• arms race;
  • bistability;
  • coevolution;
  • coevolutionarily stable state;
  • individual selection;
  • trait dynamics

Abstract We consider a mathematical model for the coevolution of a plant's defense against herbivores and the herbivore's ability to exploit the plant. The result of coevolution is predicted using the phase portrait of trait value dynamics and contour plots of fitnesses. The following results are derived: (1) The fitnesses of both plant and herbivore are higher at an “armless” state in which both plant and herbivore invest a minimum amount of energy and/or resources in defense and feeding respectively, than at the coevolutionarily stable state (CSS); (2) Perpetual increase in the trait values of both species may occur when the marginal costs of defense and feeding abilities decrease as these abilities increase; (3) If the marginal costs of defense and feeding abilities increase as the abilities increase, there is a coevolutionary equilibrium with finite trait values; (4) There may be more than one coevolutionarily stable state (CSS).