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Evolution and the

Theory of Games

Published by the Press Syndicate of the University of Cambridge The Pitt Building, Trumpington Street, Cambridge CB2 IRP 32 East 57th Street New York. NY 10022. USA 296 Beaconsfield Parade, Middle Park, Melbourne 3206, Australia.

© Cambridge University Press 1982

First published 1982

Printed in Great Britain at the Alden Press, Oxford

British Library Cataloguing in Publication Data

Smith, John Maynard

Evolution and the theory of games.

1. Evolution-Mathematical models

2. Game theory I. Title 575'.01'5193 QH366.2

ISBN 0 521 24673 3 hard covers ISBN 0 521 28884 3 paperback

Contents

Preface

The last decade has seen a steady increase in the application of concepts from the theory of games to the study of evolution. Fields as diverse as sex ratio theory, animal distribution, contest behaviour and reciprocal altruism have contributed to what is now emerging as a universal way of thinking about phenotypic evolution. This book attempts to present these ideas in a coherent form. It is addressed primarily to biologists. I have therefore been more concerned to explain and to illustrate how the theory can be applied to biological problems than to present formal mathematical proofs — a task for which I am, in any case, ill equipped. Some idea of how the mathematical side of the subject has developed is given in the appendixes.

I hope the book will also be of some interest to game theorists. Paradoxically, it has turned out that game theory is more readily applied to biology than to the field of economic behaviour for which it was originally designed. There are two reasons for this. First, the theory requires that the values of different outcomes (for example, financial rewards, the risks of death and the pleasures of a clear conscience) be measured on a single scale. Inhuman applications, this measure is provided by 'utility' — a somewhat artificial and uncomfortable concept: in biology, Darwinian fitness provides a natural and genuinely one-dimensional scale. Secondly, and more importantly, in seeking the solution of a game, the concept of human rationality is replaced by that of evolutionary stability. The advantage here is that there are good theoretical reasons to expect populations to evolve to stable states, whereas there are grounds for doubting whether human beings always behave rationally.

I have been greatly helped in thinking about evolutionary game theory by my colleagues at the University of Sussex, particularly Brian and Deborah Charlesworth and Paul Harvey. I owe a special debt to Peter Hammerstein, who has helped me to understand some  {viii}  theoretical questions more clearly. The manuscript has been read, in whole or in part, by Jim Bull, Eric Charnov, John Haigh, Peter Hammerstein, Susan Riechert and Siewert Rohwer, all of whom have helped to eliminate errors and ambiguities. Finally it is a pleasure to acknowledge the help of Sheila Laurence, in typing the manuscript and in many other ways.

November 1981

J. M. S

References

Abegglen, J.-J. (1976). On socialization in hamadryas baboons. Ph.D. thesis, University of Zurich.

Alcock, J., Jones, C.E. & Buckman, S.L. (1977). Male nesting strategies in the bee Centris pallida Fox (Anthophoridae: Hymenoptera). Am. Nat. 111, 145-55.

Andersson, M. (1980). Why are there so many threat displays? J. theor. Biol. 86, 773-81.

Axelrod, R. (1981). The emergence of cooperation among egoists. Am. political Sci. Rev. (in press).

Axelrod, R. & Hamilton, W.D. (1981). The evolution of cooperation. Science, 211, 1390-6.

Bachmann, C. & Kummer, H. (1980). Male assessment of female choice in hamadryas baboons. Behav. ecol. Sociobiol. 6, 315-21.

Baker, M.C. (1978). Flocking and feeding in the great tit Parus major - an important consideration. Am. Nat. 112, 779-81.

Baker, R.R. (1972). Territorial behaviour of the nymphalid butterflies, Aglaisurticae (L.) and Inachis io (L.). J. Anim. Ecol. 41, 453-69.

Baldwin, B.A. & Meese, G.B. (1979). Social behaviour in pigs studied by means of operant conditioning. Anim. Behav. 27, 947-57.

Balph, M.H. & Balph, D.F. (1979). On the relationship between plumage variability and social behaviour in wintering pine siskins (Carduelis pinus). Paper presented at XVIth International Ethological Conference.

Balph, M.H., Balph, D.F. & Romesburg, H.C. (1979). Social status signalling in winter flocking birds: an examination of a current hypothesis. The Auk, 96, 78-93.

Barnard, C.J. & Sibly, R.M. (1981). Producers and scroungers: a general model and its application to captive flocks of house sparrows. Anim. Behav. 29, 543-50.

Bateman, A.J. (1948). Intra-sexual selection in Drosophila. Heredity, 2, 349-68.

Bertram, B.C.R. (1976). Kin selection in lions and in evolution. In Growing Points in Ethology, ed. P.P.G. Bateson & R.A. Hinde, pp. 281-301. Cambridge University Press.

Birky, C.W. (1978). Transmission genetics of mitochondria and chloroplasts. A. Rev. Genet. 12, 471-512.

Bishop, D.T. & Cannings, C. (1978). A generalised war of attrition. J. theor. Biol. 70, 85-124.  {206} 

Bishop, D.T., Cannings, C. & Maynard Smith, J. (1978). The war of attrition with random rewards. J. theor. Biol. 74, 377-88.

Brockmann, H.J. & Dawkins, R. (1979). Joint nesting in a digger wasp as an evolutionarily stable preadaptation to social life. Behaviour, 71, 203-5.

Brockmann, H.J., Graf en, A. & Dawkins, R. (1979). Evolutionarily stable nesting strategy in a digger wasp. J. theor. Biol. 77, 473-96.

Bruning, D.F. (1973). The greater rhea chick and egg delivery route. Nat. Hist., 82, 68-75.

Bull, J.J. (1980). Sex determination in reptiles. Q. Rev. Biol. 55, 3-21. Burgess, J.W. (1976). Social spiders. Scient. Am. March, 100-6.

Bush, R.R. & Wilson, T.R. (1956). Two-choice behaviour of a paradise fish. J.exp.psychol. 51, 315-22.

Cade, W. (1979). The evolution of alternative male reproductive strategies in field crickets. In Sexual Selection and Reproductive Competition in Insects, ed. M.S. & N.A. Blum, pp. 343-79. Academic Press: New York.

Caryl, P.G. (1979). Communication by agonistic displays: what can game theory contribute to ethology? Behaviour, 68, 136-69.

Cavalli-Sforza, L.L. & Feldman, M.W. (1978). Darwinian selection and 'altruism'. Theor. Pop. Biol. 14, 268-80.

Charles Worth, B. (1977). Population genetics, demography and the sex ratio. In Measuring Selection in Natural Populations, ed. F.B. Christiansen & T.M. Fenchel, pp. 345-63. Springer-Verlag: Berlin.

— (1980). Evolution in Age-structured Populations. Cambridge University Press.

Charnov, E.L. (1979). The genetical evolution of patterns of sexuality. Am. Nat. 113,465-80.

— (1981). The Theory of Sex Allocation. Princeton University Press (in press).

Charnov, E.L. & Bull, J.J. (1977). When is sex environmentally determined? Nature, Lond. 266, 828-30.

Charnov, E.L., Gotshall, D.W. & Robinson, J.G. (1978). Sex ratio: adaptive response to population fluctuations in pandalid shrimp. Science, Wash. 200, 204-6.

Clarke, B. (1976). The ecological genetics of host-parasite relationships. In Genetic Aspects of Host-Parasite Relationships, ed. A.E.R. Taylor & R. Muller, pp. 87-103. Blackwell: Oxford.

