Evolutionary Stable Strategies: A Review of Basic Theory

Widely successful in applied population biology, the Evolutionarily Stable Strategy concept remains controversial because of the severe restrictions present in its original formulation. We review theory which explores and relaxes these restrictions, finding the concept to be quite robust and adaptable, incorporating considerations such as genetics, population diversity, environmental variability, and mutation.

[1]  J. Roughgarden.  Theory of Population Genetics and Evolutionary Ecology: An Introduction , 1995 .

[2]  R. Dawkins,et al.  Parental investment, mate desertion and a fallacy , 1976, Nature.

[3]  P. Taylor,et al.  Worker-queen conflict and sex ratio theory in social hymenoptera , 1981, Heredity.

[4]  Manfred Eigen,et al.  The Realistic Hypercycle , 1979 .

[5]  John Maynard Smith,et al.  The logic of asymmetric contests , 1976, Animal Behaviour.

[6]  W. Hamilton,et al.  The Evolution of Cooperation , 1984 .

[7]  A I Houston,et al.  How to maximize reward rate on two variable-interval paradigms. , 1981, Journal of the experimental analysis of behavior.

[8]  A. Hastings.  An evolutionary optimization principle. , 1978, Journal of theoretical biology.

[9]  Robert K. Colwell,et al.  EVOLUTION OF SEX RATIO IN STRUCTURED DEMES , 1981, Evolution; international journal of organic evolution.

[10]  E. Akin,et al.  Evolutionary dynamics of zero-sum games , 1984, Journal of mathematical biology.

[11]  R. Cressman,et al.  ESSs with two types of players II (intra- and interspecific competition between haploid species) , 1985 .

[12]  P. Hammerstein.  The role of asymmetries in animal contests , 1981, Animal Behaviour.

[13]  E. Zeeman.  Dynamics of the evolution of animal conflicts , 1981 .

[14]  T. Vincent,et al.  Stability in an evolutionary game , 1984 .

[15]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

[16]  On the optimal sex-ratio: A stability analysis based on a characterization for one-locus multiallele viability models , 1984, Journal of mathematical biology.

[17]  E. Akin.  Domination or equilibrium , 1980 .

[18]  M. Conrad,et al.  Evolutionary learning circuits. , 1974, Journal of theoretical biology.

[19]  Paul Hudson.  Games Theory — Lectures for Economists and Systems Scientists , 1977 .

[20]  Sievert Rohwer,et al.  Status Signaling in Harris Sparrows: Some Experiments in Deception , 1977 .

[21]  Richard D. Alexander,et al.  The search for a general theory of behavior , 1975 .

[22]  S. Shahshahani,et al.  A New Mathematical Framework for the Study of Linkage and Selection , 1979 .

[23]  P. Taylor,et al.  Dispersal and the sex ratio , 1980, Nature.

[24]  U. Motro.  Optimal rates of dispersal II. Diploid populations , 1982 .

[25]  W. G. S. Hines.  Mutations, perturbations and evolutionarily stable strategies , 1982 .

[26]  A. Abakuks.  CONDITIONS FOR EVOLUTIONARILY STABLE STRATEGIES , 1980 .

[27]  Robert M. May,et al.  Stability in multispecies community models , 1971 .

[28]  B. Thomas.  On evolutionarily stable sets , 1985 .

[29]  P. Schuster,et al.  Coyness, philandering and stable strategies , 1981, Animal Behaviour.

[30]  E. M. L. Beale,et al.  Nonlinear and Dynamic Programming , 1965 .

[31]  W. Hines.  An evolutionarily stable strategy model for randomly mating diploid populations. , 1980, Journal of theoretical biology.

[32]  P. Taylor.  Evolutionarily stable strategies with two types of player , 1979, Journal of Applied Probability.

[33]  John Haigh,et al.  Game theory and evolution , 1975, Advances in Applied Probability.

[34]  S. Lessard.  Evolutionary dynamics in frequency-dependent two-phenotype models. , 1984, Theoretical population biology.

[35]  W. G. S. Hines.  Strategy stability in complex randomly mating diploid populations , 1982 .

[36]  A dynamic programming approach to evolutionarily stable strategy theory , 1980, Advances in Applied Probability.

[37]  Israel Rosenfield,et al.  DNA for Beginners , 1983 .

[38]  M. Treisman.  Evolutionary limits to the frequency of aggression between related or unrelated conspecifics in diploid species with simple Mendelian inheritance. , 1981, Journal of theoretical biology.

[39]  I. Eshel,et al.  Altruism, Competition and Kin Selection in Populations , 1976 .

