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Data-Based Analysis of Winner-Loser Models of Hierarchy Formation in Animals

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Abstract

We review winner-loser models, the currently popular explanation for the occurrence of linear dominance hierarchies, via a three-part approach. (1) We isolate the two most significant components of the mathematical formulation of three of the most widely-cited models and rigorously evaluate the components’ predictions against data collected on hierarchy formation in groups of hens. (2) We evaluate the experimental support in the literature for the basic assumptions contained in winner-loser models. (3) We apply new techniques to the hen data to uncover several behavioral dynamics of hierarchy formation not previously described. The mathematical formulations of these models do not show satisfactory agreement with the hen data, and key model assumptions have either little or no conclusive support from experimental findings in the literature. In agreement with the latest experimental results concerning social cognition, the new behavioral dynamics of hierarchy formation discovered in the hen data suggest that members of groups are intensely aware both of their own interactions as well as interactions occurring among other members of their group. We suggest that more adequate models of hierarchy formation should be based upon behavioral dynamics that reflect more sophisticated levels of social cognition.

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References

  • Addison, W.E., Simmel, E.C., 1970. The relationship between dominance and leadership in a flock of ewes. Bull. Psychon. Soc. 15, 303–05.

    Google Scholar 

  • Bakker, T.C.M., Sevenster, P., 1983. Determinants of dominance in male sticklebacks (Gasterosteus aculeatus L). Behaviour 86, 55–1.

    Article  Google Scholar 

  • Bakker, T.C.M., Feuthdebruijn, E., Sevenster, P., 1989. Asymmetrical effects of prior winning and losing on dominance in sticklebacks (Gasterosteus aculeatus). Ethology 82, 224–29.

    Google Scholar 

  • Barkan, C.P.L., Craig, J.L., Strahl, S.D., Stewart, A.M., Brown, J.L., 1986. Social-dominance in communal Mexican Jays Aphelocoma ultramarina. Anim. Behav. 34, 175–87.

    Article  Google Scholar 

  • Beacham, J.L., 1988. The relative importance of body size and aggressive experience as determinants of dominance in pumpkinseed sunfish Lepomis gibbosus. Anim. Behav. 36, 621–23.

    Article  Google Scholar 

  • Beacham, J.L., 2003. Models of dominance hierarchy formation: Effects of prior experience and intrinsic traits. Behaviour 140, 1275–303.

    Article  Google Scholar 

  • Beacham, J.L., Newman, J.A., 1987. Social experience and the formation of dominance relationships in the pumpkinseed sunfish, Lepomis gibbosus. Anim. Behav. 35, 1560–563.

    Article  Google Scholar 

  • Beaugrand, J.P., Cotnoir, P.A., 1996. The role of individual differences in the formation of triadic dominance orders of male green swordtail fish (Xiphophorus helleri). Behav. Process. 38, 287–96.

    Article  Google Scholar 

  • Beecher, M.D., Campbell, S.E., 2005. The role of unshared songs in singing interactions between neighbouring song sparrows. Anim. Behav. 70, 1297–304.

    Article  Google Scholar 

  • Bonabeau, E., Theraulaz, G., Deneubourg, J.-L., 1996. Mathematical model of self-organizing hierarchies in animal societies. Bull. Math. Biol. 58, 661–17.

    Article  MATH  Google Scholar 

  • Bonabeau, E., Theraulaz, G., Deneubourg, J.-L., 1999. Dominance orders in animal societies: the self-organization hypothesis revisited. Bull. Math. Biol. 61, 727–57.

    Article  Google Scholar 

  • Bond, A.B., Kamil, A.C., Balda, R.P., 2003. Social complexity and transitive inference in corvids. Anim. Behav. 65, 479–87.

    Article  Google Scholar 

  • Broom, M., Cannings, C., 2002. Modelling dominance hierarchy formation as a multi-player game. J. Theor. Biol. 219, 397–13.