Clutton-Brock, T.H. & Albon, S.D. (1979). The roaring of red deer and the evolution of honest advertisement. Behaviour, 69, 145-70.

Clutton-Brock, T.H., Albon, S.D., Gibson, R.M. & Guinness, F.E. (1979). The logical stag: adaptive aspects of fighting in red deer (Cervus elaphus L.). Anim. Behav. 27, 211-25.

Clutton-Brock, T.H., Harvey, P.H. & Rudder, B. (1977). Sexual dimorphism, socionomic sex ratio and body weight in primates. Nature, Lond. 269, 797-9.  {207} 

Collias, N.E. (1960). An ecological and functional classification of animal sounds. In Animal Sounds and Communication, ed. W.E. Lanyon & W.T. Tavolga, pp. 368-91. Am. Inst. Biol. Sci. Pub. No. 7. Washington.

Cosmides, L.M. & Tooby, J. (1981). Cytoplasmic inheritance and intragenomic conflict. J. theor. Biol. 89, 83-129.

Davies, N.B. (1978). Territorial defence in the speckled wood butterfly (Pararge aegeria): the resident always wins. Anim. Behav. 26, 138-47.

Davies, N.B. & Halliday, T.M. (1978). Deep croaks and fighting assessment in toads Bufo bufo. Nature, Lond. 274, 683-5.

Dawkins, R. (1976). The Selfish Gene. Oxford University Press.

— (1980). Good strategy or evolutionarily stable strategy? In Sociobiology: beyond NaturejNurture, ed. G.W. Barlow & J. Silverberg, pp. 331-67. Westview Press: Boulder.

Dawkins, R. & Brockmann, H.J. (1980). Do digger wasps commit the Concorde fallacy? Anim. Behav. 28, 892-6.

Dawkins, R. & Carlisle, T.R. (1976). Parental investment, mate desertion and a fallacy. Nature, Lond. 262, 131-3.

Dingle, H. (1969). A statistical and information analysis of aggressive communication in the mantis shrimp Gonodactylus bredini Manning. Anim. Behav. 17, 561-75.

Dobzhansky, Th. (1951). Genetics and the Origin of Species, third edn. Columbia University Press.

Dominey, W. (1980). Female mimicry in male bluegill sunfish — a genetic polymorphism? Nature, Lond. 284, 546-8.

Dow, M., Ewing, A.W. & Sutherland, I. (1976). Studies on the behaviour of cyprinodont fish III. The temporal patterning of aggression in Aphysemion striatum (Boulenger). Behaviour, 59, 252-68.

Dunham, D.W. (1966). Agonistic behaviour in captive rose-breasted grosbeaks, (Pheucticus ludovicianus) (L.). Behaviour, 27, 1601-73.

Eberhard, W.G. (1980a). Horned beetles. Scient. Am., March, 124-31.

— (1980b). Evolutionary consequences of organelle competition. Q.Rev. Biol. 55, 231-49.

Eigen, M. & Schuster, P. (1977). Emergence of the hypercycle. Naturwissenschaften, 64, 541-65.

Eshel, I. (1975). Selection on sex ratio and the evolution of sex-determination. Heredity, 34, 351-61.

— (1981a). Evolutionary and continuous stability. J. theor. Biol, (in press).

— (1981b) Evolutionary stable strategies and natural selection in Mendelian populations. Theor. Pop. Biol, (in press).

Feldman, M.W. & Cavalli-Sforza, L.L. (1976). Cultural and biological evolutionary processes, selection for a trait under complex transmission. Theor. Pop. Biol. 9, 238-59.

Fischer, E.A. (1980). The relationship between mating system and simultaneous hermaphroditism in the coral reef fish, Hypoplectus nigricans (Serranidae). Anim. Behav. 28, 620-33.  {208} 

Fisher, R.A. (1930). The Genetical Theory of Natural Selection. Clarendon Press: Oxford.

Fretwell, S.D. (1972). Seasonal Environments. Princeton University Press.

Fretwell, S.D. & Lucas, H.L. (1970). On territorial behaviour and other factors influencing habitat distribution in birds. Acta biotheor. 19, 16-36.

Frith, H.J. (1962). The Mallee-Fowl. Angus & Robertson: Sydney.

Gadgil, M. (1972). Male dimorphism as a consequence of sexual selection. Am. Nat. 106, 574-80.

Gale, J.S. & Eaves, L.J. (1975). Logic of animal conflict. Nature, Lond. 254, 463-4.

Geist, V. (1966). The evolution of horn-like organs. Behaviour, 27, 175-213.

Geyl, P. (1949). The Revolt of the Netherlands. Jonathan Cape: London.

Ghiselin, M.T. (1969). The evolution of hermaphroditism among animals. Q. Rev. Biol. 44, 189-208.

Gould, S.J. & Lewontin, R.C. (1979). The spandrels of San Marco and the Panglossian paradigm: a critique of the adaptationist programme. Proc. R. Soc. B, 205, 581-98.

Grafen, A. (1979). The hawk-dove game played between relatives. Anim. Behav. 27, 905-7.

Grafen, A. & Sibly, R.M. (1978). A model of mate desertion. Anim. Behav. 26, 645-52.

Gross, M.R. & Charnov, E.L. (1980). Alternative male life histories in bluegill sunfish. Proc. nat. Acad. Sci. USA, 77, 6937-40.

Haigh, J. (1974). The existence of evolutionary stable strategies. J. theor. Biol., 47, 219-21.

Haigh, J. & Rose, M.R. (1980). Evolutionary game auctions. J. theor. Biol. 85, 381-97.

Haldane, J.B.S. (1949). Disease and evolution. La Ricerca Scientifica Suppl. 19, 68-76.

Hamilton, W.D. (1964). The genetical evolution of social behaviour, I and II. J. theor. Biol. 7, 1-16; 17-32.

— (1967). Extraordinary sex ratios. Science, Wash. 156, 477-88.

— (1979). Wingless and fighting males in figwasps and other insects. In Sexual Selection and Reproductive Competition in Insects, ed. M.S. & N.A. Blum, pp. 167-220. Academic Press: New York.

Hamilton, W.D. & May, R.M. (1977). Dispersal in stable habitats. Nature, Lond. 269, 578-81.

Hammerstein, P. (1981). The role of asymmetries i n animal contests. Anim. Behav. 29, 193-205.

Hammerstein, P. & Parker, G.A. (1981). The asymmetric war of attrition. J. theor. Biol, (in press).

Harley, C.B. (1981). Learning the evolutionary stable strategy. J. theor. Biol. 89, 611-33.

Hazlett, B. (1966). Factors affecting the aggressive behaviour of the hermit crab Calcinus tibicen. Z. Tierpsychol. 23, 655-71.  {209} 

— (1972). Stimulus characteristics of an agonistic display of the hermit crab (Calcinus tibicen). Anim. Behav. 20, 101-7.

— (1978). Shell exchange in hermit crabs: aggression, negotiation or both? Anim. Behav. 26, 1278-9.

— (1980). Communication and mutual resource exchange in North Florida hermit crabs. Behav. Ecol. Sociobiol. 6, 177-84.

Hazlett, B. & Bossert, W.H. (1965). A statistical analysis of the aggressive communications systems of some hermit crabs. Anim. Behav. 13, 357-73.

Heller, R. & Milinsky, M. (1979). Optimal foraging of sticklebacks on swarming prey. Anim. Behav. 27, 1127-41.

Heyman, G.M. (1979). Markov model description of changeover probabilities on concurrent variable interval schedules. J. exp. Analysis Behav. 31, 41-51.

