title: Evolution of pathogen virulence under selective predation: a construction method to find eco-evolutionary cycles.
abstract: We investigate eco-evolutionary cycles in the joint dynamics of pathogen virulence and predator population density when hosts carrying virulent infections are exposed to increased risk of predation. We introduce a new technique to find trade-off functions under which the model exhibits limit cycles; this technique provides a constructive proof that the system is able to generate limit cycles, and can be applied to other eco-evolutionary models as well. We also study a concrete example to confirm that eco-evolutionary cycles occur in a significant part of the parameter space and to briefly explore other evolutionary outcomes in the same model.
authors.affiliation: Department of Mathematics and Statistics, University of Helsinki, PO Box 68, FIN-00014, Finland. Electronic address: eva.kisdi@helsinki.fi.
authors.forename: Eva
authors.initials: E
authors.lastname: Kisdi
authors.forename: Stefan A H
authors.initials: SA
authors.lastname: Geritz
authors.forename: Barbara
authors.initials: B
authors.lastname: Boldin
mesh_terms: D000818:Animals; D005075:Biological Evolution; D003141:Communicable Diseases / Q000382:microbiology*; D017753:Ecosystem; D054884:Host-Pathogen Interactions / Q000502:physiology*; D008954:Models, Biological; D011156:Population Density; D011157:Population Dynamics; D011235:Predatory Behavior / Q000502:physiology*; D012641:Selection, Genetic / Q000502:physiology; D014774:Virulence / Q000502:physiology
keywords: Bogdanov–Takens bifurcation; Hopf bifurcation; Limit cycle; Trade-off; Virulence evolution