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. 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. 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.
%0 Journal Article
%1 Song.BMCEB.2015
%A Song, Yixian
%A Gokhale, Chaitanya S
%A Papkou, Andrei
%A Schulenburg, Hinrich
%A Traulsen, Arne
%D 2015
%J BMC Evolutionary Biology
%K imported tecoevo
%N 1
%P 212
%R 10.1186/s12862-015-0462-6
%T Host-parasite coevolution in populations of constant and variable size
%V 15
%X 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. 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. 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.
@article{Song.BMCEB.2015,
abstract = {{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. 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. 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.}},
added-at = {2023-08-03T15:19:07.000+0200},
author = {Song, Yixian and Gokhale, Chaitanya S and Papkou, Andrei and Schulenburg, Hinrich and Traulsen, Arne},
biburl = {https://www.bibsonomy.org/bibtex/204ba9c061f089727895369574cb27e42/gokhalecs},
doi = {10.1186/s12862-015-0462-6},
interhash = {833a7313e8585c0bd3b1bdc81e4ef06e},
intrahash = {04ba9c061f089727895369574cb27e42},
journal = {BMC Evolutionary Biology},
keywords = {imported tecoevo},
language = {English},
local-url = {file://localhost/Users/gokhale/Documents/Papers%20Library/Song_BMC%20Evolutionary%20Biology_2015_2.pdf},
number = 1,
pages = 212,
pmcid = {PMC4589230},
pmid = {26419522},
rating = {0},
timestamp = {2023-08-03T15:19:43.000+0200},
title = {{Host-parasite coevolution in populations of constant and variable size}},
volume = 15,
year = 2015
}