Hines, W.G.S. & Maynard Smith, J. (1979). Games between relatives. J. theor. Biol. 79, 19-30.

Hirschleifer, J. (1980). Evolutionary Models in Economics and Law: Cooperation versus Conflict Strategies. Dept of Economics, University of California, Los Angeles, Working Paper No. 170.

Hogan-Warburg, A.J. (1966). Social behaviour of the ruff, Philomachus pugnax (L.) Ardea, 54, 109-229.

Hrdy, S.B. (1974). Male-male competition and infanticide among the langurs (Presbytis entellus) of Abu, Rajasthan. Fiola primatol. 22, 19-58.

Hyatt, G.W. & Salmon, M. (1978). Combat in the fiddler crabs Uca pugilator and U. pugnax: a quantitative analysis. Behaviour, 65, 182-211.

Jakobsson, S., Radesater, T. & Jarvi, T. (1979). On the fighting behaviour of Nannacara anomala (Pisces, Cichlidae) cJc?- Z- Tierpsychol. 49, 210-20.

Jones, A.R. (1980). Chela injuries in the fiddler crab, Uca burger si Holthuis. Mar. Behav. Physiol. 7, 47-56.

Jones, J.W. (1969). The Salmon. Collins: London.

Kallman, K.D., Schreibman, M.P. & Borkoski, V. (1973). Genetic control of gonadotrop differentiation in the platyfish, Xiphophorus maculatus (Poeciliidae). Science, Wash. 181, 678-80.

Kalmus, H. (1941). Defence of source of food by bees. Nature, Lond. 148, 228.

Kirkpatrick, M. (1982). Sexual selection and the evolution of female choice. Evolution, 36, (in press).

Kluijver, H.N. (1951). The population ecology of the great tit, Parus m. major L. Ardea, 39,1-135.

Krebs, J.R., Kacelnik, A. & Taylor, P. (1978). Optimal sampling by foraging birds: an experiment with great tits (Parus major). Nature, Lond. 275, 27-31.

Kummer, H., Gotz, W. & Angst, W. (1974). Triadic differentiation: an inhibitory process protecting pair bonds in baboons. Behaviour 49, 62-87.  {210} 

Lack, D. (1968). Ecological Adaptations for Breeding in Birds. Methuen:

London. Lande, R. (1981). Models of speciation by sexual selection on polygenic traits. Proc. nat. Acad. Sci. USA, 78, 3721-5.

Lawlor, L.R. & Maynard Smith, J. (1976). The coe volution and stability of competing species. Am. Nat. 110, 79-99.

Leigh, E.G., Charnov, E.L. & Warner, R.R. (1976). Sex ratio, sex change, and natural selection. Proc. nat. Acad. Sci. USA, 73, 3656-60.

Lewontin, R.C. (1961). Evolution and the theory of games. J. theor. Biol. 1, 382-403.

Lloyd, D.G. (1977). Genetic and phenotypic models of natural selection. J. theor. Biol. 69, 543-60.

Luce, R.D. & Raiffa, H. (1957). Games and Decisions. Wiley: New York.

Lumsden, C.J. & Wilson, E.O. (1981). Genes, Mind, and Culture. Harvard University Press.

MacArthur, R.H. (1965). Ecological consequences of natural selection. In Theoretical and Mathematical Biology, ed. T. Waterman & H. Horowitz, pp. 388-97. Blaisdell: New York.

Maynard Smith, J. (1956). Fertility, mating behaviour and sexual selection in Drosophila subobscura. J. Genet. 54, 261-79.

— (1958). The Theory of Evolution. Penguin Books: Harmondsworth.

— (1974). The theory of games and the evolution of animal conflicts. J. theor. Bioi 47, 209-21.

— (1977). Parental investment: a prospective analysis. Anim. Behav. 25, 1-9.

— (1978). The Evolution of Sex. Cambridge University Press.

— (1980). A new theory of sexual investment. Behav. Ecol. Sociobiol. 7, 247-51.

— (1981). Will a sexual population evolve to an ESS? Am. Nat. 117, 1015-18.

Maynard Smith, J. & Parker, G.A. (1976). The logic of asymmetric contests. Anim. Behav. 24, 159-75.

Maynard Smith, J. & Price, G.R. (1973). The logic of animal conflict. Nature, Lond. 246, 15-18.

Maynard Smith, J. & Sondhi, K.C. (1960). The genetics of a pattern. Genetics, 1039-50.

McFarland, D.J. (1974). Time-sharing as a behavioural phenomenon. Advances in the Study of Behaviour, 5, 201-25.

Michener, C.D. (1974). The Social Behaviour of the Bees. Belknap: Cambridge, Mass.

Milinsky, M. (1979). An evolutionarily stable feeding strategy in sticklebacks. Z. Tierpsychol. 51, 36-40.

Mirmirani, M. & Oster, G. (1978). Competition, kin selection and evolutionary stable strategies. Theor. Pop. Biol. 13, 304-39.

Morton, E.S. (1977). On the occurrence and significance of  {211}  motivation-structural rules in some bird and mammal sounds. Am. Nat. Ill, 855-69.

Murton, R.K., Westwood, N.J. & Isaacson, A.J. (1964). A preliminary investigation of the factors regulating population size in the woodpigeon, Columba palumbus. Ibis, 106, 482-507.

Norman, R.F., Taylor, P.D. & Robertson, R.J. (1977). Stable equilibrium strategies and penalty functions in a game of attrition. J. theor. Biol. 65, 571-8.

Orlove, M.J. (1979). Putting the diluting effect into inclusive fitness. J. theor. Biol. 78, 449-50.

Packer, C. (1977a). Inter-troop transfer and inbreeding avoidance in Papio anubis in Tanzania. Ph.D. thesis, University of Sussex.

— (1977b). Reciprocal altruism in Papio anubis. Nature, Lond. 265, 441-3.

Parker, G.A. (1970a). The reproductive behaviour and the nature of sexual selection in Scatophagastercoraria L. (Diptera: Scatophagidae). ii. The fertilization rate and the spatial and temporal relationships of each sex around the site of mating and oviposition. J. Anim. Ecol. 39, 205-28.

— (1970b). The reproductive behaviour and the nature of sexual selection in Scatophagastercoraria L. (Diptera: Scatophagidae). iv. Epigamic recognition and competition between males for the possession of females. Behaviour, 37, 113-39.

— (1974a). The reproductive behaviour and the nature of sexual selection in Scatophaga stercoraria L. ix. Spatial distribution of fertilisation rates and evolution of male search strategy within the reproductive area. Evolution, 28, 93-108.

— (1974b). Assessment strategy and the evolution of animal conflicts. J. theor. Biol. 47, 223-43.

— (1974c). Courtship persistence and female guarding as male time investment strategies. Behaviour, 48, 157-84.

— (1978). Selection on non-random fusion of gametes during the evolution of anisogamy. J. theor. Biol. 73, 1-28.

— (1979). Sexual selection and sexual conflict. In Sexual Selection and Reproductive Competition in Insects, ed. M.S. & N.A. Blum, pp. 123-66. Academic Press: New York.

Parker, G.A., Baker, R.R. & Smith, V.G.F. (1972). The origin and evolution of gamete dimorphism and the male-female phenomenon. J. theor. Biol. 36, 529-53.

Parker, G.A. & Rubinstein, D.I. (1981). Role assessment, reserve strategy, and acquisition of information in asymmetric animal conflicts. Anim. Behav. 29, 135-62.

