5INTRODUCTIONof one or other aspect, to discuss how density-much-used term then-the word diversity does notdependent or nonlinear effects, interacting to var-appear in the index to May's Stability and Complexityious degrees withdemographicand environmentalinModelEcosystems(1973a),andalthoughitdoesstochasticity, can result in relatively steady, orappear in the indexes for TEI and TEII, it clearlymeans simply numbers of species).Ives carefullycyclic,orerraticallyfluctuatingpopulationdynamics.They also sketch progress that has beenenumeratesthevaried interpretations whichhavemade in looking at the'flipside of chaos',namelybeen placed on the terms complexity/diversity andthe question of whether, when we see apparentlystability.He goes on to give a thumbnail sketch ofnoisy time series, we are looking at'environmentalthe way ideas have evolved in this area, guided byand other noise'or a deterministic but chaotic sig-empirical and theoretical advances,and concludesnal.This survey is woven together with illustrativebypresenting models which illustrate how theaccounts of field studies and laboratory experi-answerstoquestionsabout communitydynamicsments.InChapter4Neewidensthediscussionofcan depend on preciselyhow the questions arepopulation dynamics to look at some of the com-framed.In Chapter 9 May,Crawley,and Sugiharaplications which arise when a single population issurveyarangeofrecentworkon‘communitypat-spatially distributed over many patches. Fore-terns:the relativeabundance of species; species-shadowing later chapters on conservation biologyarea relations; the network structure of food webs;and on infectiousdiseases,heemphasizesthatyouand other things. This survey, which in places is ado not have to destroy all of a population's habitatbit telegraphic, seeks to outline both the underlyingto extinguish it. Widening the survey to include twoobservations and the suggested theoretical expla-populations interacting as competitors,predator-nations, including null models (old and new)andprey or mutualists, Nee further indicates otherscalinglaws.aspects of the dynamics of such so-called meta-populations which may seem counter-intuitive.1.2.2ApplicationstopracticalproblemsThe next three chapters expand on interactingThe next five chapters turn to particular applica-populations. Bonsall and Hassell first survey thedynamical behaviour of prey-predator interac-tions of thesetheoretical advances.Grenfell andtions. This chapter takes for granted some of theKeeling(Chapter 10)deal withthe dynamicsby-now familiar material presented in TEIl, givingand control of infectious diseases of both hum-more attention to the way spatial complexitiesansand otheranimals.Theybeginbyexplainingcontributeto the persistenceof such associationshow basic aspects of predator-preytheory apply(and also noting that such spatial heterogeneityhere,with particular emphasison theinfection'scan even be generated by the nonlinear nature ofbasic reproductive number,Ro.Recent applica-the interactions themselves, even in an homo-tions to the outbreak of foot-and-mouth diseaseamong livestock in theUK arediscussed in somegeneous substrate).Crawley gives an overview ofthe dynamics of plant populations,interpretingdetail, although other examples could equally'plants'broadly to emphasize therange of differ-well have been chosen (HIV/AIDS, SARS, H5N1entconsiderations whichariseaswemovefromavian flu).Grenfell and Keeling emphasize thediatoms to trees.This chapter also discusses plant-essential interplay between massively detailedherbivoreinteractionsasanimportantspecial casecomputations (the foot-and-mouth disease out-break was modelled at the level of every farm inof predators and prey.Competitive interactionsBritain,an extremeexampleofan individual-levelarediscussed by Tilman in Chapter 7,drawingtogether theoretical advances with long-term andapproach toapopulation-level phenomenon)andotherfield studies.basic dynamical understanding of what is goingChapters 8 and 9 deal with the theoretical ecol-on,basedonsimplemodels.ogyof communities.Ives'chaptermighthaveInChapter11BeddingtonandKirkwoodgiveanbeen called Complexity and stability in the 1970saccountoftheecologyof fisheries andtheirprac(not Diversity and stability, diversity was not atical management.This chapter explains how the
