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Table 1 Literature overview

From: How long do Red Queen dynamics survive under genetic drift? A comparative analysis of evolutionary and eco-evolutionary models

Ref.Authors (year)focusdeterministic/ stochasticequations/ methodpopulation size
[31]Schaffer and Rosenzweig (1978)HP, CSSdeterministicODEconstrained4
[32]Seger (1988)HP, many genotypes, chaosdeterministicREconstant
[33]Nee (1989)HP, co-evolution, recombinationdeterministicREconstant
[34]Dybdahl and Lively (1998)time lag, experimentdeterministicREconstant
[35]Boots and Sasaki (1999)infection on latticebothODE, IBM, ADvariable
[36]Peters and Lively (1999)fluctuating epistasisdeterministicREconstant
[37]Sasaki (2000)multilocus GfGdeterministicODEconstant
[38]Agrawal and Lively (2001)HP, selfing vs outcrossingdeterministicREconstant
[39]Agrawal and Lively (2002)HP, GfG vs MAdeterministicREconstant
[40]Gandon (2002)HP, local adaptation (spatial)deterministicREconstant
[41]Gandon (2004)SI, multihost parasitesdeterministicODE, ADvariable
[20]Kouyos et al. (2007)HP, oscillations in stochastic modelboth7ODEconstant5
[42]Alizon and van Baalen (2008)multiple infections, within-host and SIdeterministicODE, ADvariable
[43]Agrawal (2009)HP, sex vs recombinationdeterministicREconstant
[44]Best et al. (2009)SI, transmission, susceptibilitydeterministicODE, ADconstant
[21]Engelstädter and Bonhoeffer (2009)HP, RQ oscillationsdeterministicREconstant
[45]Lively (2010)sex (long term persistence)both6REvariable
[46]Greischar and Lively (2011)HP, extinction riskdeterministicREconstrained
[47]Gilman et al. (2012)HP, multiple host traits, resistancestochasticIBMconstant, constrained4
[48]Mostowy and Engelstädter (2012)interaction matrices, sex, LDdeterministicREconstant
[28]Gokhale et al. (2013)HP, population sizestochasticIBMvariable, constrained
[49]Luijckx et al. (2013)MA, DaphniadeterministicREconstant
[50]Abou Chakra et al. (2014)HP, plastic behaviourbothODE, IBMconstant
[51]Taylor et al. (2014)HP, virus of virusdeterministicODEconstrained
[23]Ashby and Gupta (2014)SI, state-dependent sex, MAdeterministicODEvariable
[8]Ashby and King (2015)SI, diversity, transmission, sexstochasticIBMconstant
[52]Engelstädter (2015)HP, infection matricesdeterministicREconstant
[53]Rabajante et al. (2015)HP, many typesdeterministicODEconstrained
[25]Song et al. (2015)HP, population size, GfG MAdeterministicODEconstant, variable
[54]Hesse et al. (2015)environment, specialisationdeterministicODE, ADconstrained4
[24]Gómez et al. (2015)oscillation vs. arms racestochasticIBMvariable
[55]Rabajante et al. (2016)HP, rare typesdeterministic, noise1ODE, SDEconstrained
[56]Nordbotten and Stenseth (2016)HP, RQ vs stasisdeterministicPDEconstrained4
[57]Best et al. (2017)SI, no specificity, FSDdeterministic3ODE, ADconstrained4
[58]Bonachela et al. (2017)crossfeedingdeterministic2ODEconstrained
[59]Greenspoon and Mideo (2017)relatedness, transmissiondeterministicREconstant
[60]Lively (2017)allopatric, sympatric parasitesdeterministic2REconstrained
[61]Nuismer (2017)local, global adaptationdeterministic2REconstant
[62]Veller et al. (2017)HP, speed of evolution (RQ, RK)stochasticIBMconstant
[63]Ashby and Boots (2017)HP, SI, GfG MAdeterministicODEconstrained4
[27]MacPherson and Otto (2018)SI, HP, MA, RQ oscillationsdeterministicODEconstant, constrained4
[18]Ashby et al. (2019)HP, population size changedeterministicODE, ADconstrained
[]Current paper(HP, MA, RQ) population size, extinction timestochasticIBMconstant, constrained, variable
  1. Mathematical models and properties discussed in this paper sorted by publication year. Many models deal with relative allele or genotype abundances without considering ecological dynamics – these have been categorised as constant population size models. Those models that do include a changing population size and stochastic effects mostly do not analyse the stability of long term oscillations which is the focus of this paper. (See the notes on this literature survey in the Additional file 1).
  2. ODE/PDE/SDE: ordinary/partial/stochastic differential equation, IBM: individual based model (stochastic simulations), RE: recursion equation, SI: susceptible-infected (epidemiological) model, HP: explicit host-parasite model, AD: adaptive dynamics (most often ODE with added mutants), MA: matching alleles, GfG: gene for gene, RQ: Red Queen (oscillations in genotype abundances or in trait space), RK: Red King (slow evolution favoured), CSS: coevolutionary stable strategy.
  3. 1not intrinsic stochasticity
  4. 2stochastic mutants added
  5. 3adaptive dynamics simulations (no intrinsic stochasticity)
  6. 4via carrying capacity (density dependent death or competition term)
  7. 5but discussed
  8. 6some randomness in infection (±1 in next generation)
  9. 7when time discrete, only host stochastic