Evolutionary Ecology

, Volume 11, Issue 4, pp 485–501

On evolution under asymmetric competition

  • Richard Law
  • Paul Marrow
  • Ulf Dieckmann
Article

Abstract

The evolutionary consequences of asymmetric competition between species are poorly understood in comparison with symmetric competition. A model for evolution of body size under asymmetric competition within and between species is described. The model links processes operating at the scale of the individual to that of macroscopic evolution through a stochastic mutation–selection process. Phase portraits of evolution in a phenotype space characteristically show character convergence and parallel character shifts, with character divergence being relatively uncommon. The asymptotic states of evolution depend very much on the properties of asymmetric competition. Given relatively weak asymmetries between species, a single equilibrium point exists; this is a local attractor, and its position is determined by the intra- and interspecific asymmetries. When the asymmetries are made stronger, several fixed points may come about, creating further equilibrium points which are local attractors. It is also possible for periodic attractors to occur; such attractors comprise Red Queen dynamics with phenotype values that continue to change without ever settling down to constant values. From certain initial conditions, evolution leading to extinction of one of the species is also a likely outcome.

adaptive dynamics asymmetric competition co-evolution competition evolutionarily stable strategy frequency-dependent selection Red Queen dynamics Stochastic process 

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References

  1. Abrams, P.A. (1987) Alternative models of character displacement and niche shift. 2. Displacement when there is competition for a single resource. Am. Nat. 130, 271–282.CrossRefGoogle Scholar
  2. Abrams, P.A. and Matsuda, H. (1994) The evolution of traits that determine ability in competitive contests. Evol. Ecol. 8, 667–686.Google Scholar
  3. Abrams, P.A., Matsuda, H. and Harada, Y. (1993a) Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits. Evol. Ecol. 7, 465–487.Google Scholar
  4. Abrams, P.A., Harada, Y. and Matsuda, H. (1993b) On the relationship between quantitative genetic and ESS models. Evolution 47, 877–887.Google Scholar
  5. Brown, J.S. and Pavlovic, N.B. (1992) Evolution in heterogeneous environments: Effects of migration on habitat specialization. Evol. Ecol. 6, 260–382.Google Scholar
  6. Brown, J.S. and Vincent, T.L. (1987) Coevolution as an evolutionary game. Evolution 41, 66–79.Google Scholar
  7. Brown, J.S. and Vincent, T.L. (1992) Organization of predator-prey communities as an evolutionary game. Evolution 46, 1269–1283.Google Scholar
  8. Case, T.J. and Bolger, D.T. (1991) The role of interspecific competition in the biogeography of island lizards. Trends Ecol. Evol. 6, 135–139.CrossRefGoogle Scholar
  9. Christiansen, F.B. (1991) On the conditions for evolutionary stability for a continuously varying character. Am. Nat. 138, 37–50.CrossRefGoogle Scholar
  10. Clutton-Brock, T.H., Albon, S.D., Gibson, R.M. and Guinness, F.E. (1979) The logical stag: Aspects of fighting in red deer (Cervus elaphus L.). Anim. Behav. 27, 211–275.CrossRefGoogle Scholar
  11. Connell, J.H. (1980) Diversity and the coevolution of competitors, or the ghost of competition past. Oikos 53, 131–138.Google Scholar
  12. Connell, J.H. (1983) On the prevalence and relative importance of interspecific competition: Evidence from field experiments. Am. Nat. 122, 661–696.CrossRefGoogle Scholar
  13. Davies, N.B. (1978) Territorial defence in the speckled wood butterfly (Pararge aegeria): The resident always wins. Anim. Behav. 26, 138–147.CrossRefGoogle Scholar