of one or other aspect, to discuss how densitydependent or nonlinear effects, interacting to various degrees with demographic and environmental stochasticity, can result in relatively steady, or cyclic, or erratically fluctuating population dynamics. They also sketch progress that has been made in looking at the ‘flipside of chaos’, namely the question of whether, when we see apparently noisy time series, we are looking at ‘environmental and other noise’ or a deterministic but chaotic signal. This survey is woven together with illustrative accounts of field studies and laboratory experiments. In Chapter 4 Nee widens the discussion of population dynamics to look at some of the complications which arise when a single population is spatially distributed over many patches. Foreshadowing later chapters on conservation biology and on infectious diseases, he emphasizes that you do not have to destroy all of a population’s habitat to extinguish it. Widening the survey to include two populations interacting as competitors, predator– prey or mutualists, Nee further indicates other aspects of the dynamics of such so-called metapopulations which may seem counter-intuitive. The next three chapters expand on interacting populations. Bonsall and Hassell first survey the dynamical behaviour of prey–predator interactions. This chapter takes for granted some of the by-now familiar material presented in TEII, giving more attention to the way spatial complexities contribute to the persistence of such associations (and also noting that such spatial heterogeneity can even be generated by the nonlinear nature of the interactions themselves, even in an homogeneous substrate). Crawley gives an overview of the dynamics of plant populations, interpreting ‘plants’ broadly to emphasize the range of different considerations which arise as we move from diatoms to trees. This chapter also discusses plant– herbivore interactions as an important special case of predators and prey. Competitive interactions are discussed by Tilman in Chapter 7, drawing together theoretical advances with long-term and other field studies. Chapters 8 and 9 deal with the theoretical ecology of communities. Ives’ chapter might have been called Complexity and stability in the 1970s (not Diversity and stability; diversity was not a much-used term then—the word diversity does not appear in the index to May’s Stability and Complexity in Model Ecosystems (1973a), and although it does appear in the indexes for TEI and TEII, it clearly means simply numbers of species). Ives carefully enumerates the varied interpretations which have been placed on the terms complexity/diversity and stability. He goes on to give a thumbnail sketch of the way ideas have evolved in this area, guided by empirical and theoretical advances, and concludes by presenting models which illustrate how the answers to questions about community dynamics can depend on precisely how the questions are framed. In Chapter 9 May, Crawley, and Sugihara survey a range of recent work on ‘community patterns’: the relative abundance of species; species– area relations; the network structure of food webs; and other things. This survey, which in places is a bit telegraphic, seeks to outline both the underlying observations and the suggested theoretical explanations, including null models (old and new) and scaling laws. 1.2.2 Applications to practical problems The next five chapters turn to particular applications of these theoretical advances. Grenfell and Keeling (Chapter 10) deal with the dynamics and control of infectious diseases of both humans and other animals. They begin by explaining how basic aspects of predator–prey theory apply here, with particular emphasis on the infection’s basic reproductive number, R0. Recent applications to the outbreak of foot-and-mouth disease among livestock in the UK are discussed in some detail, although other examples could equally well have been chosen (HIV/AIDS, SARS, H5N1 avian flu). Grenfell and Keeling emphasize the essential interplay between massively detailed computations (the foot-and-mouth disease outbreak was modelled at the level of every farm in Britain, an extreme example of an individual-level approach to a population-level phenomenon) and basic dynamical understanding of what is going on, based on simple models. In Chapter 11 Beddington and Kirkwood give an account of the ecology of fisheries and their practical management. This chapter explains how the INTRODUCTION 5