[40]  J M Smith.  Game theory and the evolution of behaviour , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[41]  J. M. Smith,et al.  Do animals convey information about their intentions , 1982 .

[42]  J. M. Smith.  The theory of games and the evolution of animal conflicts. , 1974, Journal of theoretical biology.

[43]  M. Feldman,et al.  Cultural transmission and evolution: a quantitative approach. , 1981, Monographs in population biology.

[44]  M. Treisman.  Evolutionarily stable levels of altruism in haploid and diploid species. , 1982, Journal of theoretical biology.

[45]  Chris Cannings,et al.  Models of animal conflict , 1976 .

[46]  I. Eshel.  Evolutionary and continuous stability , 1983 .

[47]  H. Comins.  Evolutionarily stable strategies for localized dispersal in two dimensions. , 1982, Journal of theoretical biology.

[48]  M. Rose,et al.  Ecological outbreak dynamics and the cusp catastrophe , 1981 .

[49]  Josef Hofbauer,et al.  Recurrence of the unfit , 1982 .

[50]  C B Harley,et al.  When do animals learn the evolutionarily stable strategy? , 1983, Journal of theoretical biology.

[51]  Cedric A. B. Smith,et al.  The Geometry of Population Genetics , 1980 .

[52]  W. G. S. Hines,et al.  Strategy stability in complex populations , 1980, Journal of Applied Probability.

[53]  Frank C. Rohwer,et al.  Status signalling in harris sparrows: Experimental deceptions achieved , 1978, Animal Behaviour.

[54]  W. Hamilton.  The genetical evolution of social behaviour. I. , 1964, Journal of theoretical biology.

[55]  P. Taylor,et al.  Stable equilibrium strategies and penalty functions in a game of attrition. , 1977, Journal of theoretical biology.

[56]  J. Riley,et al.  Strong evolutionary equilibrium and the war of attrition. , 1980, Journal of theoretical biology.

[57]  Scott A. Boorman,et al.  The Genetics of Altruism , 1981 .

[58]  G. Parker,et al.  The asymmetric war of attrition , 1982 .

[59]  L. Cavalli-Sforza,et al.  Assortment of encounters and evolution of cooperativeness. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[60]  R M May,et al.  Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos , 1974, Science.

[61]  F. Oberdieck,et al.  An evaluation of Maynard Smith's models of sexual strategies , 1978, Animal Behaviour.

[62]  J. M. Smith,et al.  Games between relatives. , 1979, Journal of theoretical biology.

[63]  Josef Hofbauer,et al.  Competition and cooperation in catalytic selfreplication , 1981 .

[64]  G. Parker,et al.  Models of parent-offspring conflict. III. Intra-brood conflict , 1979, Animal Behaviour.

[65]  P. G. Caryl.  Telling the truth about intentions , 1982 .

[66]  R. Herrnstein.  On the law of effect. , 1970, Journal of the experimental analysis of behavior.

[67]  G. Borgia,et al.  Group Selection, Altruism, and the Levels of Organization of Life , 1978 .

[68]  Solomon Kullback,et al.  Information Theory and Statistics , 1960 .

[69]  P. G. Caryl.  Animal signals: A reply to Hinde , 1982, Animal Behaviour.

[70]  J. M. Smith,et al.  The war of attrition with random rewards. , 1978, Journal of theoretical biology.

[71]  P. G. Caryl.  COMMUNICATION BY AGONISTIC DISPLAYS: WHAT CAN GAMES THEORY CONTRIBUTE TO ETHOLOGY? , 1979 .

[72]  A. Houston.  Comments on "Learning the evolutionarily stable strategy". , 1983, Journal of theoretical biology.

[73]  U. Motro.  Optimal rates of dispersal. III. Parent-offspring conflict☆ , 1983 .

[74]  M. Ruse.  Sociobiology: Sense or Nonsense? , 1979, Episteme.

[75]  E. Charnov.  The theory of sex allocation. , 1984, Monographs in population biology.

[76]  The behaviour of strategy-frequencies in Parker's model , 1980, Advances in Applied Probability.

[77]  I. Eshel.  Evolutionarily stable strategies and viability selection in mendelian populations , 1982 .

[78]  John R. Krebs,et al.  The Evolution of Alarm Calls: Altruism or Manipulation? , 1975, The American Naturalist.

[79]  S. Levin.  Population Dynamic Models in Heterogeneous Environments , 1976 .

[80]  Michael Ruse,et al.  Book reviews-the Darwinian revolution: Science red in tooth and claw , 1980 .

[81]  J. Riley,et al.  Evolutionary equilibrium strategies. , 1979, Journal of theoretical biology.

[82]  J. M. Smith.  The evolution of behavior. , 1978, Scientific American.