  14. Dieckmann, U. (1994) Coevolutionary Dynamics of Stochastic Replicator Systems. Berichte des Forschungszentrums Jülich (Jül-3018), Jülich, Germany.Google Scholar
  15. Dieckmann, U. and Law, R. (1996) The dynamical theory of coevolution: A derivation from stochastic ecological processes. J. Math. Biol. 34, 579–612.CrossRefPubMedGoogle Scholar
  16. Dieckmann, U., Marrow, P. and Law, R. (1995) Evolutionary cycling in predator-prey interactions: Population dynamics and the Red Queen. J. Theor. Biol. 176, 91–102.CrossRefPubMedGoogle Scholar
  17. Englund, C., Johansson, F. and Olsson, T.I. (1992) Asymmetric competition between different taxa: Poecilid fishes and water striders. Oecologia 92, 498–502.CrossRefGoogle Scholar
  18. Fisher, R.A. (1958) The Genetical Theory of Natural Selection, 2nd edn. Dover Publications, New York.Google Scholar
  19. Geritz, S.A.H., Kisdi, É., Meszéna, G. and Metz, J.A.J. (in press) Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol. Ecol. Google Scholar
  20. Goel, N.S. and Richter-Dyn, N. (1974) Stochastic Models in Biology. Academic Press, New York.Google Scholar
  21. Goldberg, D.E. (1987) Neighbourhood competition in an old-field plant community. Ecology 68, 1211–1223.Google Scholar
  22. Hofbauer, J. and Sigmund, K. (1990) Adaptive dynamics and evolutionary stability. Appl. Math. Lett. 3, 75–79.CrossRefGoogle Scholar
  23. Hutchinson, G.E. (1959) Homage to Santa Rosalia, or why are there so many kinds of animals. Am. Nat. 93, 145–159.CrossRefGoogle Scholar
  24. Iwasa, Y., Pomiankowski, A. and Nee, S. (1991) The evolution of costly mate preferences. II. The ‘handicap’ principle. Evolution 45, 1431–1442.Google Scholar
  25. Lande, R. (1982) A quantitative genetic theory of life history evolution. Ecology 63, 607–615.Google Scholar
  26. Lawton, J.H. and Hassell, M.P. (1981) Asymmetrical competition in insects. Nature 289, 793–795.Google Scholar
  27. Marrow, P., Law, R. and Cannings, C. (1992) The coevolution of predator-prey interactions: ESSs and Red Queen dynamics. Proc. R. Soc. Lond. B 250, 133–141.Google Scholar
  28. Marrow, P., Dieckmann, U. and Law, R. (1996) Evolutionary dynamics of predator-prey systems: An ecological perspective. J. Math. Biol. 34, 556–578.CrossRefPubMedGoogle Scholar
  29. Matsuda, H. and Abrams, P.A. (1994) Runaway selection to self-extinction under asymmetrical competition. Evolution 48, 1764–1772.Google Scholar
  30. Maynard Smith, J. (1982) Evolution and the Theory of Games. Cambridge University Press, Cambridge.Google Scholar
  31. Maynard Smith, J. and Brown, R.L. (1986) Competition and body size. Theor. Pop. Biol. 30, 166–179.CrossRefGoogle Scholar
  32. Metz, J.A.J., Nisbet, R.M. and Geritz, S.A.H. (1992) How should we define ‘fitness’ for general ecological scenarios? Trends Ecol. Evol. 7, 198–202.CrossRefGoogle Scholar
  33. Metz, J.A.J., Geritz, S. and Iwasa, Y. (1994) On the Classification of Evolutionarily Singular Strategies. University of Leiden Preprint, Leiden, The Netherlands.Google Scholar
  34. Morin, C. and Johnson, E.A. (1988) Experimental studies of asymmetric competition among anurans. Oikos 53, 398–407.Google Scholar
  35. Parker, G.A. (1983) Arms races in evolution — an ESS to the opponent-independent costs game. J. Theor. Biol. 101, 619–648.CrossRefGoogle Scholar
  36. Parker, G.A. (1985) Population consequences of evolutionarily stable strategies. In Behavioural Ecology: Ecological Consequences of Adaptive Behaviour (R.M. Sibly and R.H. Smith, eds), pp. 33–58. Blackwell Scientific, Oxford.Google Scholar
  37. Parker, G.A. and Maynard Smith, J. (1990) Optimality theory in evolutionary biology. Nature Lond. 348, 27–33.CrossRefGoogle Scholar
  38. Pease, C.M. (1984) On the evolutionary reversal of competitive dominance. Evolution 38, 1099–1115.Google Scholar