Parker, G.A. & Thompson, E.A. (1980). Dung fly struggles: a test of the war of attrition. Behav. Ecol. Sociobiol. 7, 37-44.

Perrill, S.A., Gerhardt, H.C. & Daniel, R. (1978). Sexual parasitism in the green tree frog (Hyla cinered). Science, Wash. 200, 1179-80.

Rand, W.M. & Rand, A.S. (1976). Agonistic behaviour in nesting iguanas:  {212}  a stochastic analysis of dispute settlement dominated by the minimization of energy costs. Z. Tierpsychol. 40, 279-99.

Raup, D.M. (1966). Geometric analysis of shell coiling: general problems. J. Palaeontol. 40, 1178-90.

Ridley, M. (1978). Paternal care. Anim. Behav. 26, 904-32. Riechert, S.E. (1978). Games spiders play: behavioural variability in territorial disputes. Behav. Ecol. Sociobiol. 3, 135-62.

— (1979). Games spiders play: ii. Resource assessment strategies. Behav. Ecol. Sociobiol. 6, 121-8.

— (1981). Spider interaction strategies: communication vs coercion. In Biology of Spider Communication, ed. P.N. Witt & J. Rovner. Princeton University Press, (in press).

Riley, J.G. (1978). Evolutionary Equilibrium Strategies. Dept of Economics, University of California, Los Angeles, Working Paper No. 109.

Roberts, W.A. (1966). Learning and motivation in the immature rat. Am. J. Psychol 79, 3-23.

Rohwer, S. (1977). Status signalling in Harris sparrows: some experiments in deception. Behaviour, 61, 107-29.

Rohwer, S. & Ewald, P.W. (1981). The cost of dominance and advantage of subordinance in a badge signalling system. Evolution, 35, 441-54.

Rohwer, S., Ewald, P.W. & Rohwer, F.G. (1981). Variation in size, appearance and dominance within and between the sex and age classes of Harris' sparrows. Bird Banding, (in press).

Rohwer, S. & Rohwer, F.C. (1978). Status signalling in Harris sparrows: experimental deceptions achieved. Anim. Behav. 26, 1012-22.

Schuster, P. & Sigmund, K. (1981). Coyness, philandering and stable strategies. Anim. Behav. 29, 186-92.

Scudo, F.M. (1964). Sex population genetics. Ric. Sci. 34, 93-146.

Selander, R.K. (1972). Sexual selection and dimorphism in birds. In Sexual Selection and the Descent of Man, ed. B. Campbell, pp. 180-230. Heinemann: London.

Selten, R. (1975). Bargaining under incomplete information — a numerical example. In Dynamische Wirtschafts-analyse, ed. O. Becker & R. Richter, pp. 203-32. J.C.B. Mohr: Tubingen.

— (1980). A note on evolutionary stable strategies in asymmetric animal conflicts. J. theor. Biol. 84,93-101.

Shaw, R.F. & Mohler, J.D. (1953). The selective advantage of the sex ratio. Am. Nat. 87, 337-42.

Sigurjonsdottir, H. & Parker, G.A. (1981). Dung fly struggles: evidence for assessment strategy. Behav. Ecol. Sociobiol. 8, 219-30.

Simpson, M.J.A. (1968). The display of Siamese fighting fish, Betta splendens. Anim. Behav. Monog. 1, 1-73.

Slatkin, M. (1979). The evolutionary response to frequency- and density-dependent interactions. Am. Nat. 114, 384-98.  {213} 

Slatkin, M. & Wilson, D.S. (1979). Coevolution in structured demes. Proc. nat. Acad. ScL USA, 76, 2084-7.

Slobodkin, L.B. & Rapoport, A. (1974). An optimal strategy of evolution. Q. Rev. Biol. 49, 181-200.

Spurway, H. (1949). Remarks on Vavilov's law of homologous variation. La Ricerca Scientifica Suppl. 19, 3-9.

Stearns, S.C. (1976). Life history tactics: a review of the ideas. Q. Rev. Biol. 51, 3-47.

Stokes, A.W. (1962a). Agonistic behaviour among blue tits at a winter feeding station. Behaviour, 19, 118-38.

— (1962b). The comparative ethology of great, blue, marsh and coal tits at a winter feeding station. Behaviour, 19, 208-18.

Taylor, P.D. & Jonker, L.B. (1978). Evolutionarily stable strategies and game dynamics. Math. Biosc. 40, 145-56.

Trivers, R.L. (1971). The evolution of reciprocal altruism. Q. Rev. Biol. 46, 35-57.

— (1972). Parental investment and sexual selection. In Sexual Selection and the Descent of Man, ed. B. Campbell, pp. 136-79. Heinemann: London.

— (1974). Parent-offspring conflict. Am. Zool. 14, 249-64.

Trivers, R.L. & Hare, H. (1976). Haplodiploidy and the evolution of the social insects. Science, Wash. 191, 249-63.

Van Rhijn, J.G. (1973). Behavioural dimorphism in male ruffs Philomachus pugnax (L.). Behaviour, 47, 153-229.

Vehrencamp, S.L. (1979). The roles of individual, kin and group selection in the evolution of sociality. In Social Behaviour and Communication, ed. P. Marler & J. Vandenbergh, pp. 351-94. Plenum Press: New York.

Von Neumann, J. & Morgenstern, O. (1953). Theory of Games and Economic Behaviour. Princeton University Press.

West-Eberhard, M.J. (1975). The evolution of social behaviour by kin selection. Q. Rev. Biol. 50, 1-33.

Wiese, L. (1981). On the evolution of anisogamy from isogamous monoecy and on the origin of sex. J. theor. Biol. 89, 573-80.

Wiese, L., Wiese, W. & Edwards, D.A. (1979). Inducible anisogamy and the evolution of oogamy from isogamy. Ann. Bot. 44, 131-9.

Wilson, D.S. (1980). The Natural Selection of Populations and Communities. Benjamin Cummings: California.

Wilson, E.O. (1978). On Human Nature. Harvard University Press.

Witham, T.G. (1980). The theory of habitat selection: examined and extended using Pemphigus. Am. Nat. 115, 449-66.

Zahavi, A. (1981). Natural selection, sexual selection and the selection of signals. Proc. 2nd Int. Congr. Syst. & Evol. Vancouver, Canada, 1980, (in press).

Zeeman, E.C. (1979). Population dynamics from game theory. Proc. Int. Conf Global Theory of Dynamical Systems. Northwestern: Evanston.

— (1981). Dynamics of the evolution of animal conflicts. J. theor. Biol. 89, 249-70.

