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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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Selective advantage of sexual over asexual reproduction (rmm = 0, rmM = 0, rMM = 0.1) in the sequential-updating model for different interaction matrices, simulated deterministically (a) and stochastically with populations sizes N = 1000 (b), N = 10 000 (c), and N = 100 000 (d). For further details see legend of figure 5.
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Figure 7: Selective advantage of sexual over asexual reproduction (rmm = 0, rmM = 0, rMM = 0.1) in the sequential-updating model for different interaction matrices, simulated deterministically (a) and stochastically with populations sizes N = 1000 (b), N = 10 000 (c), and N = 100 000 (d). For further details see legend of figure 5.

Mentions: The preceding discussion was based on the matching allele interaction type. In order to investigate the impact of the interaction type, we measured the selection on a recombination/sex modifier for the generalized matching allele interaction type (see section "Methods") with selection coefficients s1 and s2 ranging from 0 to 1 with a gradation of 0.01 (i.e. for 104 different interaction matrices). The results are summarized in Figures 5, 6, 7, 8. Figures 5 (selection for/against sex) and 6 (selection for lower/higher recombination) correspond to the standard model and Figures 7 and 8 to the alternative model. These figures show that for most interaction types, the impact of population size is qualitatively the same as for the matching allele interaction type: In the standard model, drift only increases the strength of selection on the modifier when s1 and s2 are small. In the alternative model, however, drift increases the strength of selection for the whole range of s1 and s2. The only exception to this pattern can be found in the in the vicinity of the MMA (i.e when the number of matched loci determines the fitness in an approximately multiplicative way). In this region, we observe a strong selection against sex/recombination even in the deterministic regime. The figures show that with decreasing population size this region (where selection against recombination is strong) shrinks and the strength of selection against sex/recombination decreases. The reason for this effect is that systems with an (almost) multiplicative fitness function exhibit a different dynamic behavior than those with stronger interactions: Instead of periodic alternations of positive and negative LD, the system converges to a state in which the LD does not change its sign anymore (see discussion). Other than this effect around the MMA, finite population size does not have any appreciable effect on the direction of selection on the modifier: Independently of population size, sex wins against asex for the vast majority of interaction types (in both the standard and alternative model), and high recombination wins against low recombination only if the selection coefficients are strong enough.


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)

Selective advantage of sexual over asexual reproduction (rmm = 0, rmM = 0, rMM = 0.1) in the sequential-updating model for different interaction matrices, simulated deterministically (a) and stochastically with populations sizes N = 1000 (b), N = 10 000 (c), and N = 100 000 (d). For further details see legend of figure 5.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 7: Selective advantage of sexual over asexual reproduction (rmm = 0, rmM = 0, rMM = 0.1) in the sequential-updating model for different interaction matrices, simulated deterministically (a) and stochastically with populations sizes N = 1000 (b), N = 10 000 (c), and N = 100 000 (d). For further details see legend of figure 5.
Mentions: The preceding discussion was based on the matching allele interaction type. In order to investigate the impact of the interaction type, we measured the selection on a recombination/sex modifier for the generalized matching allele interaction type (see section "Methods") with selection coefficients s1 and s2 ranging from 0 to 1 with a gradation of 0.01 (i.e. for 104 different interaction matrices). The results are summarized in Figures 5, 6, 7, 8. Figures 5 (selection for/against sex) and 6 (selection for lower/higher recombination) correspond to the standard model and Figures 7 and 8 to the alternative model. These figures show that for most interaction types, the impact of population size is qualitatively the same as for the matching allele interaction type: In the standard model, drift only increases the strength of selection on the modifier when s1 and s2 are small. In the alternative model, however, drift increases the strength of selection for the whole range of s1 and s2. The only exception to this pattern can be found in the in the vicinity of the MMA (i.e when the number of matched loci determines the fitness in an approximately multiplicative way). In this region, we observe a strong selection against sex/recombination even in the deterministic regime. The figures show that with decreasing population size this region (where selection against recombination is strong) shrinks and the strength of selection against sex/recombination decreases. The reason for this effect is that systems with an (almost) multiplicative fitness function exhibit a different dynamic behavior than those with stronger interactions: Instead of periodic alternations of positive and negative LD, the system converges to a state in which the LD does not change its sign anymore (see discussion). Other than this effect around the MMA, finite population size does not have any appreciable effect on the direction of selection on the modifier: Independently of population size, sex wins against asex for the vast majority of interaction types (in both the standard and alternative model), and high recombination wins against low recombination only if the selection coefficients are strong enough.

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