  39. Perfecto, I. (1994) Foraging behaviour as a determinant of asymmetric competitive interaction between two ant species in a tropical ecosystem. Oecologia 98, 184–192.CrossRefGoogle Scholar
  40. Pimentel, D. (1968) Population regulation and genetic feedback. Science 159, 1432–1437.Google Scholar
  41. Robinson, S.K. and Terborgh, J. (1995) Interspecific aggression and habitat selection by Amazonian birds. J. Anim. Ecol. 64, 1–11.Google Scholar
  42. Rosenzweig, M.L. and McCord, R.D. (1991) Incumbent replacement: Evidence for long-term evolutionary progress. Paleobiology 17, 202–213.Google Scholar
  43. Roughgarden, J. (1983a) The theory of coevolution. In Coevolution (D.J. Futuyma and M. Slatkin, eds), pp. 33–64. Sinauer Associates, Sunderland, MA.Google Scholar
  44. Roughgarden, J. (1983b) Coevolution between competitors. In Coevolution (D.J. Futuyma and M. Slatkin, eds), pp. 383–403. Sinauer Associates, Sunderland, MA.Google Scholar
  45. Roughgarden, J.D. and Pacala, S.W. (1989) Taxon cycle among Anolis lizard populations: Review of the evidence. In Speciation and Its Consequences (D. Otte and J.A. Endler, eds), pp. 403–432. Sinauer Associates, Sunderland, MA.Google Scholar
  46. Rummell, J.D. and Roughgarden, J. (1983) Some differences between invasion-structured and coevolution-structured competitive communities: A preliminary theoretical analysis. Oikos 41, 477–486.Google Scholar
  47. Rummell, J.D. and Roughgarden, J. (1985) A theory of faunal buildup for competition communities. Evolution 39, 1009–1033.Google Scholar
  48. Schoener, T.W. (1983) Field experiments on interspecific competition. Am. Nat. 122, 240–285.CrossRefGoogle Scholar
  49. Schwinning, S. and Fox, G.A. (1995) Population dynamic consequences of competitive symmetry in annual plants. Oikos 72, 422–432.Google Scholar
  50. Slatkin, M. (1980) Ecological character displacement. Ecology 61, 163–177.Google Scholar
  51. Takada, T. and Kigami, J. (1991) The dynamical attainability of ESS in evolutionary games. J. Math. Biol. 29, 513–529.CrossRefPubMedGoogle Scholar
  52. Taper, M.L. and Case, T.J. (1985) Quantitative genetic models for the coevolution of character displacement. Ecology 66, 355–371.Google Scholar
  53. Taper, M.L. and Case, T.J. (1992a) Models of character displacement and the theoretical robustness of taxon cycles. Evolution 46, 317–333.Google Scholar
  54. Taper, M.L. and Case, T.J. (1992b) Coevolution among competitors. In Oxford Surveys in Evolutionary Biology, Vol. 8 (D.J. Futuyma and J. Antonovics, eds). pp. 63–109. Oxford University Press, Oxford.Google Scholar
  55. Taylor, P.D. (1989) Evolutionary stability in one parameter models under weak selection. Theor. Pop. Biol. 36, 125–143.CrossRefGoogle Scholar
  56. Thompson, P. and Fox, B.J. (1993) Asymmetric competition in Australian heathland rodents: A reciprocal removal experiment demonstrating the influence of size-class structure. Oikos 67, 264–278.Google Scholar
  57. van Kampen, N.G. (1992) Stochastic Processes in Physics and Chemistry. North-Holland, Amsterdam.Google Scholar
  58. Van Valen, L. (1973) A new evolutionary law. Evol. Theory 1, 1–30.Google Scholar
  59. Vincent, T.L. and Brown, J.S. (1988) The evolution of ESS theory. Ann. Rev. Ecol. Syst. 19, 423–443.CrossRefGoogle Scholar
  60. Weiner, J. (1990) Asymmetric competition in plant populations. Trends Ecol. Evol. 5, 360–364.CrossRefGoogle Scholar

Copyright information

© Chapman and Hall 1997

Authors and Affiliations

  • Richard Law
    • 1
  • Paul Marrow
    • 2
  • Ulf Dieckmann
    • 2
  1. 1.Department of BiologyUniversity of YorkYorkUK
  2. 2.Institute of Evolutionary and Ecological SciencesUniversity of LeidenLeidenThe Netherlands

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