6THEORETICALECOLOGYdynamicsof fishpopulations—as single species orpopulation, and to do so in a way where crops arein multispecies communitiesinteracts with prac-adapted to their environment (as distinct from pasttical policy options (quotas, tariffs, licenses, etc.),practice, where too often the environment wasinwayswhichcanbecomplicatedand sometimeswrenched to serve the crops by fossil-fuel energycounter-intuitive.This is an area in which science-subsidies). Conway stresses that engagement andbased advice can be in conflict with politicalempowerment of local people is essential if thisDoubly Green Revolution is to be realized, whichconsiderations, sometimes in ways which haveinteresting resonance with the problems discussedagain harks back to Nowak and Sigmund.in Nowak and Sigmund's opening chapter on theChapter 13 by Dobson, Turner, and Wilcoveevolution of cooperation.In passing,weobservedeals directly with conservation biology, survey-ing some of the factors which threaten species withthat a vast amount of interesting ecological data,and also of excellent theoretical work, is to beextinction,indicating possible remedial actions,found in the grey literature associated with thebut also noting someof the economic and politicalwork of bodieslikethe International Council forrealities that can impede effectiveaction.ChaptertheExplorationoftheSeas(ICES)ortheScientific14,on ClimateChange and Conseruation Biology,byCommitteeoftheInternational WhalingCommis-Kerr and Kharouba, amplifies one particularlysion (IWC); it is unfortunate that too little of thisimportant threat to the survival of species, namelymakes its way into mainstream ecological meet-the effects that climate change are likely to have onings and scientific journals.We think Chapter 11 isspecieshabitats and ranges.particularly interesting for the way it reaches intoThe concluding Chapter 15 offers a selective andthis grey literature.opinionated review of some of themajor environ-The term Doubly Green Revolution was coinedmental threats that loom for us and other speciesby Gordon Conway,one of the three continuingover the comingfewcenturies.Theemphasis is onauthors from TEII (along with Hassell and May).issues where ecological knowledge can provideaHere, in Chapter 12, he surveys the triumphs andguide to appropriate action, or to areas whereproblems of the earlier Green Revolution, whichcurrent lack of ecological understanding is a han-has doubled global food production on only 10%dicap.One thing is sure: the future for other livingadditional land area over thepast 30 years or so.things on planet Earth, not just humans, dependsLooking to the future, he suggests how new tech-on our understanding and managing ecosystemsnologies offer the potential to feed tomorrow'sbetter than we have been doing recently
dynamics of fish populations—as single species or in multispecies communities—interacts with practical policy options (quotas, tariffs, licenses, etc.), in ways which can be complicated and sometimes counter-intuitive. This is an area in which sciencebased advice can be in conflict with political considerations, sometimes in ways which have interesting resonance with the problems discussed in Nowak and Sigmund’s opening chapter on the evolution of cooperation. In passing, we observe that a vast amount of interesting ecological data, and also of excellent theoretical work, is to be found in the grey literature associated with the work of bodies like the International Council for the Exploration of the Seas (ICES) or the Scientific Committee of the International Whaling Commission (IWC); it is unfortunate that too little of this makes its way into mainstream ecological meetings and scientific journals. We think Chapter 11 is particularly interesting for the way it reaches into this grey literature. The term Doubly Green Revolution was coined by Gordon Conway, one of the three continuing authors from TEII (along with Hassell and May). Here, in Chapter 12, he surveys the triumphs and problems of the earlier Green Revolution, which has doubled global food production on only 10% additional land area over the past 30 years or so. Looking to the future, he suggests how new technologies offer the potential to feed tomorrow’s population, and to do so in a way where crops are adapted to their environment (as distinct from past practice, where too often the environment was wrenched to serve the crops by fossil-fuel energy subsidies). Conway stresses that engagement and empowerment of local people is essential if this Doubly Green Revolution is to be realized, which again harks back to Nowak and Sigmund. Chapter 13 by Dobson, Turner, and Wilcove deals directly with conservation biology, surveying some of the factors which threaten species with extinction, indicating possible remedial actions, but also noting some of the economic and political realities that can impede effective action. Chapter 14, on Climate Change and Conservation Biology, by Kerr and Kharouba, amplifies one particularly important threat to the survival of species, namely the effects that climate change are likely to have on species’ habitats and ranges. The concluding Chapter 15 offers a selective and opinionated review of some of the major environmental threats that loom for us and other species over the coming few centuries. The emphasis is on issues where ecological knowledge can provide a guide to appropriate action, or to areas where current lack of ecological understanding is a handicap. One thing is sure: the future for other living things on planet Earth, not just humans, depends on our understanding and managing ecosystems better than we have been doing recently. 6 THEORETICAL ECOLOGY