[83]  G. Parker,et al.  Assessment strategy and the evolution of fighting behaviour. , 1974, Journal of theoretical biology.

[84]  G. Parker,et al.  Role assessment, reserve strategy, and acquisition of information in asymmetric animal conflicts , 1981, Animal Behaviour.

[85]  Mutations and stable strategies. , 1978, Journal of theoretical biology.

[86]  J. Krebs,et al.  Behavioural Ecology: An Evolutionary Approach , 1978 .

[87]  Marcus W. Feldman,et al.  On the Theory of Parent-Offspring Conflict: A Two-Locus Genetic Model , 1982, The American Naturalist.

[88]  N. Davies,et al.  Territorial defence in the speckled wood butterfly (Pararge aegeria): The resident always wins , 1978, Animal Behaviour.

[89]  G. Parker,et al.  The evolution of territory size-some ESS models. , 1980, Journal of theoretical biology.

[90]  J. Guckenheimer,et al.  Random evolutionarily stable strategies. , 1978, Theoretical population biology.

[91]  Robert Gilmore,et al.  Catastrophe Theory for Scientists and Engineers , 1981 .

[92]  E. Charnov,et al.  Why be an hermaphrodite? , 1976, Nature.

[93]  B. Thomas,et al.  Evolutionary stable sets in mixed-strategist models , 1985 .

[94]  W. Hines,et al.  Can and will a sexual diploid population attain an evolutionary stable strategy , 1984 .

[95]  A. Hastings.  Disturbance, coexistence, history, and competition for space , 1980 .

[96]  U Motro,et al.  Kin selection and strong evolutionary stability of mutual help. , 1981, Theoretical population biology.

[97]  NON-LINEAR ESS MODELS AND POLYMORPHISM , 1985 .

[98]  G. Oster,et al.  Competition, kin selection, and evolutionary stable strategies. , 1978, Theoretical population biology.

[99]  Geoff A. Parker,et al.  Arms races in evolution—An ESS to the opponent-independent costs game , 1983 .

[100]  Josef Hofbauer,et al.  A general cooperation theorem for hypercycles , 1981 .

[101]  V. Wynne-Edwards.  Animal dispersion in relation to social behaviour , 1962 .

[102]  The Evolution of Stable Strategies , 1983 .

[103]  K. Aoki.  Additive polygenic formulation of Hamilton's model of kin selection1 , 1982, Heredity.

[104]  R. Fagen,et al.  When Doves Conspire: Evolution of Nondamaging Fighting Tactics in a Nonrandom-Encounter Animal Conflict Model , 1980, The American Naturalist.

[105]  M. Bulmer.  Worker-queen conflict in annual social hymenoptera , 1981 .

[106]  K Sigmund,et al.  A note on evolutionary stable strategies and game dynamics. , 1979, Journal of theoretical biology.

[107]  R. Michod,et al.  Measures of Genetic Relationship and the Concept of Inclusive Fitness , 1979, The American Naturalist.

[108]  George Williams.  Group Selection , 1971 .

[109]  W. Hamilton.  Extraordinary Sex Ratios , 1967 .

[110]  R M May,et al.  Evolutionarily stable dispersal strategies. , 1980, Journal of theoretical biology.

[111]  B. Thomas,et al.  On a global representation of dynamical characteristics in ESS-models. , 1982, Bio Systems.

[112]  E. Wilson.  Sociobiology: The New Synthesis , 1976 .

[113]  E. Akin,et al.  Dynamics of games and genes: Discrete versus continuous time , 1983 .

[114]  A. Stokes,et al.  Agonistic Behaviour Among Blue Tits At a Winter Feeding Station , 1962 .

[115]  Peter Schuster,et al.  The Abstract Hypercycle , 1979 .

[116]  S. Williams.  On the applicability of game theory to evolution: a response. , 1981, Journal of theoretical biology.

[117]  C. Harley.  Learning the evolutionarily stable strategy. , 1981, Journal of theoretical biology.

[118]  John Maynard Smith,et al.  Hypercycles and the origin of life , 1979, Nature.

[119]  W. Hines.  Competition with an evolutionary stable strategy. , 1977, Journal of theoretical biology.

[120]  M. West-Eberhard.  Sexual selection, social competition and evolution , 1979 .

[121]  David P. Barash,et al.  Sociobiology and Behaviour , 1976 .

[122]  R. May,et al.  The Evolution of Behaviour , 1982 .

[123]  Robert M. May,et al.  Dispersal in stable habitats , 1977, Nature.

[124]  J. M. Smith,et al.  Group Selection , 1976, The Quarterly Review of Biology.

