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Lotka-Volterra dynamics kills the Red Queen: population size fluctuations and associated stochasticity dramatically change host-parasite coevolution.

Gokhale CS, Papkou A, Traulsen A, Schulenburg H - BMC Evol. Biol. (2013)

Bottom Line: This belief is founded on previous theoretical work, which assumes infinite or constant population size.Together, these two factors cause fast allele fixation.Fixation is not restricted to common alleles, as expected from drift, but also seen for originally rare alleles under a wide parameter space, potentially facilitating spread of novel variants.

View Article: PubMed Central - HTML - PubMed

Affiliation: Evolutionary Theory Group, Max Planck Institute for Evolutionary Biology, August Thienemann Str-2, 24306, Plön, Germany. gokhale@evolbio.mpg.de.

ABSTRACT

Background: Host-parasite coevolution is generally believed to follow Red Queen dynamics consisting of ongoing oscillations in the frequencies of interacting host and parasite alleles. This belief is founded on previous theoretical work, which assumes infinite or constant population size. To what extent are such sustained oscillations realistic?

Results: Here, we use a related mathematical modeling approach to demonstrate that ongoing Red Queen dynamics is unlikely. In fact, they collapse rapidly when two critical pieces of realism are acknowledged: (i) population size fluctuations, caused by the antagonism of the interaction in concordance with the Lotka-Volterra relationship; and (ii) stochasticity, acting in any finite population. Together, these two factors cause fast allele fixation. Fixation is not restricted to common alleles, as expected from drift, but also seen for originally rare alleles under a wide parameter space, potentially facilitating spread of novel variants.

Conclusion: Our results call for a paradigm shift in our understanding of host-parasite coevolution, strongly suggesting that these are driven by recurrent selective sweeps rather than continuous allele oscillations.

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Related in: MedlinePlus

Allele fixation/extinction times for any of the interacting types when we do include a slight interaction between the otherwise independent Lotka-Volterra cycles. As compared to Figure 2 the fixation times in the case without Lotka-Volterra oscillations reduce with slight interaction between independent cycles. However for the case with Lotka-Volterra oscillations the fixation times are practically unchanged. For all simulations the initial condition were H1=H2=Navg/2, P1=90Navg/100, P2=10Navg/100, and the parameters μ=5, c=2.5, b=10/Navg and ε=0.1b with averages over 106 realizations).
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Figure 5: Allele fixation/extinction times for any of the interacting types when we do include a slight interaction between the otherwise independent Lotka-Volterra cycles. As compared to Figure 2 the fixation times in the case without Lotka-Volterra oscillations reduce with slight interaction between independent cycles. However for the case with Lotka-Volterra oscillations the fixation times are practically unchanged. For all simulations the initial condition were H1=H2=Navg/2, P1=90Navg/100, P2=10Navg/100, and the parameters μ=5, c=2.5, b=10/Navg and ε=0.1b with averages over 106 realizations).

Mentions: Even for this case, including Lotka-Volterra interactions causes a faster extinction of the Red Queen cycles involving all four types. As an example we provide simulation results where in addition to similar parameters as in Figure 2 we add a ε=0.1b (Figure 5). Although the fixation time is elevated as compared to the case with no interactions (Figure 2), they are still not comparable to the extremely high fixations times observed when Lotka-Volterra dynamics is excluded.


Lotka-Volterra dynamics kills the Red Queen: population size fluctuations and associated stochasticity dramatically change host-parasite coevolution.

Gokhale CS, Papkou A, Traulsen A, Schulenburg H - BMC Evol. Biol. (2013)

Allele fixation/extinction times for any of the interacting types when we do include a slight interaction between the otherwise independent Lotka-Volterra cycles. As compared to Figure 2 the fixation times in the case without Lotka-Volterra oscillations reduce with slight interaction between independent cycles. However for the case with Lotka-Volterra oscillations the fixation times are practically unchanged. For all simulations the initial condition were H1=H2=Navg/2, P1=90Navg/100, P2=10Navg/100, and the parameters μ=5, c=2.5, b=10/Navg and ε=0.1b with averages over 106 realizations).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4225518&req=5

Figure 5: Allele fixation/extinction times for any of the interacting types when we do include a slight interaction between the otherwise independent Lotka-Volterra cycles. As compared to Figure 2 the fixation times in the case without Lotka-Volterra oscillations reduce with slight interaction between independent cycles. However for the case with Lotka-Volterra oscillations the fixation times are practically unchanged. For all simulations the initial condition were H1=H2=Navg/2, P1=90Navg/100, P2=10Navg/100, and the parameters μ=5, c=2.5, b=10/Navg and ε=0.1b with averages over 106 realizations).
Mentions: Even for this case, including Lotka-Volterra interactions causes a faster extinction of the Red Queen cycles involving all four types. As an example we provide simulation results where in addition to similar parameters as in Figure 2 we add a ε=0.1b (Figure 5). Although the fixation time is elevated as compared to the case with no interactions (Figure 2), they are still not comparable to the extremely high fixations times observed when Lotka-Volterra dynamics is excluded.

Bottom Line: This belief is founded on previous theoretical work, which assumes infinite or constant population size.Together, these two factors cause fast allele fixation.Fixation is not restricted to common alleles, as expected from drift, but also seen for originally rare alleles under a wide parameter space, potentially facilitating spread of novel variants.

View Article: PubMed Central - HTML - PubMed

Affiliation: Evolutionary Theory Group, Max Planck Institute for Evolutionary Biology, August Thienemann Str-2, 24306, Plön, Germany. gokhale@evolbio.mpg.de.

ABSTRACT

Background: Host-parasite coevolution is generally believed to follow Red Queen dynamics consisting of ongoing oscillations in the frequencies of interacting host and parasite alleles. This belief is founded on previous theoretical work, which assumes infinite or constant population size. To what extent are such sustained oscillations realistic?

Results: Here, we use a related mathematical modeling approach to demonstrate that ongoing Red Queen dynamics is unlikely. In fact, they collapse rapidly when two critical pieces of realism are acknowledged: (i) population size fluctuations, caused by the antagonism of the interaction in concordance with the Lotka-Volterra relationship; and (ii) stochasticity, acting in any finite population. Together, these two factors cause fast allele fixation. Fixation is not restricted to common alleles, as expected from drift, but also seen for originally rare alleles under a wide parameter space, potentially facilitating spread of novel variants.

Conclusion: Our results call for a paradigm shift in our understanding of host-parasite coevolution, strongly suggesting that these are driven by recurrent selective sweeps rather than continuous allele oscillations.

Show MeSH
Related in: MedlinePlus