CHAPTER 2How populations cohere: fiverulesfor cooperationMartinA.Nowak and KarlSigmundSubsequent chapters in this volume deal withis a fundamental principle that is required forpopulations as dynamic entities in time and space.every level of biological organization.IndividualPopulationsare,of course,madeupofindividuals,cellsrelyoncooperationamongtheircomponents.and the parameters which characterize aggregateMulticellular organisms exist because of coopera-behaviorpopulation growth rate and so on-tion among their cells.Social insects are masters ofultimately derive from the behavioral ecology andcooperation.Most aspects of human society arelife-history strategies of these constituent indivi-based onmechanismsthatpromote cooperation.duals.In evolutionary terms,the propertiesWhenever evolution constructs something entirelyof populations can only be understood in termsnew (such as multicellularity or human language),of individuals, which comes down to studyingcooperation is needed.Evolutionary constructionhow life-history choices (and consequent gene-isbased on cooperation.frequency distributions)are shaped by environ-Thefive rulesfor cooperation which we examinemental forces.in this chapter are: kin selection, direct reciprocity,Many important aspects of group behavior-indirect reciprocity,graph selection, and groupfromalarmcallsof birds andmammalstotheselection.Each of these canpromote cooperation ifcomplex institutions that have enabled humanspecific conditions arefulfilled.societiestoflourish-poseproblemsofhowcoopera-tivebehavior can evolve and bemaintained.The2.1 Kin selectionpuzzlewas emphasized byDarwin,and remainsThe heated conversation took place in an unheatedthe subject of active research today.In this book, we leave the large subject of indi-British pub over somepints of warm bitter.Sud-vidual organisms' behavioral ecology and life-denly J.B.S. Haldane remarked, T will jump intohistory choices to texts in that field (e.g. Krebs andthe river to save two brothers or eight cousins.Davies, 1997). Instead, we lead with a survey ofThe founding father of population genetics andwork,much of it very recent, on five differentdedicated communist in his spare time neverbothered to develop this insight any further.Thekindsofmechanismwherebycooperativebehaviorwitness of the revelation was Haldane's eagermay bemaintained inapopulation,despite theinherent difficulty that cheats may prosper bypupil, the young John Maynard Smith. But givenenjoying the benefits of cooperation without pay-John's high regard for entertaining stories andingtheassociated costsgood beer, can we trust hismemory?Cooperation means that a donor pays a cost, c,The insight that Haldane might have had in thefor a recipient to get a benefit, b. In evolutionarypub was precisely formulated by William Hamilton.biology,cost and benefit are measured in terms ofHe wrote a PhD thesis on this topic, submitted afitness. While mutation and selection represent thelongpaper to the Journal ofTheoretical Biology,andspent much of the next decade in the Brazilianmain forces of evolutionarydynamics,cooperation7
CHAPTER 2 How populations cohere: five rules for cooperation Martin A. Nowak and Karl Sigmund Subsequent chapters in this volume deal with populations as dynamic entities in time and space. Populations are, of course, made up of individuals, and the parameters which characterize aggregate behavior—population growth rate and so on— ultimately derive from the behavioral ecology and life-history strategies of these constituent individuals. In evolutionary terms, the properties of populations can only be understood in terms of individuals, which comes down to studying how life-history choices (and consequent genefrequency distributions) are shaped by environmental forces. Many important aspects of group behavior— from alarm calls of birds and mammals to the complex institutions that have enabled human societies to flourish—pose problems of how cooperative behavior can evolve and be maintained. The puzzle was emphasized by Darwin, and remains the subject of active research today. In this book, we leave the large subject of individual organisms’ behavioral ecology and lifehistory choices to texts in that field (e.g. Krebs and Davies, 1997). Instead, we lead with a survey of work, much of it very recent, on five different kinds of mechanism whereby cooperative behavior may