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Are the better cooperators dormant or quiescent?

  • Sellinger, Thibaut1
  • Müller, Johannes2
  • Hösel, Volker3
  • Tellier, Aurélien1
  • 1 Section of Population Genetics, Center of Life and Food Sciences Weihenstephan, Technische Universität München, Freising 85354, Germany. , (Germany)
  • 2 Center for Mathematics, Technische Universität München, Garching 85748, Germany; Institute for Computational Biology, Helmholtz Center Munich, Neuherberg 85764, Germany. Electronic address: [email protected] , (Germany)
  • 3 Center for Mathematics, Technische Universität München, Garching 85748, Germany. , (Germany)
Published Article
Mathematical biosciences
Publication Date
Oct 21, 2019
DOI: 10.1016/j.mbs.2019.108272
PMID: 31647933


Despite the wealth of empirical and theoretical studies, the origin and maintenance of cooperation is still an evolutionary riddle. In this context, ecological life-history traits which affect the efficiency of selection may play a role despite being often ignored. We consider here species such as bacteria, fungi, invertebrates and plants which exhibit resting stages in the form of a quiescent state or a seed bank. When quiescent, individuals are inactive and reproduce upon activation, while under seed bank parents produce offspring remaining dormant for different amount of time. We assume weak frequency-dependent selection modeled using game-theory and the prisoner's dilemma (cooperation/defect) as payoff matrix. The cooperators and defectors are allowed to evolve different quiescence or dormancy times. By means of singular perturbation theory we reduce the model to a one-dimensional equation resembling the well known replicator equation, in which the gain functions are scaled with lumped parameters reflecting the time scale of the resting state of the cooperators and defectors. If both time scales are identical cooperation cannot persist in a homogeneous population. If, however, the time scale of the cooperator is distinctively different from that of the defector, cooperation may become a locally asymptotically stable strategy. Interestingly enough, in the seed bank case the cooperator needs to become active faster than the defector, while in the quiescent case the cooperator has to be slower. We use adaptive dynamics to identify situations where cooperation may evolve and form a convergent stable ESS. We conclude by highlighting the relevance of these results for many non-model species and the maintenance of cooperation in microbial, invertebrate or plant populations. Copyright © 2019. Published by Elsevier Inc.

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