    Article  MathSciNet  Google Scholar 

  • Brown, J.A., Colgan, P.W., 1986. Individual and species recognition in centrarchid fishes: evidence and hypotheses. Behav. Ecol. Sociobiol. 19, 373–79.

    Article  Google Scholar 

  • Burke, T.E., 1979. An Analysis of Social Behaviour in Crickets. University of Oxford, Oxford.

    Google Scholar 

  • Chase, I.D., 1974. Models of hierarchy formation in animal societies. Behav. Sci. 19, 374–82.

    Article  Google Scholar 

  • Chase, I.D., 1982. Behavioral sequences during dominance hierarchy formation in chickens. Science 216, 439–40.

    Article  Google Scholar 

  • Chase, I.D., 1985. The sequential analysis of aggressive acts during hierarchy formation—an application of the jigsaw puzzle approach. Anim. Behav. 33, 86–00.

    Article  Google Scholar 

  • Chase, I.D., 2006. Music notation: a new method for visualizing social interaction in animals and humans. Front. Zool. 3, 18.

    Article  Google Scholar 

  • Chase, I.D., Rohwer, S., 1987. Two methods for quantifying the development of dominance hierarchies in large groups with applications to Harris’ sparrows. Anim. Behav. 35, 1113–128.

    Article  Google Scholar 

  • Chase, I.D., Bartolomeo, C., Dugatkin, L.A., 1994. Aggressive interactions and inter-contest interval: how long do winners keep winning. Anim. Behav. 48, 393–00.

    Article  Google Scholar 

  • Chase, I.D., Tovey, C., Spangler-Martin, D., Manfredonia, M., 2002. Individual differences versus social dynamics in the formation of animal dominance hierarchies. Proc. Natl. Acad. Sci. U.S.A. 99, 5744–749.

    Article  Google Scholar 

  • Chase, I.D., Tovey, C., Murch, P., 2003. Two’s company, three’s a crowd: differences in dominance relationships in isolated versus socially embedded pairs of fish. Behaviour 140, 1193–217.

    Article  Google Scholar 

  • Cheney, D.L., Seyfarth, R.M., 1990. How Monkeys See the World: Inside the Mind of Another Species. University of Chicago Press, Chicago.

    Google Scholar 

  • Cheney, D.L., Seyfarth, R.M., 2007. Baboon Metaphysics: The Evolution of a Social Mind. University of Chicago Press, Chicago.

    Google Scholar 

  • Cloutier, S., Beaugrand, J.P., Lague, P.C., 1996. The role of individual differences and patterns of resolution in the formation of dominance orders in domestic hen triads. Behav. Process. 38, 227–39.

    Article  Google Scholar 

  • Clutton-Brock, T.H., Albon, S.D., Guinness, F.E., 1984. Maternal dominance, breeding success and birth sex-ratios in red deer. Nature 308, 358–60.

    Article  Google Scholar 

  • D’Eath, R.B., Keeling, L.J., 2003. Social discrimination and aggression by laying hens in large groups: from peck orders to social tolerance. Appl. Anim. Behav. Sci. 84, 197–12.

    Article  Google Scholar 

  • D’Ettorre, P., Heinze, J., 2005. Individual recognition in ant queens. Curr. Biol. 15, 2170–174.

    Article  Google Scholar 

  • Davis, H., 1992. Transitive inference in rats (Rattus norvegicus). J. Comp. Psychol. 106, 342–49.

    Article  Google Scholar 

  • Doreian, P., 2006. Actor network utilities and network evolution. Soc. Netw. 28, 137–64.

    Article  Google Scholar 

  • Drews, C., 1993. The concept and definition of dominance in animal behavior. Behaviour 125, 283–13.

    Article  Google Scholar 

  • Drummond, H., 2006. Dominance in vertebrate broods and litters. Q. Rev. Biol. 81, 3–2.