be maintained in a population, despite the inherent difficulty that cheats may prosper by enjoying the benefits of cooperation without paying the associated costs. Cooperation means that a donor pays a cost, c, for a recipient to get a benefit, b. In evolutionary biology, cost and benefit are measured in terms of fitness. While mutation and selection represent the main forces of evolutionary dynamics, cooperation is a fundamental principle that is required for every level of biological organization. Individual cells rely on cooperation among their components. Multicellular organisms exist because of cooperation among their cells. Social insects are masters of cooperation. Most aspects of human society are based on mechanisms that promote cooperation. Whenever evolution constructs something entirely new (such as multicellularity or human language), cooperation is needed. Evolutionary construction is based on cooperation. The five rules for cooperation which we examine in this chapter are: kin selection, direct reciprocity, indirect reciprocity, graph selection, and group selection. Each of these can promote cooperation if specific conditions are fulfilled. 2.1 Kin selection The heated conversation took place in an unheated British pub over some pints of warm bitter. Suddenly J.B.S. Haldane remarked, ‘I will jump into the river to save two brothers or eight cousins.’ The founding father of population genetics and dedicated communist in his spare time never bothered to develop this insight any further. The witness of the revelation was Haldane’s eager pupil, the young John Maynard Smith. But given John’s high regard for entertaining stories and good beer, can we trust his memory? The insight that Haldane might have had in the pub was precisely formulated by William Hamilton. He wrote a PhD thesis on this topic, submitted a long paper to the Journal of Theoretical Biology, and spent much of the next decade in the Brazilian 7
8THEORETICALECOLOGYjungle.This was one of the most important papersdefect it is also better to defect, because P>S.in evolutionary biology in the second half of theHence, no matter what the other person will do ittwentieth century(Hamilton, 1964a,1964b).Theis best to defect. If both players analyze thegametheorywastermedkinselectionbyMaynardSmithin this rational way then they will end updefect-(1964).The crucial equation is the following.ing.The dilemma is that they both could haveCooperation among relatives can be favored byreceived a higher payoff if theyhad chosen tonatural selection if the coefficient of genetic relat-cooperate. But cooperation is irrational.edness, r, between the donor and the recipientWe can also imagine a population of cooperatorsexceeds the cost/benefitratio ofthealtruistic act:anddefectorsandassumethatthepayoffforeachplayer is determined by many random interactionsr>c/b(2.1)withothers.Letxdenotethefrequencyof coopera-tors and 1-x the frequency of defectors.TheKin-selectiontheoryhasbeentested in numerousexpected payoff for a cooperator is fc=Rx+experimental studies.Indeed, many cooperativeS(1-x). The expected payoff for a defector isacts among animals occur between close kinfp=Tx+P(1-x).Therefore, for any x,defectors(Frank, 1998; Hamilton, 1998). The exact relation-havea higher payoff than cooperators.In evolu-shipbetweenkin selectionand othermechanismstionary game theory,payoff is interpreted as fit-such as group selection and spatial reciprocity,ness. Successful strategies reproduce faster andhowever, remains unclear.A recent study evenoutcompetelesssuccessfulones.Reproductioncansuggests that much of cooperation in social insectsbe cultural or genetic. In the non-repeated Pris-isduetogroup selectionratherthankin selectiononer'sDilemma,in a well-mixed population,(Wilson and Holldobler,2005).Notethat kindefectors outcompete cooperators.Natural selec-selection is more likely to work in quite smalltion favors defectors.groups; in large groups, unless highly inbred, theCooperation becomes an option if thegame isaveragevalueofrwill betiny.repeated. Suppose there are m rounds.Let uscompare two strategies, always defect (ALLD),and GRIM, which cooperates on thefirst move,2.2 Direct reciprocitythencooperatesaslongastheopponentcoopera-In 1971,Robert Trivers published a landmarktes,butpermanentlyswitchesto defection if thepaper entitled The evolution of reciprocal altru-opponent defects once.The expected payoff forism' (Trivers, 1971).Trivers analyzed the questionGRIM versus GRIM is nR. The expected payoff forhow natural selection could leadto cooperationALLD versus GRIM is T+(m-1)P.If nR>T+between unrelated individuals.He discusses three(m-1)P then ALLDcannot spread in a GRIMbiological examples: cleaning