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

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.

Epistasis between deleterious mutations and the evolution of recombination

Epistasis and the evolution of recombination are closely intertwined: epistasis generates linkage disequilibria (i.e. statistical associations between alleles), whereas recombination breaks them up. The mutational deterministic hypothesis (MDH) states that high recombination rates are maintained because the breaking up of linkage disequilibria generated by negative epistasis enables more efficient purging of deleterious mutations. However, recent theoretical and experimental work challenges the MDH. Experimental evidence suggests that negative epistasis, required by the MDH, is relatively uncommon. On the theoretical side, population genetic models suggest that, compared with the combined effects of drift and selection, epistasis generates a negligible amount of linkage disequilibria. Here, we assess these criticisms and discuss to what extent they invalidate the MDH as an explanation for the evolution of recombination.

Stochastic or deterministic: what is the effective population size of HIV-1?

Various studies have attempted to estimate the effective population size of HIV-1 to determine the strength of stochastic effects in within-host evolution. The largely discrepant estimates, the complexity of the concept of the effective population size and the resulting uncertainty about the underlying assumptions make the interpretation of these estimates difficult. Here, we explain the concept and critically assess the current estimates. We discuss the biologically relevant factors that affect the estimate and use of the effective population size. We argue that these factors lead to an underestimation of the effective population size and, thus, to an overestimation of the strength of stochastic effects in HIV-1 evolution.

Effect of varying epistasis on the evolution of recombination

Whether recombination decelerates or accelerates a population's response to selection depends, at least in part, on how fitness-determining loci interact. Realistically, all genomes likely contain fitness interactions both with positive and with negative epistasis. Therefore, it is crucial to determine the conditions under which the potential beneficial effects of recombination with negative epistasis prevail over the detrimental effects of recombination with positive epistasis. Here, we examine the simultaneous effects of diverse epistatic interactions with different strengths and signs in a simplified model system with independent pairs of interacting loci and selection acting only on the haploid phase. We find that the average form of epistasis does not predict the average amount of linkage disequilibrium generated or the impact on a recombination modifier when compared to results using the entire distribution of epistatic effects and associated single-mutant effects. Moreover, we show that epistatic interactions of a given strength can produce very different effects, having the greatest impact when selection is weak. In summary, we observe that the evolution of recombination at mutation-selection balance might be driven by a small number of interactions with weak selection rather than by the average epistasis of all interactions. We illustrate this effect with an analysis of published data of Saccharomyces cerevisiae. Thus to draw conclusions on the evolution of recombination from experimental data, it is necessary to consider the distribution of epistatic interactions together with the associated selection coefficients.