Evolutionary Ecology

, Volume 11, Issue 4, pp 485–501

On evolution under asymmetric competition

  • Richard Law
  • Paul Marrow
  • Ulf Dieckmann


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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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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