overlapping generations, selection.Contrary to whatissometimesclaimed,group
particular recognition mechanism) underlying higher selection models are not fundamentally different from
relatedness during cooperative rather than competitive classical models and it is possible in every instance to
interactions.Inthesupplementarymaterialweshowthat translate from one approach to the other without
itispossibletodisentanglebetweencomponentsofdirect disturbing the mathematics describing the net result of
and kin selection in spatial structuring models and thus selection, (see eqn A6 of the supplementary material)
toidentifytheselectiveforcespromotinginvestmentinto (Hamilton,1975;Grafen,1984;Dugatkin&Reeve,1994;
helping. Frank,1998; Rousset,2004).
The second class of models are reproductive skew Thetransitionfromunicellularitytomulticellularityis
models which include ecological, genetic and social a classical example used to exemplify the role of group
factors in a single explanatory framework and aim at selection (Michod, 1998). Importantly, however, the
determining how these factors jointly influence the highlevelofcooperationbetweencellsinamulticellular
apportionment of reproduction (reproductive skew) organism can just as well be explained by kin selection
among group members (Vehrencamp, 1983; Reeve & (Queller, 2000). Indeed, a key factor necessary for the
Ratnieks, 1993; Reeve & Keller, 1995). In essence, evolutionofthehighlycooperativenatureofinteractions
reproductive skew models delineate the possible repro- between cells is probably a high relatedness, which is
ductive strategies available to a FI and define the generally attained by multicellular organisms going
conditions under which the best strategy is to cooperate through a unicellular phase such as the egg stage
andsacrificepartorallofitsdirectoffspringproduction. (Wolpert &Szathmary, 2002).
Importantly, all these models are based on the explicit The other important selective force that operates in
comparison of inclusive fitness of individuals adopting many group selection models is cooperative action
alternate reproductive strategies. An analysis of these providing direct benefits to the FI. A classical example
modelsrevealsthatindividualswillstayinthegroupand is Wilson’s (1977) model of random group formation
forego direct reproduction only when such an act where cooperation evolves only so far that the direct
provides either direct benefits (i.e. fB)C>0 and the benefits to the FI exceeds the costs. Unfortunately,
act is cooperative, for example because such a strategy in-group selection models it is not always easy to
increasesgroupsurvivalortheprobabilityofinheritinga determine the relative importance of relatedness and
territory (Kokko & Johnston, 1999; Ragsdale, 1999) or directbenefits.Thisisparticularlytrueinsettingswhere
becauseindividualscanincreasethereproductiveoutput groupscompeteagainsteachotherandreproduceas,for
of related individuals (i.e. xrB )C>0 and the act is instance,inthestochasticcorrectormodel(Szathmary&
altruistic;e.g.,(Reeve&Keller,1995;Reeveetal.,1998). Demeter,1987).Thedifficultywiththisclassofmodelsis
Thethirdclassofmodelsareso-called‘tag-recognition’ that the costs and benefits are functions of group
(Rioloetal.,2001)and‘grouping’(Aviles,2002)models. composition and growth rate, which are highly depend-
The tag-recognition system is when an altruistic gene is ent on interactions within and between groups. The
partially linked to a tag that can be recognized by other complexityofthesituationmakesitdifficulttodelineate
membersinthepopulation.Inotherwords,thesemodels analytically the relative importance of kin selection and
fall in the greenbeard category with incomplete linkage direct benefits. But realising that the actual force
between the altruistic and recognition traits. Realising promoting cooperation under group selection is a com-
thisisusefulforatleasttworeasons.First,itwouldhave bination of kin selection and direct benefits allows us to
prevented confusion about the actual selective force at delineate more clearly the role of the factors promoting
work. Second, it would have helped to realise that the orrepressing cooperationandaltruism.
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1374 L. LEHMANN AND L. KELLER
Conclusion Acknowledgments
The conceptual framework developed here emphasizes We thank Stuart West for encouraging us to write our
that there are four general situations conducive to paper as a target article as well as him, Robert Boyd,
helping and that all models proposed so far can be Franc¸ois Balloux, Michel Chapuisat, Ernst Fehr, Pierre
classified accordingly. Hence, cooperation and altruism Fontanillas, Sebastian Bonhoeffer, Timothy Killingback,
can evolve only when there are direct benefits to the FI Karen Parker, Nicolas Perrin, Virginie Ravigne´, Max
performing a cooperative act, repeated interactions with Reuter, Karl Sigmund, Claus Wedekind, Tom Wense-
direct or indirect information on the behaviour of the leers,DavidSloanWilsonandtwoanonymousreviewers
partner in previous moves, preferential interactions forveryusefulcommentsonthemanuscriptandFranc¸-
between related individuals and/or a linkage disequilib- ois Rousset for providing a draft of his book. This work
riumbetween genes coding for altruism andphenotypic was funded by grants of Swiss NSF to LK and Nicolas
traits that can be identified. In the three later cases Perrin.
helping evolves because there is a positive association
between individuals at the genotypic and/or phenotypic
Conflicts of interest
levels. The other parameter of paramount importance is
the cost-to-benefit ratio of helping acts that can be The authors declare that they have no competing
alteredbycoercion, punishmentandpolicing. However, financial interests.
becausetheselaterbehavioursarecostlytheycanevolve
and remain stable only when at least one of the four
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