title: Host-parasite coevolution in populations of constant and variable size.
abstract: BACKGROUND
  The matching-allele and gene-for-gene models are widely used in mathematical approaches that study the dynamics of host-parasite interactions. Agrawal and Lively (Evolutionary Ecology Research 4:79-90, 2002) captured these two models in a single framework and numerically explored the associated time discrete dynamics of allele frequencies.
  
  
  RESULTS
  Here, we present a detailed analytical investigation of this unifying framework in continuous time and provide a generalization. We extend the model to take into account changing population sizes, which result from the antagonistic nature of the interaction and follow the Lotka-Volterra equations. Under this extension, the population dynamics become most complex as the model moves away from pure matching-allele and becomes more gene-for-gene-like. While the population densities oscillate with a single oscillation frequency in the pure matching-allele model, a second oscillation frequency arises under gene-for-gene-like conditions. These observations hold for general interaction parameters and allow to infer generic patterns of the dynamics.
  
  
  CONCLUSIONS
  Our results suggest that experimentally inferred dynamical patterns of host-parasite coevolution should typically be much more complex than the popular illustrations of Red Queen dynamics. A single parasite that infects more than one host can substantially alter the cyclic dynamics.
authors.affiliation: Max Planck Institute for Evolutionary Biology, August-Thienemann-Str. 2, Plön, 24306, Germany. song@evolbio.mpg.de.
authors.forename: Yixian
authors.initials: Y
authors.lastname: Song
authors.affiliation: New Zealand Institute for Advanced Study, Massey University, Auckland, New Zealand. C.Gokhale@massey.ac.nz.
authors.forename: Chaitanya S
authors.initials: CS
authors.lastname: Gokhale
authors.affiliation: Department of Evolutionary Ecology and Genetics, University of Kiel, Kiel, Germany. apapkou@zoologie.uni-kiel.de.
authors.forename: Andrei
authors.initials: A
authors.lastname: Papkou
authors.affiliation: Department of Evolutionary Ecology and Genetics, University of Kiel, Kiel, Germany. hschulenburg@zoologie.uni-kiel.de.
authors.forename: Hinrich
authors.initials: H
authors.lastname: Schulenburg
authors.affiliation: Max Planck Institute for Evolutionary Biology, August-Thienemann-Str. 2, Plön, 24306, Germany. traulsen@evolbio.mpg.de.
authors.forename: Arne
authors.initials: A
authors.lastname: Traulsen
mesh_terms: D000818:Animals; D005075:Biological Evolution; D005787:Gene Frequency; D056084:Genetic Fitness; D006790:Host-Parasite Interactions; D008957:Models, Genetic; D010271:Parasites / Q000235:genetics*; D011156:Population Density; D011157:Population Dynamics