Haldane's formula in Cannings models: the case of moderately strong selection.

For a class of Cannings models we prove Haldane's formula, [Formula: see text], for the fixation probability of a single beneficial mutant in the limit of large population size N and in the regime of moderately strong selection, i.e. for [Formula: see text] and [Formula: see text]. Here, [Formula: see text] is the selective advantage of an individual carrying the beneficial type, and [Formula: see text] is the (asymptotic) offspring variance. Our assumptions on the reproduction mechanism allow for a coupling of the beneficial allele's frequency process with slightly supercritical Galton-Watson processes in the early phase of fixation.

Kinetic Fingerprinting Links Bacteria-Phage Interactions with Emergent Dynamics: Rapid Depletion of Klebsiella pneumoniae Indicates Phage Synergy.

The specific temporal evolution of bacterial and phage population sizes, in particular bacterial depletion and the emergence of a resistant bacterial population, can be seen as a kinetic fingerprint that depends on the manifold interactions of the specific phage-host pair during the course of infection. We have elaborated such a kinetic fingerprint for a human urinary tract Klebsiella pneumoniae isolate and its phage vB_KpnP_Lessing by a modeling approach based on data from in vitro co-culture. We found a faster depletion of the initially sensitive bacterial population than expected from simple mass action kinetics. A possible explanation for the rapid decline of the bacterial population is a synergistic interaction of phages which can be a favorable feature for phage therapies. In addition to this interaction characteristic, analysis of the kinetic fingerprint of this bacteria and phage combination revealed several relevant aspects of their population dynamics: A reduction of the bacterial concentration can be achieved only at high multiplicity of infection whereas bacterial extinction is hardly accomplished. Furthermore the binding affinity of the phage to bacteria is identified as one of the most crucial parameters for the reduction of the bacterial population size. Thus, kinetic fingerprinting can be used to infer phage-host interactions and to explore emergent dynamics which facilitates a rational design of phage therapies.

Characterizing human cytomegalovirus reinfection in congenitally infected infants: an evolutionary perspective.

Given the strong selective pressures often faced by populations when colonizing a novel habitat, the level of variation present on which selection may act is an important indicator of adaptive potential. While often discussed in an ecological context, this notion is also highly relevant in our clinical understanding of viral infection, in which the novel habitat is a new host. Thus, quantifying the factors determining levels of variation is of considerable importance for the design of improved treatment strategies. Here, we focus on such a quantification of human cytomegalovirus (HCMV) - a virus which can be transmitted across the placenta, resulting in foetal infection that can potentially cause severe disease in multiple organs. Recent studies using genomewide sequencing data have demonstrated that viral populations in some congenitally infected infants diverge rapidly over time and between tissue compartments within individuals, while in other infants, the populations remain highly stable. Here, we investigate the underlying causes of these extreme differences in observed intrahost levels of variation by estimating the underlying demographic histories of infection. Importantly, reinfection (i.e. population admixture) appears to be an important, and previously unappreciated, player. We highlight illustrative examples likely to represent a single-population transmission from a mother during pregnancy and multiple-population transmissions during pregnancy and after birth.

Limits and patterns of cytomegalovirus genomic diversity in humans.

Human cytomegalovirus (HCMV) exhibits surprisingly high genomic diversity during natural infection although little is known about the limits or patterns of HCMV diversity among humans. To address this deficiency, we analyzed genomic diversity among congenitally infected infants. We show that there is an upper limit to HCMV genomic diversity in these patient samples, with ∼ 25% of the genome being devoid of polymorphisms. These low diversity regions were distributed across 26 loci that were preferentially located in DNA-processing genes. Furthermore, by developing, to our knowledge, the first genome-wide mutation and recombination rate maps for HCMV, we show that genomic diversity is positively correlated with these two rates. In contrast, median levels of viral genomic diversity did not vary between putatively single or mixed strain infections. We also provide evidence that HCMV populations isolated from vascular compartments of hosts from different continents are genetically similar and that polymorphisms in glycoproteins and regulatory proteins are enriched in these viral populations. This analysis provides the most highly detailed map of HCMV genomic diversity in human hosts to date and informs our understanding of the distribution of HCMV genomic diversity within human hosts.

Competing islands limit the rate of adaptation in structured populations.

Beneficial mutations can co-occur when population structure slows down adaptation. Here, we consider the process of adaptation in asexual populations distributed over several locations ("islands"). New beneficial mutations arise at constant rate ub, and each mutation has the same selective advantage s>0. We assume that populations evolve within islands according to the successional mutations regime of Desai and Fisher (2007), that is, the time to local fixation of a mutation is short compared to the expected waiting time until the next mutation occurs. To study the rate of adaptation, we introduce an approximate model, the successional mutations (SM) model, which can be simulated efficiently and yields accurate results for a wide range of parameters. In the SM model, mutations fix instantly within islands, and migrants can take over the destination island if they are fitter than the residents. For the special case of a population distributed equally across two islands with population size N, we approximate the model further for small and large migration rates in comparison to the mutation rate. These approximations lead to explicit formulas for the rate of adaptation which fit the original model for a large range of parameter values. For the d island case we provide some heuristics on how to extend the explicit formulas and check these with computer simulations. We conclude that the SM model is a good approximation of the adaptation process in a structured population, at least if mutation or migration is limited.

The ancestral selection graph under strong directional selection.

The ancestral selection graph (ASG) was introduced by  Neuhauser and Krone (1997) in order to study populations of constant size which evolve under selection. Coalescence events, which occur at rate 1 for every pair of lines, lead to joint ancestry. In addition, splitting events in the ASG at rate α, the scaled selection coefficient, produce possible ancestors, such that the real ancestor depends on the ancestral alleles. Here, we use the ASG in the case without mutation in order to study fixation of a beneficial mutant. Using our main tool, a reversibility property of the ASG, we provide a new proof of the fact that a beneficial allele fixes roughly in time (2logα)/α if α is large.

The effect of recurrent mutation on the linkage disequilibrium under a selective sweep.

A selective sweep describes the reduction of diversity due to strong positive selection. If the mutation rate to a selectively beneficial allele is sufficiently high, Pennings and Hermisson (Mol Biol Evol 23(5):1076-1084, 2006a) have shown, that it becomes likely, that a selective sweep is caused by several individuals. Such an event is called a soft sweep and the complementary event of a single origin of the beneficial allele, the classical case, a hard sweep. We give analytical expressions for the linkage disequilibrium (LD) between two neutral loci linked to the selected locus, depending on the recurrent mutation to the beneficial allele, measured by D and ̂σ(2)(D), a quantity introduced by Ohta and Kimura (Genetics 63(1):229-238, 1969), and conclude that the LD-pattern of a soft sweep differs substantially from that of a hard sweep due to haplotype structure. The analytical results are compared with simulations.