[125]  W. G. S. Hines,et al.  On learning and the evolutionarily stable strategy , 1983 .

[126]  R. Selten.  A note on evolutionarily stable strategies in asymmetric animal conflicts. , 1980, Journal of theoretical biology.

[127]  K. Aoki.  A quantitative genetic model of two-policy games between relatives. , 1984, Journal of theoretical biology.

[128]  G. Parker,et al.  Models of parent-offspring conflict. II. Promiscuity , 1978, Animal Behaviour.

[129]  G. A. Parker,et al.  Models of parent-offspring conflict. I. Monogamy , 1978, Animal Behaviour.

[130]  Constancy of mean strategy versus constancy of gene frequencies in a sexual diploid population , 1986 .

[131]  J M Smith,et al.  Evolution and the theory of games , 1976 .

[132]  R. Trivers.  Parent-Offspring Conflict , 1974 .

[133]  J. Haigh,et al.  Evolutionary game auctions. , 1980, Journal of theoretical biology.

[134]  K Sigmund,et al.  The role of Mendelian genetics in strategic models on animal behaviour. , 1983, Journal of theoretical biology.

[135]  Sewall Wright,et al.  Coefficients of Inbreeding and Relationship , 1922, The American Naturalist.

[136]  H. Guess.  Evolution in finite populations with infinitely many types. , 1974, Theoretical population biology.

[137]  W. Hines,et al.  Evolutionarily stable strategies in diploid populations with general inheritance patterns , 1983, Journal of Applied Probability.

[138]  R. Dawkins,et al.  Replicator selection and the extended phenotype. , 2010, Zeitschrift fur Tierpsychologie.

[139]  T. Clutton‐Brock,et al.  The logical stag: Adaptive aspects of fighting in red deer (Cervus elaphus L.) , 1979, Animal Behaviour.

[140]  John Maynard Smith,et al.  The Theory of Evolution , 1958 .

[141]  R. Cressman,et al.  Evolutionary games and two species population dynamics , 1986, Journal of mathematical biology.

[142]  E. Akin,et al.  Cevolutionary instability of mixed Nash solutions , 1983, Journal of mathematical biology.

[143]  G. Parker,et al.  An evolutionarily stable strategy approach to indiscriminate spite , 1979, Nature.

[144]  Alan Grafen,et al.  The hawk-dove game played between relatives , 1979, Animal Behaviour.

[145]  G. Parker,et al.  Models of parent-offspring conflict. IV. Suppression: Evolutionary retaliation by the parent , 1979, Animal Behaviour.

[146]  M. Eigen,et al.  The Hypercycle: A principle of natural self-organization , 2009 .

[147]  Richard Sibly,et al.  A model of mate desertion , 1978, Animal Behaviour.

[148]  S. Rohwer.  The Evolution of Reliable and Unreliable Badges of Fighting Ability , 1982 .

[149]  P. Taylor,et al.  Evolutionarily Stable Strategies and Game Dynamics , 1978 .

[150]  P. Schuster,et al.  On $\omega $-Limits for Competition Between Three Species , 1979 .

[151]  E. C. Zeeman,et al.  Population dynamics from game theory , 1980 .

[152]  C. Cannings,et al.  The Generalized War of Attrition , 1997 .

[153]  N. Stenseth,et al.  On evolutionarily stable strategies , 1984 .

[154]  Richard E. Michod,et al.  The Theory of Kin Selection , 1982 .

[155]  L Reijnders,et al.  On the applicability of game theory to evolution. , 1978, Journal of theoretical biology.

[156]  G. Oster,et al.  Competition between phenotypes , 1976, Journal of mathematical biology.

[157]  E. Akin.  Cycling in simple genetic systems , 1982 .

[158]  R. A. Fisher,et al.  The Genetical Theory of Natural Selection , 1931 .

[159]  B. Thomas,et al.  On evolutionarily stable strategies in populations with subpopulations having isolated strategy repertoires. , 1979, Bio Systems.

[160]  J. Coste,et al.  Asymptotic Behaviors in the Dynamics of Competing Species , 1979 .

[161]  P. Schuster,et al.  Dynamical Systems Under Constant Organization II: Homogeneous Growth Functions of Degree $p = 2$ , 1980 .

[162]  PLAYER I. TWO-SPECIES HAPLOID OR RANDOMLY MATING DIPLOID , 1985 .

[163]  A. Ludlow.  The Behaviour of a Model Animal , 1976 .

[164]  W. Hines.  Three characterizations of population strategy stability , 1980 .

[165]  William Gurney,et al.  Modelling fluctuating populations , 1982 .

