Browsing by Subject "Fold bifurcation of periodic orbits"

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  • Lehtinen, Sami O.; Geritz, Stefan A.H. (2019)
    We investigate the coevolution of cannibalistic predators and timid prey, which seek refuge upon detecting a predator. To understand how the species affect each other’s evolution, we derived the ecological model from individual-level processes using ordinary differential equations. The ecological dynamics exhibit bistability between equilibrium and periodic attractors, which may disappear through catastrophic bifurcations. Using the critical function analysis of adaptive dynamics, we classify general trade-offs between cannibalism and prey capture that produce different evolutionary outcomes. The evolutionary analysis reveals several ways in which cannibalism emerges as a response to timidity of the prey. The long-term coevolution either attains a singularity, or becomes cyclic through two mechanisms: genetical cycles through Hopf bifurcation of the singularity, or ecogenetical cycles involving abrupt switching between ecological attractors. Further diversification of cannibalism occurs through evolutionary branching, which is predicted to be delayed when simultaneous prey evolution is necessary for the singularity’s attainability. We conclude that predator-prey coevolution produces a variety of outcomes, in which evolutionary cycles are commonplace.
  • Lehtinen, Sami O.; Geritz, Stefanus A.H. (2019)
    We investigate the evolution of timidity in a prey species whose predator has cannibalistic tendencies. The ecological model is derived from individual-level processes, in which the prey seeks refuge after detecting a predator, and the predator cannibalises on the conspecific juveniles. Bifurcation analysis of the model reveals ecological bistability between equilibrium and periodic attractors. Using the framework of adaptive dynamics, we classify ten qualitatively different evolutionary scenarios induced by the ecological bistability. These scenarios include ecological attractor switching through catastrophic bifurcations, which can reverse the direction of evolution. We show that such reversals often result in evolutionary cycling of the level of timidity. In the absence of cannibalism, the model never exhibits ecological bistability nor evolutionary cycling. We conclude that cannibalistic predator behaviour can completely change both the ecological dynamics and the evolution of prey. (C) 2019 The Authors. Published by Elsevier Ltd.