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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: 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.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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Typical simulation run in the deterministic versions of the standard model (a), the sequential-updating model (b), and the continuous-time model (c). The variable t represents the number of host generations. The figures show the LD oscillations during 10000 host generations. The following parameters were used: rmm = 0.1, sH = sP = 0.05.
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Figure 1: Typical simulation run in the deterministic versions of the standard model (a), the sequential-updating model (b), and the continuous-time model (c). The variable t represents the number of host generations. The figures show the LD oscillations during 10000 host generations. The following parameters were used: rmm = 0.1, sH = sP = 0.05.

Mentions: A peculiar and hitherto unnoticed consequence of deterministic modeling of host-parasite coevolution is that the amplitude of the resulting linkage disequilibrium (LD) oscillations may decrease over time and eventually reach negligibly small values. LD oscillations can be damped in all three models (see Figure 1 for typical simulation runs). The dampening is a general phenomenon in the two alternative models, but in the standard model, it is only observed when selection coefficients are small (approximately sH and sP<0.4; see section "Methods"). Moreover, for weak selection, the type of LD oscillations in the standard model depends on the initial conditions: either the oscillations are weak but stable, or the oscillations are damped. For random initial allele frequencies, both scenarios seem to occur with similar frequency.


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)

Typical simulation run in the deterministic versions of the standard model (a), the sequential-updating model (b), and the continuous-time model (c). The variable t represents the number of host generations. The figures show the LD oscillations during 10000 host generations. The following parameters were used: rmm = 0.1, sH = sP = 0.05.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Typical simulation run in the deterministic versions of the standard model (a), the sequential-updating model (b), and the continuous-time model (c). The variable t represents the number of host generations. The figures show the LD oscillations during 10000 host generations. The following parameters were used: rmm = 0.1, sH = sP = 0.05.
Mentions: A peculiar and hitherto unnoticed consequence of deterministic modeling of host-parasite coevolution is that the amplitude of the resulting linkage disequilibrium (LD) oscillations may decrease over time and eventually reach negligibly small values. LD oscillations can be damped in all three models (see Figure 1 for typical simulation runs). The dampening is a general phenomenon in the two alternative models, but in the standard model, it is only observed when selection coefficients are small (approximately sH and sP<0.4; see section "Methods"). Moreover, for weak selection, the type of LD oscillations in the standard model depends on the initial conditions: either the oscillations are weak but stable, or the oscillations are damped. For random initial allele frequencies, both scenarios seem to occur with similar frequency.

Bottom Line: 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.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