[166]  J. G. van Rhijn,et al.  Being honest about one's intentions: an evolutionary stable strategy for animal conflicts. , 1980, Journal of theoretical biology.

[167]  P. Taylor.  SEX RATIO COMPENSATION IN ANT POPULATIONS , 1981, Evolution; international journal of organic evolution.

[168]  S. Karlin,et al.  Theoretical studies on sex ratio evolution. , 1989, Monographs in population biology.

[169]  G. Parker,et al.  Selfish genes, evolutionary games, and the adaptiveness of behaviour , 1978, Nature.

[170]  Michael J. Sanderson,et al.  Evolution of Social Behavior by Reciprocation , 1982 .

[171]  W. G. S. Hines.  Multi-species population models and evolutionarily stable strategies , 1981 .

[172]  M. Treisman,et al.  Prior fitness and the evolutionarily stable strategy for intraspecific conflict. , 1980, Journal of theoretical biology.

[173]  M. Eigen,et al.  The hypercycle. A principle of natural self-organization. Part A: Emergence of the hypercycle. , 1977, Die Naturwissenschaften.

[174]  Sievert Rohwer,et al.  THE SOCIAL SIGNIFICANCE OF AVIAN WINTER PLUMAGE VARIABILITY , 1975, Evolution; international journal of organic evolution.

[175]  Peter Hammerstein,et al.  Game Theory in the Ecological Context , 1983 .

[176]  G M Heyman,et al.  Is matching compatible with reinforcement maximization on concurrent variable interval variable ratio? , 1979, Journal of the experimental analysis of behavior.

[177]  T. Clutton‐Brock,et al.  THE ROARING OF RED DEER AND THE EVOLUTION OF HONEST ADVERTISEMENT , 1979 .

[178]  Thomas Caraco,et al.  The scanning behavior of juncos: A game-theoretical approach , 1982 .

[179]  Evolutionarily stable strategies and the evolution of life history strategies: I. Density dependent models. , 1978, Journal of theoretical biology.

[180]  Geoffrey Parker,et al.  SEXUAL SELECTION AND SEXUAL CONFLICT , 1979 .

[181]  J. M. Smith,et al.  The Coevolution and Stability of Competing Species , 1976, The American Naturalist.

[182]  M. Moynihan.  Why is lying about intentions rare during some kinds of contests , 1982 .

[183]  D. Wilson.  THE GROUP SELECTION CONTROVERSY: History and Current Status , 1983 .

[184]  R. Dawkins,et al.  The extended phenotype : the gene as the unit of selection , 1982 .

[185]  J. Hofbauer.  A DIFFERENCE EQUATION MODEL FOR THE HYPERCYCLE , 1984 .

[186]  S. Gadgil,et al.  On evolutionarily stable compositions of populations of interacting genotypes. , 1980, Journal of theoretical biology.

[187]  R. Dawkins,et al.  Evolutionarily stable nesting strategy in a digger wasp. , 1979, Journal of theoretical biology.

[188]  S. I. Rothstein.  Gene Frequencies and Selection for Inhibitory Traits, with Special Emphasis on the Adaptiveness of Territoriality , 1979, The American Naturalist.

[189]  Evolutionarily stable strategies of diploid populations with semi-dominant inheritance patterns , 1984 .

[190]  M R Rose,et al.  Cheating in evolutionary games. , 1978, Journal of theoretical biology.

[191]  B. Thomas.  Genetical ESS-models. II. Multi-strategy models and multiple alleles. , 1985, Theoretical population biology.

[192]  E. Akin.  Exponential Families and Game Dynamics , 1982, Canadian Journal of Mathematics.

[193]  B. Thomas.  Genetical ESS-models. I. Concepts and basic model. , 1985, Theoretical population biology.

[194]  J. M. Smith.  Will a Sexual Population Evolve to an Ess? , 1981, The American Naturalist.

[195]  S. Riechert.  Web-site selection in the desert spider Agelenopsis aperta , 1976 .

[196]  P. Taylor,et al.  Local mate competition and the sex ratio , 1980 .

[197]  On the local stability of an evolutionarily stable strategy in a diploid population , 1984 .

[198]  P Cull,et al.  Global stability of population models. , 1981, Bulletin of mathematical biology.

[199]  B. Thomas,et al.  Ess-theory for finite populations. , 1981, Bio Systems.

[200]  M. Eigen,et al.  Emergence of the Hypercycle , 1979 .

[201]  J. Turner.  Oscillations of frequency in batesian mimics, hawks and doves, and other simple frequency dependent polymorphisms , 1980, Heredity.

[202]  J. S. GALE,et al.  Logic of animal conflict , 1975, Nature.