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The Red Queen and the persistence of linkage-disequilibrium oscillations in finite and infinite populations.

Kouyos RD, Salathé M, Bonhoeffer S - BMC Evol. Biol. (2007)

Bottom Line: Here, we show that altering the standard model from discrete to continuous time or from simultaneous to sequential updating results in damped LD oscillations.In addition, we show that the amplitude of the oscillations and therefore the strength of the resulting selection for or against recombination are inversely proportional to the size of the (host) population.As a consequence, the RQH can strongly depend on population size and should therefore not be interpreted as a purely deterministic hypothesis.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institute of Integrative Biology, ETH Zürich, ETH-Zentrum CHN, 8092 Zürich, Switzerland. roger.kouyos@env.ethz.ch

ABSTRACT

Background: The Red Queen Hypothesis (RQH) suggests that the coevolutionary dynamics of host-parasite systems can generate selection for increased host recombination. Since host-parasite interactions often have a strong genetic basis, recombination between different hosts can increase the fraction of novel and potentially resistant offspring genotypes. A prerequisite for this mechanism is that host-parasite interactions generate persistent oscillations of linkage disequilibria (LD).

Results: We use deterministic and stochastic models to investigate the persistence of LD oscillations and its impact on the RQH. The standard models of the Red Queen dynamics exhibit persistent LD oscillations under most circumstances. Here, we show that altering the standard model from discrete to continuous time or from simultaneous to sequential updating results in damped LD oscillations. This suggests that LD oscillations are structurally not robust. We then show that in a stochastic regime, drift can counteract this dampening and maintain the oscillations. In addition, we show that the amplitude of the oscillations and therefore the strength of the resulting selection for or against recombination are inversely proportional to the size of the (host) population.

Conclusion: We find that host parasite-interactions cannot generally maintain oscillations in the absence of drift. As a consequence, the RQH can strongly depend on population size and should therefore not be interpreted as a purely deterministic hypothesis.

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The effect of population size N on the amplitude of LD oscillations in the standard model (a) and in the sequential-updating model (b). The amplitude of the LD oscillations is measured as the maximum difference of linkage disequilibrium (ΔLD) between t = 10 000 and t = 20 000. The following parameter was used: rmm = 0.1.
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Figure 3: The effect of population size N on the amplitude of LD oscillations in the standard model (a) and in the sequential-updating model (b). The amplitude of the LD oscillations is measured as the maximum difference of linkage disequilibrium (ΔLD) between t = 10 000 and t = 20 000. The following parameter was used: rmm = 0.1.

Mentions: In the stochastic regime, LD oscillations can be maintained indefinitely even in the alternative model (Figure 2). This result holds for a wide range of mutation rates, recombination rates, and population sizes (see supplementary table S1, Additional file 1). Of special interest is the impact of population size on the LD amplitude that can be maintained at steady state (shown in Figure 3 for both the standard and the alternative model). In the standard model, stochasticity increases the amplitudes of LD oscillations only for small selection coefficients, i.e. for those parameter values where damped oscillations occur in the deterministic model. In the alternative model, on the other hand, the amplitudes of LD oscillations increase with decreasing population size independent of selection coefficients. In particular, the amplitudes of LD oscillations tend to negligibly small values as population size grows to very large values (i.e. as the system approaches the deterministic range). Thus, while mutation and recombination can dampen the LD oscillations, finite population size counters this process.


The Red Queen and the persistence of linkage-disequilibrium oscillations in finite and infinite populations.

Kouyos RD, Salathé M, Bonhoeffer S - BMC Evol. Biol. (2007)

The effect of population size N on the amplitude of LD oscillations in the standard model (a) and in the sequential-updating model (b). The amplitude of the LD oscillations is measured as the maximum difference of linkage disequilibrium (ΔLD) between t = 10 000 and t = 20 000. The following parameter was used: rmm = 0.1.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2198919&req=5

Figure 3: The effect of population size N on the amplitude of LD oscillations in the standard model (a) and in the sequential-updating model (b). The amplitude of the LD oscillations is measured as the maximum difference of linkage disequilibrium (ΔLD) between t = 10 000 and t = 20 000. The following parameter was used: rmm = 0.1.
Mentions: In the stochastic regime, LD oscillations can be maintained indefinitely even in the alternative model (Figure 2). This result holds for a wide range of mutation rates, recombination rates, and population sizes (see supplementary table S1, Additional file 1). Of special interest is the impact of population size on the LD amplitude that can be maintained at steady state (shown in Figure 3 for both the standard and the alternative model). In the standard model, stochasticity increases the amplitudes of LD oscillations only for small selection coefficients, i.e. for those parameter values where damped oscillations occur in the deterministic model. In the alternative model, on the other hand, the amplitudes of LD oscillations increase with decreasing population size independent of selection coefficients. In particular, the amplitudes of LD oscillations tend to negligibly small values as population size grows to very large values (i.e. as the system approaches the deterministic range). Thus, while mutation and recombination can dampen the LD oscillations, finite population size counters this process.

Bottom Line: Here, we show that altering the standard model from discrete to continuous time or from simultaneous to sequential updating results in damped LD oscillations.In addition, we show that the amplitude of the oscillations and therefore the strength of the resulting selection for or against recombination are inversely proportional to the size of the (host) population.As a consequence, the RQH can strongly depend on population size and should therefore not be interpreted as a purely deterministic hypothesis.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institute of Integrative Biology, ETH Zürich, ETH-Zentrum CHN, 8092 Zürich, Switzerland. roger.kouyos@env.ethz.ch

ABSTRACT

Background: The Red Queen Hypothesis (RQH) suggests that the coevolutionary dynamics of host-parasite systems can generate selection for increased host recombination. Since host-parasite interactions often have a strong genetic basis, recombination between different hosts can increase the fraction of novel and potentially resistant offspring genotypes. A prerequisite for this mechanism is that host-parasite interactions generate persistent oscillations of linkage disequilibria (LD).

Results: We use deterministic and stochastic models to investigate the persistence of LD oscillations and its impact on the RQH. The standard models of the Red Queen dynamics exhibit persistent LD oscillations under most circumstances. Here, we show that altering the standard model from discrete to continuous time or from simultaneous to sequential updating results in damped LD oscillations. This suggests that LD oscillations are structurally not robust. We then show that in a stochastic regime, drift can counteract this dampening and maintain the oscillations. In addition, we show that the amplitude of the oscillations and therefore the strength of the resulting selection for or against recombination are inversely proportional to the size of the (host) population.

Conclusion: We find that host parasite-interactions cannot generally maintain oscillations in the absence of drift. As a consequence, the RQH can strongly depend on population size and should therefore not be interpreted as a purely deterministic hypothesis.

Show MeSH
Related in: MedlinePlus