Subject index

F = figure or illustration, n = footnote, passim = scattered references

actions: explanation of, 204;

range of during contest, 149

acts, scale of aggression of, 149

'adaptationist programme', 6

age class, uninvadable, 144

aggressiveness, scale of increasing, 149

Agelenopsis aperta, 77, 107, 151, 177, 178:

    contest of behaviour in, 115-22;

    habitat of, 77;

    model contest in, 188, 120;

    value of web and content costs, 118

agonistic encounters, in Stone's sheep, 110

allele, 21, 40, 48, 179:

at sex-linked locus, 87

altruism, reciprocal, 170, 174

analysis of pairwise contests, between animals, 2

ancestral population, state of, 8

animals: analysis of pairwise contests in, 2;

    behaviour of, 177;

    fighting behaviour of, 3;

    set of possible behaviour in, 58

animal contests, information transfer in, 148-51

anisogamy, 3, 53:

    evolution of 47-53;

    of phenotype, 43

anisogamy problem, 197

Announcer-Dove-Cheater game, 165F

aphid, 92

asexual reproduction, 20-2

assessment:

    in animal contests, 107;

    of resource-holding power, 114, 150;

    phase of, 106,

    size, 109

assessor, 108, 114:

    factors favouring as ESS, 109

assessor ES, 109

assessor strategy, 109, 110

assortative mating, 133

asymmetric contest, 22-3, 114;

    explanation of, 204;

    uncorrelated, 95

asymmetric games, 200:

    classification and examples of, 106-22;

    with cyclic dynamics, 199-202;

    ownership 94-105;

    payoff matrix for, 200F;

    sex and generation, 123-39;

    two-strategy, 201

asymmetry:

    of size and ownership, 122;

    uncorrelated, 95, 124

attractor, 19

baboon, see Papio anubis

bargaining, 147-66

battle of the sexes, 131, 200

bauplan, 7

beetle, horned, see Podischuus agenor

bees:

    Caucasian, 97;

    Centris pallida, 72-3, 76, 114;

    Italian, 97

behaviour:

    change in, 148;

    in contest, 110;

    cyclic with internal stationary

    point, 201;

    honest, 156;

    initial, 61;

    instinctive, 67;

    learnt, 67;

    optimal, 62;

    oscillatory, 202;

    set of possible, 58;

    territorial, 98-9;

    variable, 68, 69, 86

Bishop and Canning's theorem, 15, 29, 58, 181, 192, 196

black hamlet, see Hypoplectus nigricans

bluff, as transitory phenomenon, 151, 156

Bourgeois strategy, 22, 94

breeding success:

    in birds, 37F;

    of population, 143

Bufo bufo, croak in flight assessment, 112-14

butterflies:

    peacock, 99-100;

    speckled wood, 98-9;

    swallowtail, 99

CH, see conditional Hawk

CSS, see culturally stable strategy

Carduelis pinus, 86

Cassin's finch (Carpodacus cassinii), 85

Centris pallida, 72-3, 76, 114

Cervus elaphus, 140, 141, 142, 148;

contests between males, 11 IF;

    escalated fights in, 111;

    roaring in 216

assessment of fighting ability, 110-14

Chlamydomonas chlamydogma, 49;

C. moewusiiy 49;

C. reinhardtii, 49

Chlamydomonas sp.:

    clones in, 49;

    macrogametes in, 49, 51, 52, 53;

    microgametes in, 49, 51, 53;

    mitosis in, 49

cichlid, 150

clones, in Chlamydomonas sp., 49

commitment, 147-66

concurrent variable interval game, 64-7

conditional Hawk (CH), 118

conflict:

    between genes, 123;

    male-female, 129;

    parent-offspring, 123;

contest behaviour:

    influence of asymmetry on, 115;

    in Agelenopsis, 115-17

contests:

    asymmetric 22-3, 66, 121;

    between owner and intruder, 94;

    between male dung flies, 33;

    between relatives, 176;

    between sexes, 141;

    between sexes of

    Hamadryas baboon, 97-8;

    compromise in, 159;

    escalated, 22, 36, 66, 68, 94, 101, 109, 119, 151, 152;

    frequency-dependent, 30, 34, 75;

    intruder in, 94, 95, 96;

    pairwise, 23, 31, 35, 56, 76, 77, 141, 142, 174, 175, 191;

    symmetric, 22-3

cooperation:

    evolution of, 167-73;

    requirements for, 169-70

crab, fiddler, 115

cricket, 89

culturally stable strategy (CSS), 54, 80

DSS, see developmentally stable strategy

Darwinian fitness, of an individual, 11

deer, red, see Cervus elaphus

developmental constraints, 5

developmentally stable strategy (DSS), 54

dimorphism, 90:

    evolutionarily stable, 87;

    in figwasps, 86;

    in primates, 9;

    sexual (in ruff), 88

diploid inheritance, sexual, 40;

    two-strategy game with, 40-3

diploid population, infinite random-mating in, 40

dispersal, evolution of, 1;

    in a uniform environment, 92-3

dispersal behaviour, in birds, 1

displacement, sequential, in social spider, 96

display, 149;

    during contest, 12;

    with varying intensity, 154

Dove (D), 12, 40

Dove v. Dove, 13

dung fly see Scatophaga stercoraria

ESS, see evolutionarily stable strategy

egg-trading, 3, 160:

    definition of (in black hamlet), 159

element, stocastic, 15

elephant, African, musth (i.e. state of frenzy) in, 161

environmental, dispersal in, 92-3

equilibrium:

    stable, 42;

    strategy, 29;

    unstable, 42

escalated contest, 12, 22, 36, 94, 101, 109, 151, 152, 158

escalated fight, 108, 147;

    in Hamadryas , baboon, 98;

    in red deer, 111

escalation region, 119

Euphesiopteryx ochracea, 89

evolution:

    of anisogamy, 47-53;

    of cooperation, 167-73;

    of dispersal, 1;

    general theory of, 8;

    method of modelling, 1;

    at phenotypic level, 1;

    of polygynous mammals, 3;

    population dynamics and stability in, 2;

    of sex ration, 2, 45;

    specific theory of, 8;

    of territorial behaviour, 153-9;

    of wing form, 1

evolutionarily stable (ES) learning rule, 56, 57, 59, 67, 176

evolutionarily stable strategy (ESS), passim throughout book:

    asymmetric, 132;

    common-sense, 102, 104, 105, 125;

    explanation of, 204;

    learning the, 54-67;

    mixed, 16, 17, 19, 29, 30, 43, 68-107 passim, 162-204 passim;

    paradoxical, 102, 103, 104, 105, 125;

    pure, 16, 102, 178;

    from recurrence equations, 198-9;

    rule for, 56, 57, 67;

    strong, 186, 187;

    types of, 125;

    weak, 186, 187

evolutionary game theory, 175:

and population genetics, 178

extinction of species, probability of, 2

fighting behaviour, in animals, 3

finite population games, 20

figwasp, 86-7  {217} 

fish:

    Aphysemion striatum, 149-50;

    Betta splendens, 149

fitness, Darwinian, 11:

    frequency-dependent, 3, 197;

    of individuals, 30, 50;

    neighbour

    modulated, 191;

    personal, 191;

    zero, 38

fitness matrix, 193:

    derived inclusive, 176;

    for sex ratio game, 25;

    for two-strategy game, 193

flocks, status in, 82-6

fly, dung, see Scatophaga stercoraria

free distribution, ideal, 63, 90-2

frequency-deperidfent contest, 30, 34, 75

frequency-dependent fitness, 3, 197

frequency-dependent game, 55, 56, 57, 66

frequency-dependent mating success, 89

frequency-dependent payoff, 69

frequency-dependent selection, 4, 86, 89, 151, 174

frequency-independent game, 55-66 passim

frog, green tree, 78-9

game against nature, 140

    Announcer-Dove-Cheater, 165F

    asymmetric, 37, 66:

    classification and examples of, 106-22;

    with cyclic dynamics, 199-202;

    ownership in, 94-105;

    sex and generation, 123-39;

    two-strategy, 201

    between relatives, 191-4

    of complete information, 152, 158

    concurrent variable interval, 64-7

    with cyclic dynamics, 130-1

    foraging, 55

    frequency-dependent, 55, 56, 57, 66

    frequency-independent, 55-66 passim

        Hawk-Dove, 5, 6, 11-20 passim, 22, 34, 62-3, 66, 68-94 passim, 101, 102, 118, 162, 165:

