Limits...
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.

Show MeSH

Related in: MedlinePlus

Selective advantage of sexual over asexual reproduction (rmm = 0, rmM = 0, rMM = 0.1) (a,c) and of high over low recombination (b,d) in both the standard model (a,b) and the sequential-updating model (c,d), plotted for different selection coefficients (s) and different population sizes. The y-axis corresponds to the selection on the modifier (of sex/recombination), which is measured as the frequency change during a simulation run (i.e. 1000 host generations after introduction of the modifier allele M), averaged over 10000 simulation runs (100 for the deterministic model) with different random initial conditions.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC2198919&req=5

Figure 4: Selective advantage of sexual over asexual reproduction (rmm = 0, rmM = 0, rMM = 0.1) (a,c) and of high over low recombination (b,d) in both the standard model (a,b) and the sequential-updating model (c,d), plotted for different selection coefficients (s) and different population sizes. The y-axis corresponds to the selection on the modifier (of sex/recombination), which is measured as the frequency change during a simulation run (i.e. 1000 host generations after introduction of the modifier allele M), averaged over 10000 simulation runs (100 for the deterministic model) with different random initial conditions.

Mentions: Figure 4 shows the impact of population size on the evolution of recombination for both the standard model (panels a and b) and for the alternative model (panel c and d). Notice that we measure the selection on the modifier between generations 1000 and 2000 (see section methods). Thus, although the LD oscillations (and with them the selection on the modifier) vanish eventually in the cases with damped oscillations, they are still present (although very weakly) when we track the modifier. In the standard model, drift increases the strength of selection on the modifier if selection on the interaction loci is weak but decreases the strength of selection on the modifier when selection on the interaction loci is strong. In the first region, damped LD oscillations occur and drift considerably increases the amplitude of the oscillations, whereas the LD oscillations are always stable in the second region and drift affects the amplitude only marginally (see also Figure 3). This pattern suggests that drift increases the strength of selection on the modifier if it increases the amplitude of the LD oscillations, but rather decreases this selection if it does not affect the LD oscillations. In accordance with this interpretation, drift always increases the strength of selection on the modifier in the alternative model (in which LD oscillations are always damped), i.e. the strength of selection on the modifier strongly increases with decreasing population size.


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) (a,c) and of high over low recombination (b,d) in both the standard model (a,b) and the sequential-updating model (c,d), plotted for different selection coefficients (s) and different population sizes. The y-axis corresponds to the selection on the modifier (of sex/recombination), which is measured as the frequency change during a simulation run (i.e. 1000 host generations after introduction of the modifier allele M), averaged over 10000 simulation runs (100 for the deterministic model) with different random initial conditions.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: Selective advantage of sexual over asexual reproduction (rmm = 0, rmM = 0, rMM = 0.1) (a,c) and of high over low recombination (b,d) in both the standard model (a,b) and the sequential-updating model (c,d), plotted for different selection coefficients (s) and different population sizes. The y-axis corresponds to the selection on the modifier (of sex/recombination), which is measured as the frequency change during a simulation run (i.e. 1000 host generations after introduction of the modifier allele M), averaged over 10000 simulation runs (100 for the deterministic model) with different random initial conditions.
Mentions: Figure 4 shows the impact of population size on the evolution of recombination for both the standard model (panels a and b) and for the alternative model (panel c and d). Notice that we measure the selection on the modifier between generations 1000 and 2000 (see section methods). Thus, although the LD oscillations (and with them the selection on the modifier) vanish eventually in the cases with damped oscillations, they are still present (although very weakly) when we track the modifier. In the standard model, drift increases the strength of selection on the modifier if selection on the interaction loci is weak but decreases the strength of selection on the modifier when selection on the interaction loci is strong. In the first region, damped LD oscillations occur and drift considerably increases the amplitude of the oscillations, whereas the LD oscillations are always stable in the second region and drift affects the amplitude only marginally (see also Figure 3). This pattern suggests that drift increases the strength of selection on the modifier if it increases the amplitude of the LD oscillations, but rather decreases this selection if it does not affect the LD oscillations. In accordance with this interpretation, drift always increases the strength of selection on the modifier in the alternative model (in which LD oscillations are always damped), i.e. the strength of selection on the modifier strongly increases with decreasing population size.

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