symbiosis in fish,population when rare. This is an argument ofwarning calls in birds, and human interactions.evolutionary stability.Interestingly,Trivers (1971)Trivers cites Luce and Raiffa (1957) and RapoportquotesHamilton(pers.commun.yforthisidea.andChammah(1965)forthePrisoner'sDilemma,Asmallproblemwiththeaboveanalysisisthatwhich is a game where two players have thegiven a known number of rounds itis best tooption to cooperate or to defect.Ifboth cooperatedefectin thelastround and bybackwards induc-they receive the reward, R. If both defect theytion it is also best to defect in the penultimatereceivethe punishment,P.If onecooperates andround and so on. Therefore, it is more natural tothe other defects,then the cooperator receivestheconsider a repeated gamewith aprobability w ofsucker's payoff, S, while the defector receives thehaving another round. In this case, the expectedtemptation, T.The Prisoner's Dilemma is definednumber of rounds is 1/(1-w),and GRIM is stablebytherankingT>R>P>S.against invasion by ALLD provided w>(T-R)/Would you cooperate or defect? Assuming the(T - P).We can also formulate thePrisoner's Dilemmaother person will cooperate it is better to defect,because T>R.Assuming the other person willasfollows.The cooperatorhelpsat a cost,c,and
jungle. This was one of the most important papers in evolutionary biology in the second half of the twentieth century (Hamilton, 1964a, 1964b). The theory was termed kin selection by Maynard Smith (1964). The crucial equation is the following. Cooperation among relatives can be favored by natural selection if the coefficient of genetic relatedness, r, between the donor and the recipient exceeds the cost/benefit ratio of the altruistic act: r > c=b ð2:1Þ Kin-selection theory has been tested in numerous experimental studies. Indeed, many cooperative acts among animals occur between close kin (Frank, 1998; Hamilton, 1998). The exact relationship between kin selection and other mechanisms such as group selection and spatial reciprocity, however, remains unclear. A recent study even suggests that much of cooperation in social insects is due to group selection rather than kin selection (Wilson and Ho¨lldobler, 2005). Note that kin selection is more likely to work in quite small groups; in large groups, unless highly inbred, the average value of r will be tiny. 2.2 Direct reciprocity In 1971, Robert Trivers published a landmark paper entitled ‘The evolution of reciprocal altruism’ (Trivers, 1971). Trivers analyzed the question how natural selection could lead to cooperation between unrelated individuals. He discusses three biological examples: cleaning symbiosis in fish, warning calls in birds, and human interactions. Trivers cites Luce and Raiffa (1957) and Rapoport and Chammah (1965) for the Prisoner’s Dilemma, which is a game where two players have the option to cooperate or to defect. If both cooperate they receive the reward, R. If both defect they receive the punishment, P. If one cooperates and the other defects, then the cooperator receives the sucker’s payoff, S, while the defector receives the temptation, T. The Prisoner’s Dilemma is defined by the ranking T > R > P > S. Would you cooperate or defect? Assuming the other person will cooperate it is better to defect, because T > R. Assuming the other person will defect it is also better to defect, because P > S. Hence, no matter what the other person will do it is best to defect. If both players analyze the game in this rational way then they will end up defecting. The dilemma is that they both could have received a higher payoff if they had chosen to cooperate. But cooperation is irrational. We can also imagine a population of cooperators and defectors and assume that the payoff for each player is determined by many random interactions with others. Let x denote the frequency of cooperators and 1 x the frequency of defectors. The expected payoff for a cooperator is fC ¼ Rx þ S(1 x). The expected payoff for a defector is fD ¼ Tx þ P(1 x). Therefore, for any x, defectors have a higher payoff than cooperators. In evolutionary game theory, payoff is interpreted as fitness. Successful strategies reproduce faster and outcompete less successful ones. Reproduction can be cultural or genetic. In the non-repeated Prisoner’s Dilemma, in a well-mixed population, defectors outcompete cooperators. Natural selection favors defectors. Cooperation becomes an option if the game is repeated. Suppose there are m rounds. Let us compare two strategies, always defect (ALLD), and GRIM, which cooperates on the first move, then cooperates as long as the opponent cooperates, but permanently switches to defection if the opponent defects once. The expected payoff for GRIM versus GRIM is nR. The expected payoff for ALLD versus GRIM is T þ (m 1)P. If nR > T þ (m 1)P then ALLD cannot spread in a GRIM population when rare. This is an argument of evolutionary stability. Interestingly, Trivers (1971) quotes ‘Hamilton (pers. commun.)’ for this idea. A small problem with the above analysis is that given a known number of rounds it is best to defect in the last round and by backwards induction it is also best to defect in the penultimate round and so on. Therefore, it is more natural to consider a repeated game with a probability w of having another round. In this case, the expected number of rounds is 1/(1 w), and GRIM is stable against invasion by ALLD provided w > (T R)/ (T P). We can also formulate the Prisoner’s Dilemma as follows. The cooperator helps at a cost, c, and 8 THEORETICAL ECOLOGY
HOWPOPULATIONSCOHEREthe other individual receives a benefit,b.DefectorsThe tournaments were conducted without strategicdo not help.Therefore wehave T=b,R=b-c,noise. In a real world, trembling hands and fuzzyP-0, and S=-c. The family of games that isminds cause erroneous moves. If two TFT playersdescribed by the parameters b and c is a subset ofinteract with each other, a single mistake leadsallpossiblePrisoner'sDilemmagamesas longasto a long sequence of alternating defection andb>c.For the repeated Prisoner'sDilemma,we findcooperation.In the long run two TFT players getthat ALLDcannot invadeGRIM ifthe same low payoff as two players who flip coinsfor every move in order to decide whether to(2.2)w>c/bcooperateortodefect.ErrorsdestroyTFTOur own investigations in thisareabegan afterThe probability of having another round mustreading a News and Views article in Nature whereexceed the cost/benefit ratio of the altruistic actthe author made three important points: first, he(Axelrod and Hamilton,1981;Axelrod,1984).often leaves university meetings with a renewedNotice, however,the implicitassumption here thatappreciationfor theproblemof how naturalthe payoff for future rounds is not discounted (ie.selection can favor cooperative acts given thatdistantbenefits countasmuchaspresent ones).Inselfish individuals gain from cheating second,evolutionary reality, this is unlikely.We canstrategies in the repeated Prisoner's Dilemmaaddress this by incorporating an appropriate dis-should not be error-free but subjected to noise;count factor in w (May,1987), but note, from eqn 2,third, evolutionary stability should be tested notthat this makes cooperation less likely.against single invaders but against heterogeneousThus, the repeated Prisoner's Dilemma allowsensembles of invaders (May,1987).This was thecooperation, but the question arises: what is a goodmotivationforthefollowing work.strategy for playing this game? This question wasposed bythepolitical scientist,RobertAxelrod.InIn 1989,weconducted evolutionary tourna-1979,hedecidedtoconduct atournamentofments.Instead of inviting experts to submit pro-computerprogramsplayingtherepeatedPrisonersgrams,weaskedmutationand selection toexploreDilemma. He received 14 entries,of which the(some portion of)the strategy space of the repe-surprise winner was tit-for-tat (TFT), the simplestated Prisoner's Dilemma inthepresence of noise.ofall strategies that were submitted.TFT coopera-The initial random ensemble of strategies wastes in the first move, and then does whateverquicklydominated by ALLD.If the opposition isthe opponent did in the previous round. TFTrandom, it is best to defect. A large portion of thecooperates if you cooperate, TFT defects if youPopulation began to adopt the ALLD strategy anddefect. It was submitted by the game theoristeverything seemed lost. But after some time, aAnatol Rapoport (whoisalso the co-author of thesmall cluster of players adopted a strategy verybook Prisoner'sDilemma; Rapoport and Chammah,close to TFT. If this cluster is sufficiently large,then it can increase in abundance,and the entire1965).Axelrodanalvzedtheeventsofthetourna-ment,published a detailed account and invitedPopulation swings from ALLD to TFT.Reciprocitypeopleto submitstrategiesforsecond cham-(andthereforeccoperation)hasemerged.Wecanpionship.This timehereceived 63entries.Johnshowthat TFTisthe best catalystfor the emer-Maynard Smith submitted tit-for-two-tats, a var-gence of cooperation.But TFT's moment of gloryiantofTFTwhichdefectsonlyaftertheopponentwas brief and fleeting.In all cases, TFT was rapidlyhasdefectedtwiceina row.Onlyoneperson,replaced by another strategy.On close inspection,Rapoport, submitted TFT, and it won again.At thisthis strategy turned out to be generous tit-for-tattime,TFT was considered to be the undisputed(GTFT), which always cooperates if the opponentchampion in the heroic world of the repeatedhas cooperated on the previous move, but some-Prisoner's Dilemma.times(probabilistically)even cooperateswhentheBut one weakness became apparent very soonopponent has defected.Natural selection had dis-(Molander,1985).TFT cannot correct mistakes.coveredforgiveness(NowakandSigmund,1992)