        asymmetric, 101, 105;

        between relatives, 192F;

        payoff for, 95F;

        with diploid inheritance, 42

    Hawk-Dove-Assessor, 108, 109

    Hawk-Dove-Bourgeois, 22, 96, 99, 114, 168

    Hawk-Dove-Retaliator, 18, 19, 188, 189, 190

    Hawk-Dove-Retaliator-Bully, 188, 190

    of imperfect information, 37

    of incomplete information, 152, 153, 158, 162

    individual, 55

    mating, 55

    of opponent-independent costs, 141F

    peck-order, 55

    population, 55, 66;

    finite, 20

    population foraging, 63-4, 65

    Prisoner's Dilemma 162F, 166, 167, 168, 171, 174, 202F:

        asymmetric, 164;

        commitment in, 163;

        reiterated, 202-3;

        repeated, 164F

    with random rewards, 106

    repeated, 66

    Rock-Scissors-Paper (R-S-P), 19, 20

    sex-ratio, 24, 44, 186:

    fitness matrix for 25F

    size, 140-6, 144F:

    allowance for senescence, 146F

    social contact, 173

    symmetric, 68, 94, 162, 200

    territory, 157F

    two-armed bandit, 61-2, 66

    two-strategy 40-3, 180-2, 193F

game theory:

    analysis of, 136;

    classical, 2;

    evolutionary, 3, 8, 67, 68, 92;

    field of application of, 175-6;

    matrix notation for, 180;

    and population genetics, 175, 177

game theory model, 4, 5

gamete, 123;

    bipolarity of, 48

gap, 195, 196

gasteropod shells, 7

Gaussian curve, 136

genes:

    conflict between, 123;

    cytoplasmic, 48;

    linkage disequilibrium in, 94;

    non-random association between, 133;

    pleiotropism in, 94

genetic covariance, 133, 135

genetic homozygote, 40, 76

genetic model:

    for conflicts 123;

    games with, 40-53;

    of population, 4

genetic polymorphism, 4, 21, 43, 102:

    stable, 16, 17, 43, 76, 78, 86

genetic relatedness, degree of, 20

genotype, 16, 41;

    homozygous, 178, 179

Grafen condition, 191-2, 193

grosbeak, evening, 85

Gryllus integer, 89

guarding, by single parent, 127

Hamadryas baboon, 99:

    bonding in, 99,  {218} 

    contest between males over females, 97-8;

    escalated fight in, 98

Harley's theorem, 57

Harris sparrow, 82, 161, 165, 166:

    colour of plumage, 68;

    testosterone in, 83

Hawk (H), 12, 40

Hawk-Bully polymorphism, 191

Hawk-Dove game, 5, 6, 11-20, 22, 34, 62-3, 66, 68-94 passim, 101, 102, 118, 162, 165:

    asymmetric, 101, 105;

    with diploid inheritance, 42;

    payoff for, 95F;

    between relatives, 192F

Hawk-Dove-Assessor game, 108, 109

Hawk-Dove-Bourgeois game, 22, 96, 99, 114, 168

Hawk-Dove model, 105

Hawk-Dove phenotype, 41

Hawk-Dove-Retaliator game, 18, 19, 188, 189:

    modified, 190

Hawk-Dove-Retaliator-Bully game, 188, 190

hereditary mechanism, for evolutionary process, 170-3

heredity, problems of, 6

hermit crab, shell trading in, 161

Hesperiphona vespertina, 85

heterozygote, 88

homologous variation, Vavilov's law of, 7

homozygote, 21, 88;

    genetic, 40, 76

homozygous genotype, 178, 179

honesty, 147-65

host-parasite interaction, 126

house sparrow, 85

Hyla cinerea, 78-9

Hypoplectus nigricans, 159-61:

    simultaneous hermaphroditism in, 159

Inachis io, 99-100

inclusive fitness matrix, for two-strategy game, 193F

incestuous mating, 130

individual, Darwinian fitness of, 11;

    inclusive fitness of, 191;

    mating success of, 145

information transfer, during contest, 147;

    problem of, 29

inheritance, asexual, 11, 14;

    parthenogenic, 40;

    sexual diploid, 40

injury, risk of, 34

intruder, 103, 119;

    in contest, 94, 95, 96;

    into resource, 106;

    into territory, 22, 77

isogamous population, 50

isogamy, 48, 50

Junco hyemalis (dark-eyed junco), 85

kinship, in social behaviour, 167

Lande's model of speciation, 133-7

learning mechanism, 31

learning rules, 20:

    evolutionarily stable, 56, 57;

    relative payoff sum, 60-77 passim, 176

lek species, 88, 142

Lepomis macrochirus, 90

life history strategy, 140-6, 177

lion, ownership in mating, 100-1

macrogamete, in Chlamydomonas sp., 49, 51, 53;

    production of, 52

male parental care, 128

mating game, 55

mating, incestuous, 130

mating success of individual, variations of, 145

mating type, 49

meiosis, 47:

chromosomes in, 81

microgamete in Chlamydomonas sp., 49, 51, 53

mixed ESS, 16, 17, 19, 29, 30, 43, 68-107 passim, 162-204 passim

mixed phenotype, 40

mixed strategy, 11-17 passim, 26, 79, 80, 102-26 passim, 181-6 passim

models:

    basic, 10;

    for evolution of cooperative behaviour, 169-70;

    extended, 23-7,

    (fitness matrix for) 24F;

    genetic, 123,

    (of evolution of sex ratio) 45;

    Hawk-Dove, 105;

    Hawk-Dove-Bourgeois, 97, 99;

    Lande's, 133-7;

    optimisation, 5;

    of pairwise contests, 11;

    population genetic, 4;

    of territorial behaviour, 153;

    two-locus, 134;

    variable rewards, 38;

    war of attrition, 34, 105

monomorphic population, 185

mortality, constant force of, 143

motivation, 36:

    differences in, 35;

    information about, 147

mutant, 14  {219} 

mutant strategy, 10

mutualism, 170:

    between species, 167

Nannacara anomala, 50

natural selection, parameter set by, 82

Oecibus civitas, 96

optimal strategy, 140, 197

optimisation model, 5

optimisation problem, with fixed constraints, 140

optimisation theory, 1, 175, 176

overdominance, 21, 42

Ovis dalli stonei, agonistic encounters in, 110

owner, 32, 103, 119:

    during contest, 94, 95, 96;

    payoff to, 101;

    of resource, 106;

    of a territory, 22, 28, 77

pairwise contests, 23, 31, 35, 56, 76, 77, 141, 142, 174, 175, 191:

    in animals, 2;

    model of, 11

Pandalus jordani, 70

Papilio zelicaon, 99

Papio anubis, fighting ability in, 100

Pararge aegeria, 98-9

parental care, 8, 126-30:

    deserting in, 126;

    game theory model of, 126;

    guarding in, 126;

    pay off in, 127;

    post-copulatory guarding by, 129;

    single-parent guarding, 127

parthenogenesis:

    in females, 93;

    inheritance, 40

Parus major, 91;

    breeding success in, 92

Passer domesticus, 85

paternity, confidence of, 128, 129

payoff, 15, 55-68 passim, 80, 94, 106, 124, 178, 195, 196, 203:

    for asymmetric game, 200;

    equality of, 34, 105;

    explanation of, 204;

    frequency-dependent, 69;

    for Hawk-Dove game, 12F;

    in parental care, 127;