    Article  Google Scholar 

  • Drummond, H., Canales, C., 1998. Dominance between booby nestlings involves winner and loser effects. Anim. Behav. 55, 1669–676.

    Article  Google Scholar 

  • Drummond, H., Osorno, J.L., 1992. Training siblings to be submissive losers: dominance between booby nestlings. Anim. Behav. 44, 881–93.

    Article  Google Scholar 

  • Dugatkin, L.A., 1997. Winner and loser effects and the structure of dominance hierarchies. Behav. Ecol. 8, 583–87.

    Article  Google Scholar 

  • Dugatkin, L.A., 2001. Bystander effects and the structure of dominance hierarchies. Behav. Ecol. 12, 348–52.

    Article  Google Scholar 

  • Dugatkin, L.A., Earley, R.L., 2003. Group fusion: the impact of winner, loser, and bystander effects on hierarchy formation in large groups. Behav. Ecol. 14, 367–73.

    Article  Google Scholar 

  • Dugatkin, L.A., Earley, R.L., 2004. Individual recognition, dominance hierarchies and winner and loser effects. Proc. R. Soc. Lond. Ser. B Biol. Sci. 271, 1537–540.

    Article  Google Scholar 

  • Earley, R.L., Dugatkin, L.A., 2002. Eavesdropping on visual cues in green swordtail (Xiphophorus helleri) fights: a case for networking. Proc. R. Soc. Lond. Ser. B Biol. Sci. 269, 943–52.

    Article  Google Scholar 

  • Ellis, L., 1995. Dominance and reproductive success among nonhuman animals: a cross-species comparison. Ethol. Sociobiol. 16, 257–33.

    Article  Google Scholar 

  • Francis, R.C., 1983. Experiential effects of agonistic behavior in the paradise fish, Macropodus opercularis. Behaviour 85, 292–13.

    Article  Google Scholar 

  • Francis, R.C., 1987. The interaction of genotype and experience in the dominance success of paradise fish (Macropodus opercularis). Biol. Behav. 12, 1–1.

    MathSciNet  Google Scholar 

  • Frey, D.F., Miller, R.J., 1972. The establishment of dominance relationships in blue gourami, Trichogaster trichopterus (Pallas). Behaviour 42, 8–2.

    Article  Google Scholar 

  • Gherardi, F., Atema, J., 2005. Memory of social partners in hermit crab dominance. Ethology 111, 271–85.

    Article  Google Scholar 

  • Gillian, D.J., 1981. Reasoning in the chimpanzee: II. Transitive inference. J. Exp. Psychol. Anim. Behav. Process. 7, 87–08.

    Article  Google Scholar 

  • Goessmann, C., Hemelrijk, C., Huber, R., 2000. The formation and maintenance of crayfish hierarchies: behavioral and self-structuring properties. Behav. Ecol. Sociobiol. 48, 418–28.

    Article  Google Scholar 

  • Grosenick, L., Clement, T.S., Fernald, R.D., 2007. Fish can infer social rank by observation alone. Nature 445, 429–32.

    Article  Google Scholar 

  • Hausfater, G., Altmann, J., Altmann, S., 1982. Long-term consistency of dominance relations among female baboons (Papio cynocephalus). Science 217, 752–55.

    Article  Google Scholar 

  • Heinze, J., 1990. Dominance behavior among ant females. Naturwissenschaften 77, 41–3.

    Article  Google Scholar 

  • Hemelrijk, C.K., 1999. An individual orientated model of the emergence of despotic and egalitarian societies. Proc. R. Soc. Lond. Ser. B: Biol. Sci. 266, 361–69.

    Article  Google Scholar 

  • Hemelrijk, C.K., 2000. Towards the integration of social dominance and spatial structure. Anim. Behav. 59, 1035–048.

    Article  Google Scholar 

  • Hogue, M.E., Beaugrand, J.P., Lague, P.C., 1996. Coherent use of information by hens observing their former dominant defeating or being defeated by a stranger. Behav. Process. 38, 241–52.