the other individual receives a benefit, b. Defectors do not help. Therefore we have T ¼ b, R ¼ b c, P ¼ 0, and S ¼ c. The family of games that is described by the parameters b and c is a subset of all possible Prisoner’s Dilemma games as long as b > c. For the repeated Prisoner’s Dilemma, we find that ALLD cannot invade GRIM if w > c=b ð2:2Þ The probability of having another round must exceed the cost/benefit ratio of the altruistic act (Axelrod and Hamilton, 1981; Axelrod, 1984). Notice, however, the implicit assumption here that the payoff for future rounds is not discounted (i.e. distant benefits count as much as present ones). In evolutionary reality, this is unlikely. We can address this by incorporating an appropriate discount factor in w (May, 1987), but note, from eqn 2, that this makes cooperation less likely. Thus, the repeated Prisoner’s Dilemma allows cooperation, but the question arises: what is a good strategy for playing this game? This question was posed by the political scientist, Robert Axelrod. In 1979, he decided to conduct a tournament of computer programs playing the repeated Prisoner’s Dilemma. He received 14 entries, of which the surprise winner was tit-for-tat (TFT), the simplest of all strategies that were submitted. TFT cooperates in the first move, and then does whatever the opponent did in the previous round. TFT cooperates if you cooperate, TFT defects if you defect. It was submitted by the game theorist Anatol Rapoport (who is also the co-author of the book Prisoner’s Dilemma; Rapoport and Chammah, 1965). Axelrod analyzed the events of the tournament, published a detailed account and invited people to submit strategies for a second championship. This time he received 63 entries. John Maynard Smith submitted tit-for-two-tats, a variant of TFT which defects only after the opponent has defected twice in a row. Only one person, Rapoport, submitted TFT, and it won again. At this time, TFT was considered to be the undisputed champion in the heroic world of the repeated Prisoner’s Dilemma. But one weakness became apparent very soon (Molander, 1985). TFT cannot correct mistakes. The tournaments were conducted without strategic noise. In a real world, trembling hands and fuzzy minds cause erroneous moves. If two TFT players interact with each other, a single mistake leads to a long sequence of alternating defection and cooperation. In the long run two TFT players get the same low payoff as two players who flip coins for every move in order to decide whether to cooperate or to defect. Errors destroy TFT. Our own investigations in this area began after reading a News and Views article in Nature where the author made three important points: first, he often leaves university meetings with a renewed appreciation for the problem of how natural selection can favor cooperative acts given that selfish individuals gain from cheating; second, strategies in the repeated Prisoner’s Dilemma should not be error-free but subjected to noise; third, evolutionary stability should be tested not against single invaders but against heterogeneous ensembles of invaders (May, 1987). This was the motivation for the following work. In 1989, we conducted evolutionary tournaments. Instead of inviting experts to submit programs, we asked mutation and selection to explore (some portion of) the strategy space of the repeated Prisoner’s Dilemma in the presence of noise. The initial random ensemble of strategies was quickly dominated by ALLD. If the opposition is random, it is best to defect. A large portion of the population began to adopt the ALLD strategy and everything seemed lost. But after some time, a small cluster of players adopted a strategy very close to TFT. If this cluster is sufficiently large, then it can increase in abundance, and the entire population swings from ALLD to TFT. Reciprocity (and therefore cooperation) has emerged. We can show that TFT is the best catalyst for the emergence of cooperation. But TFT’s moment of glory was brief and fleeting. In all cases, TFT was rapidly replaced by another strategy. On close inspection, this strategy turned out to be generous tit-for-tat (GTFT), which always cooperates if the opponent has cooperated on the previous move, but sometimes (probabilistically) even cooperates when the opponent has defected. Natural selection had discovered forgiveness (Nowak and Sigmund, 1992). HOW POPULATIONS COHERE 9