    positive, 20,

    (inequality of) 101;

    for war of attrition, 194F

payoff matrix, 12, 17, 18, 22, 101, 103F, 108, 141, 164, 180, 189, 190, 199:

    for territory game, 157F, 158F

Pemphigus betae, 92

phenotype, 5, 21, 41, 187, 198;

    analysis of 4;

    arbitrary, 179;

    mixed, 40;

    pure, 40;

    with sexual reproduction, 43-7

phenotypic evolution, 176

phenotypic fitness, in ruff (Philomachus pugnax), 89

phenotypic set, 43:

    concave, 44, 46;

    convex, 44, 46

phenotypic variation:

    in population, 144;

    range of, 7

Philomachus pugnax, 88

pig:

    dominant, 54;

    subordinate, 54

platyfish, 87

Podischuus agenor, 70-2;

    allometry in, 71

polygenic system, 22

polygynous mammals, evolution of, 3

polymorphic state, evolutionarily stable, 11

polymorphism, 19, 41, 89, 102, 185, 186, 189:

    genetic, 4, 21, 43, 102;

    genetically stable, 16, 17, 43, 76, 78, 86;

    Hawk-Bully, 191;

    protected, 179;

    in ruff, 89;

    stationary, 193

population:

    ancestral, 8;

    asexual, 17;

    dynamics of, 14,

    (evolutionarily stable) 50;

    equilibrium of, 26;

    explanation of, 204;

    frequency distribution in, 86;

    infinite, 14;

    isogamous, 50;

    monomorphic, 185;

    phenotypically uniform, 144;

    phenotypically variable, 144;

    polymorphic, 19, 20, 40, 69, 175, 184, 185;

    random-mating, 21, 40;

    random-mixing, 20;

    sexual diploid, 17;

    stable state of, 14«;

    stable strategy of, 14w;

    stability of, 183-8;

    structured, 27

population dynamics, 2, 183-8;

    in evolution, 2

population equilibria, 2

population foraging game, 63-4, 65

population games, 55, 66;

    finite, 20

population genetics:

    and game theory, 175, 177;

    equilibria in, 8;

    laws of, 5

population genetic model, 4

population stability, 183-8:

    in evolution, 2

preference function, 133

primates, size dimorphism in, 9

Prisoner's Dilemma, 162F, 166, 167, 168, 171, 174:

    asymmetric, 164;

    commitment in, 163;

    reiterated, 202-3;

    repeated (payoff matrix in), 164F

probability density function, 29

probability matching, 66, 76

probability of extinction, of a species, 2  {220} 

probability of playing, 181

probability of survival, 53, 142

pure strategy, 15-40 passim, 58-82 passim, 126, 182-99 passim

RHP, see resource-holding power RPS, see relative payoff sum

random-mating diploid population, 20, 40, 43

random-mixing population, 20

random reward, 194-5

reciprocal altruism, Triver's concept of, 164, 170, 174

recurrence equations, 198, 199

relative payoff sum learning rule (RPS), 60-77 passim, 176

residual values, 59

resource, 11, 94, 95, 107;

    allocation of, 140;

    divisible, 152; intruder into, 106;

    owner of, 106; value of, 101

resource-holding power (RHP), 36, 106, 114, 147, 148;

    assessment of, 114, 150;

    transmission of information about, 148

retaliation, 188-91

Retaliator strategy, 17, 191

retreat, during contest, 12

Rock-Scissors-Paper game (R-S-P), 19, 20

ruff, 88

salmon, mating of, 69

Scatophaga stercoria, 30-3, 76, 91, 121:

    contest between males, 33;

    mating success of males, 31

selection, frequency-dependent, 4, 86, 89, 151, 174

Selten's theorem, 108;

    definition of, 107

set:

    phenotypic, 43, 175,

    (concave) 44, 46,

    (convex) 44, 46;

    strategy, 106,

    (with continuous variables) 197-8,

    (for war of attrition) 195F, 196F

set of possible strategies, 43

set of recurrence behaviour, 58

set of recurrence equations, 198-9

sex ratio, 81-2, 177:

    between queen bee and workers, 123;

    evolutionarily stable 186;

    evolution of, 2, 45;

    genetic model of, 45;

    of phenotype, 43;

    of stable population, 25;

    unbeatable, 27

sex ratio game, 24, 44, 186:

    fitness matrix for, 25F

sex ratio problem, 197

sexual allocation, 2, 177

sexual diploid inheritance, 40

sexual investment, 43

sexual reproduction, phenotypes with, 43-7

sexual selection, 2, 131-7, 176;

    game theory analysis in, 132;

    population-genetics treatment in, 132

shrimp see Pandalus jourdani

signal, varied set of possible, 153

signalling:

    and subsequent action, 148;

    by animals, 148

siskin, pine, 86

size game, 140-6, 144F;

    allowance for senescence, 146F

Sphex ichneumoneus, 38-9, 56, 74-5, 76

spider:

    funnel web, see Agelenopsis aperta;

social, see Oecibus civitas

stability:

    global, 46;

    problem of, 17

stability criteria, 14

stability of population, 183-8

stability of retaliation, 17

status, in flocks, 82-6

Stone's sheep, see Ovis dolli stonei

strategy, 20, 174

    Assessor, 109, 110

    Bluffing, 156

    Bourgeois, 22, 94

    calling, in Hyla cinerea, 79

    choice of, 34

    culturally stable (CSS), 54, 80

    definition of, 10

    developmentally stable (DSS), 54

    equilibrium, 29

    evolutionarily stable (ESS), passim throughout book

    explanation of, 204

    honest, 156

    life history, 140-6, 177

    mixed, 11-17 passim, 26, 79, 80, 102-26 passim, 181-6 passim:

        classification of mechanisms, 68-80;

        examples of, 81-93;

        neutrally stable, 107

    optimal, 140, 197

    paradoxical, 102

    precocious parasitic, 69

    pure, 15-40 passim, 58-82 passim, 126, 182-99 passim

    pure conditional, 73

    Retaliator, 17, 191

    satellite, in Hyla cinerea, 79

    stealing, 69  {221} 

    successful, 168-9

    unbeatable, 23, 43

    uninvadable, 10, 11, 43, 46, 175, 177, 188

strategy set, 21

sunfish, bluegill, 90

swimming, adaptations for, 7

symmetric contest, 22-3;

    explanation of, 204

symmetric game, 68, 94, 162, 200

TFT see TIT FOR TAT

territorial behaviour:

    evolution of, 153-9;

    model of, 153

territory, 95:

    intruder into, 22;

    owner of, 22;

    value of, 154F, 155F

theorems:

    Bishop and Cannings, 15, 29, 107, 181, 182-3, 192, 196;

    Harley's, 57;