    Article  Google Scholar 

  • Holekamp, K.E., Smale, L., 1993. Ontogeny of dominance in free-living spotted hyenas: juvenile rank relations with other immature individuals. Anim. Behav. 46, 451–66.

    Article  Google Scholar 

  • Hsu, Y.Y., Wolf, L.L., 1999. The winner and loser effect: integrating multiple experiences. Anim. Behav. 57, 903–10.

    Article  Google Scholar 

  • Jackson, W.M., 1988. Can individual differences in history of dominance explain the development of linear dominance hierarchies. Ethology 79, 71–7.

    Article  Google Scholar 

  • Jackson, W.M., Winnegrad, R.L., 1988. Linearity in dominance hierarchies: a second look at the individual attributes model. Anim. Behav. 36, 1237–240.

    Article  Google Scholar 

  • Johnstone, R.A., 2001. Eavesdropping and animal conflict. Proc. Nat. Acad. Sci. U.S.A. 98, 9177–180.

    Article  Google Scholar 

  • Karavanich, C., Atema, J., 1998. Individual recognition and memory in lobster dominance. Anim. Behav. 56, 1553–560.

    Article  Google Scholar 

  • Lai, W.-S., Ramiro, L.-L.R., Yu, H.A., Johnston, R.E., 2005. Recognition of familiar individuals in golden hamsters: a new method and functional neuroanatomy. J. Neurosci. 25, 11239–1247.

    Article  Google Scholar 

  • Landau, H.G., 1951. On dominance relations and structures of animal societies. Bull. Math. Biophys. 13, 1–9.

    Article  MathSciNet  Google Scholar 

  • Lazareva, O.F., 2004. Transitive responding in hooded crow requires linearly ordered stimuli. J. Exp. Anal. Behav. 82, 1–9.

    Article  Google Scholar 

  • Magnusson, D., Endler, N.S., 1977. Personality at the Crossroads, p. 464. Lawrence Erlbaum Associates, Hillsdale.

    Google Scholar 

  • McGregor, P.K., 2005. Animal Communication Networks, Cambridge University Press, Cambridge.

    Google Scholar 

  • McLeman, M.A., Mendl, M., Jones, R.B., White, R., Wathes, C.M., 2005. Discrimination of conspecifics by juvenile domestic pigs, Sus scrofa. Anim. Behav. 70, 451–61.

    Article  Google Scholar 

  • Mesterton-Gibbons, M., Sherratt, T.N., 2007. Social eavesdropping: A game-theoretic analysis. Bull. Math. Biol. 69, 1255–276.

    Article  MATH  MathSciNet  Google Scholar 

  • Nakamaru, M., Sasaki, A., 2003. Can transitive inference evolve in animals playing the hawk-dove game? J. Theor. Biol. 222, 461–70.

    MathSciNet  Google Scholar 

  • Nelissen, M.H.J., 1985. Structure of the dominance hierarchy and dominance determining group factors in Melanochromic auratus (Pices, Cichlidae). Behaviour 94, 85–07.

    Article  Google Scholar 

  • Oliveira, R.F., McGregor, P.K., Latruffe, C., 1998. Know thine enemy: fighting fish gather information from observing conspecific interactions. Proc. R. Soc. Lond. Ser. B Biol. Sci. 265, 1045–049.

    Article  Google Scholar 

  • Oliveira, R.F., Lopes, M., Carneiro, L.A., Canario, A.V.M., 2001. Watching fights raises fish hormone levels—Cichlid fish wrestling for dominance induce an androgen surge in male spectators. Nature 409, 475–75.

    Article  Google Scholar 

  • Paz-y-Mino, G., Bond, A.B., Kamil, A.C., Balda, R.P., 2004. Pinyon jays use transitive inference to predict social dominance. Nature 430, 778–81.