    Selten's 107, 108

theory of optimisation, 1

threat display, 151

TIT FOR TAT (TFT), 168, 169, 170, 171, 202, 203

tit, great, see Parus major

toad, see Bufo bufo

two-armed bandit game, 61-2, 66

two-strategy game, 40-3, 180-2, 193

Uca pugilator, 115

Vavilov's law of homologous variation, 7

variable rewards model, 38

Volterra's equations, 9

wage bargaining case, 152-3, 162

war of attrition, 21, 28-39:

    asymmetric, 33, 105, 107,

    (with individual ego) 104;

    distribution of acceptable duration, 35F;

    duration of contest, 35;

    model of, 34, 105;

    modification of, 141;

    symmetric, 32, 103;

    with random rewards 194-6

wasp, digger, see Sphex ichneumonens

Weismann's concept, 6

wings:

    rectangular, 7;

triangular, 7

wood pidgeon, hierarchy in, 146

Xiphophorus maculatus, 87

zygote, 47, 48, 123:

    survival in, 51

Author index

Abegglen, J.-J., 98

Albon, S.D., 110, 111, 114

Alcock, J., 72, 73

Andersson, M., 148, 149, 151

Angst, W., 97

Axelrod, R., 167, 168, 169, 170, 171, 174, 178, 202

Bachmann, C, 98

Baker, M. C, 84

Baker, R. R., 47, 48, 99

Baldwin, B. A., 54, 56

Balph, D. F., 85, 86

Balph, M. H., 85, 86

Barnard, C. J., 85

Bateman, A. J., 129

Bertram, B.C. R., 130

Birky, C. W., 48

Bishop, D. T., 15, 30, 34, 182, 196

Borkoski, V., 87

Bossert, W. H., 148

Brockmann, H. J., 6, 38, 56, 74, 75

Bruning, D. F., 129

Buckman, S. L., 72, 73

Bull, J. J., 82

Burgess, J. W., 96

Bush, R. R., 62

Cade, W., 89

Cannings, C, 15, 30, 34, 182, 196

Carlisle, T. R., 128

Caryl, P. G., 149, 189

Cavalli-Sforza, L. L., 54, 172, 191

Charlesworth, B., 140, 179

Charnov, E L., 2, 40, 70, 82, 89, 177

Clarke, B., 126

Clutton-Brock, T. H., 9, 110, 111, 114

Collias, N. E., 110

Cosmides, L. M., 48, 123

Daniel, R, 78

Davies, N. B., 98, 99, 112, 113

Dawkins, R., 6, 38, 54, 56, 74, 75, 80, 128, 130, 131, 200

Dingle, H., 148

Dobzhansky, Th., 132

Dominey, W., 89 Dow, M., 148, 149, 150

Dunham, D. W., 148, 149

Eaves, L. J., 189, 191

Eberhard, W.G., 70, 71, 123

Edwards, D. A., 48, 49

Eigen, M., 178, 183

Eshel, L, 40, 179, 185, 186, 187

Ewald, P. W., 82, 83, 84, 85

Ewing, A, W., 149, 150

Feldman, M. W., 54, 172, 191

Fischer, E. A., 159, 160

Fisher, R. A., 2, 23, 43, 81, 131, 132, 167, 174, 187

Fretwell, S. D., 23, 63, 90, 91, 174

Frith, H. J., 129

Gadgil, M., 86, 174

Gale, J. S., 189, 191

Geist, V., 110, 191

Gerhardt, H.C., 78

Geyl, P., 9

Ghiselin, M. T., 70

Gibson, R M., 110

Gotshall, D W., 70

Gotz, W., 97

Gould, S. J., 5, 7

Grafen, A., 6, 56, 74, 126, 137, 186, 187, 191, 193

Gross, M. R., 89, 90

Guinness, F. E., 110

Haigh, J., 141, 180

Haldane, J. B. S., 126, 167

Halliday, T. M., 112, 113

Hamilton, W. D., 2, 23, 27, 43, 87, 90, 92, 93, 139, 167, 169, 170, 174, 191

Hammerstein, P., 24, 37, 104, 114, 175

Hare, H., 123, 137

Harley, C. B., 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 176  {223} 

Harvey, P. H., 9

Hazlett, B., 148, 161

Heller, R., 64

Heyman, G. M., 66

Hines, W. G. S., 193

Hirshleif er, J., 161

Hogan-Warburg, A. J., 88, 89

Hrdy, S. B., 130

Hyatt, G. W., 115

Isaacson, A. J., 146

Jakobsson, S., 149, 150

Jarvi, T., 149, 150

Jones, A. R., 115

Jones, C. E., 72, 73

Jones, J. W., 69

Jonker, L. B., 183, 185

Kacelnik, A., 62

Kallman, K. D., 87

Kalmus, H., 97

Kirkpatrick, M., 134

Kluijver, H. N., 91

Krebs, J. R., 62

Kummer, H., 97, 98, 99

Lack, D., 129

Lande, R., 132, 133, 134, 135, 136

Lawlor, L. R., 2

Leigh, E. G, 70

Lewontin, R C, 2, 5, 7

Lloyd, D. G., 41

Lucas, H.L., 63, 90, 174

Luce, R. D., 2

Lumsden, C J., 54, 172

MacArthur, R. H., 46, 174

McFarland, D. J., 67, 176

May, R. M., 2, 23, 92, 93

Maynard Smith, J., 2, 4, 7, 10, 14, 21, 30, 47, 48, 81, 95, 103, 104, 109, 126, 129, 188, 189, 190, 191, 193, 196, 198

Meese, G. B, 54, 56

Michener, C. D, 167

Milinsky, M., 63, 64, 92

Mirmirani, M., 2, 27, 140, 141, 177

Mohler, J. D., 23, 174

Morgenstern, O., 1

Morton, E. S., 110

Murton, R. K., 146

Norman, R. F., 33

Orlove, M. J., 191

Oster, G., 2, 27, 140, 141, 177

Packer, C, 100, 110, 123, 129, 170, 171

Parker, G. A., 30, 31, 32, 33, 36, 47, 48, 49, 91, 95, 96, 104, 109, 121, 123, 129, 130, 131, 141, 174

Perill, S. A., 78

Price, G. R., 2, 10, 14, 188, 189, 190, 191

Radesater, T., 149, 150

Raiffa, H., 2

Rand, A. S., 149

Rand, W. M., 149

Rapoport, A., 2, 168

Raup, D. M., 7

Ridley, M., 128, 129

Riechert, S. E., 77, 115, 116, 119, 149, 151, 177

Riley, J. G., 20

Roberts, W. A., 62

Robertson, R. J., 33

Robinson, J. G., 70

Rohwer, F. C, 82, 83

Rohwer, S., 68, 82, 83, 84, 85, 166

Romesburg, D. F., 85

Rose, M. R., 141

Rubinstein, D. L., 104

Rudder, B., 9

Salmon, M., 115

Schreibman, M.P., 87

Schuster, P., 178, 183, 200

Scudo, F. M., 81

Selander, R.K., 9

Selten, R., 107, 108, 152

Shaw, R. F., 23, 174

Sibly, R. M., 85, 126

Sigmund, K., 200

Sigurjonsdottir, H., 121

Simpson, M. J. A., 148, 149, 150

Slatkin, M., 21, 170

Slobodkin, L. B., 2

Smith, V. G. F., 47, 48

Sondhi, K. C., 4

S^urway, H., 7

Stearns, S. C., 140

Stokes, A. W., 148, 149

Sutherland, L, 149, 150

Taylor, P., 62

Taylor, P. D., 33, 183, 185

Thompson, E. A., 30, 32, 33

Tooby, J., 48, 123  {224} 

Trivers, R. L., 93, 123, 128, 129, 137, 164, 167, 170, 174

Van Rhijn, J. G., 88, 89

Vehrencamp, S. L., 129, 137, 138

Von Neumann, J., 1

Warner, R. R., 70

Weise, L., 48, 49

Weise, W., 48, 49

West-Eberhard, M. J., 167

Westwood, N. J., 146

Wilson, D. S., 170

Wilson, E. O., 54, 171, 172

Wilson, T. R., 62

Witham, T. G., 92

Zahavi, A., 148

Zeeman, E. C., 183, 185, 188, 190