    Article  Google Scholar 

  • Post, W., 1992. Dominance and mating success in male boat-tailed grackles. Anim. Behav. 44, 917–29.

    Article  Google Scholar 

  • Raleigh, M.J., McGuire, M.T., Brammer, G.L., Pollack, D.B., Yuwiler, A., 1991. Serotonergic mechanisms promote dominance acquisition in adult male Vervet monkeys. Brain Res. 559, 181–90.

    Article  Google Scholar 

  • Roberts, W.A., Phelps, M.T., 1994. Transitive inference in rats—a test of the spatial coding hypothesis. Psychol. Sci. 5, 368–74.

    Article  Google Scholar 

  • Sapolsky, R.M., Share, L.J., 1994. Rank-related differences in cardiovascular function among wild baboons: role of sensitivity to glucocorticoids. Am. J. Primatol. 32, 261–75.

    Article  Google Scholar 

  • Savin-Williams, R.C., 1980. Dominance hierarchies in groups of middle to late adolescent males. J. Youth Adolesc. 9, 75–5.

    Article  Google Scholar 

  • Seitz, K., 2003. The dominance hierarchy as a supraindividual trait: historical perspectives and future directions. Master’s thesis, Binghamton University.

  • Skiena, S., 1990. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Addison–Wesley, Reading.

    MATH  Google Scholar 

  • Skvoretz, J., Faust, K., Fararo, T.J., 1996. Social, structure, networks, and E-state structuralism models. J. Math. Soc. 21, 57–6.

    MATH  Google Scholar 

  • Slater, P.J.B., 1986. Individual-differences and dominance hierarchies. Anim. Behav. 34, 1264–265.

    Article  Google Scholar 

  • Steirn, J.N., Weaver, J.E., Zentall, T.R., 1995. Transitive inference in pigeons: Simplified procedures and a test of value transfer theory. Anim. Learn. Behav. 23, 76–2.

    Google Scholar 

  • Tibbetts, E.A., 2002. Visual signals of individual identity in the wasp Polistes fuscatus. Proc. R. Soc. Lond. Ser. B Biol. Sci. 269, 1423–428.

    Article  Google Scholar 

  • Todd, J.H., Attema, J., Bardach, J.E., 1967. Chemical communication in social behavior of a fish, the yellow bullhead (Ictalurus natalis). Science 158, 672–73.

    Article  Google Scholar 

  • Vannini, M., Sardini, A., 1971. Aggressivity and dominance in river crab Potomon fluviantile (Herbst). Monit. Zool. Ital. 5, 173–13.

    Google Scholar 

  • von Fersen, L., Wynne, C.D., Delius, J.D., Staddon, J.E., 1991. Transitive inference formation in pigeons. J. Exp. Psychol. Anim. Behav. Process. 17, 334–41.

    Article  Google Scholar 

  • Wilson, E.O., 1975. Sociobiology. Harvard University Press, Cambridge.

    Google Scholar 

  • Yurkovic, A., Wang, O., Basu, A.C., Kravitz, E.A., 2006. Learning and memory associated with aggression in Drosophila melanogaster. Proc. Natl. Acad. Sci. U.S.A. 103, 17519–27524.

    Article  Google Scholar 

  • Zucker, N., Murray, L., 1996. Determinants of dominance in the tree lizard Urosaurus ornatus: The relative importance of mass, previous experience and coloration. Ethology 102, 812–25.

    Article  Google Scholar 

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  1. Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY, 11794-3600, USA

    W. Brent Lindquist

  2. Department of Sociology and Graduate Program in Ecology and Evolution, Stony Brook University, Stony Brook, NY, 11794-4356, USA

    Ivan D. Chase

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  1. W. Brent Lindquist
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Lindquist, W.B., Chase, I.D. Data-Based Analysis of Winner-Loser Models of Hierarchy Formation in Animals. Bull. Math. Biol. 71, 556–584 (2009). https://doi.org/10.1007/s11538-008-9371-9

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