On the fixation probability of an advantageous allele in a population with skewed offspring distribution

Consider an advantageous allele that arises in a haploid population of size $N$ evolving in continuous time according to a skewed reproduction mechanism, which generates under neutrality genealogies lying in the domain of attraction of a Beta$(2-\alpha, \alpha)$-coalescent for $\alpha \in (1,2)$. We prove in a setting of moderate selection that the fixation probability $\pi_N$ of the advantageous allele is asymptotically equal to $\alpha^{1/(\alpha-1)} s_N^{1/(\alpha-1)}$ , where $s_N$ is the selection strength of the advantageous allele. Our proof uses duality with a suitable $\Lambda$-ancestral selection graph.Comment: 20 page

Spatial Invasion of Cooperative Parasites

In this paper we study invasion probabilities and invasion times of cooperative parasites spreading in spatially structured host populations. The spatial structure of the host population is given by a random geometric graph on $[0,1]^n$, $n\in \mathbb{N}$, with a Poisson($N$)-distributed number of vertices and in which vertices are connected over an edge when they have a distance of at most $r_N\in \Theta\left(N^{\frac{\beta-1}{n}}\right)$ for some $0<\beta<1$ and $N\rightarrow \infty$. At a host infection many parasites are generated and parasites move along edges to neighbouring hosts. We assume that parasites have to cooperate to infect hosts, in the sense that at least two parasites need to attack a host simultaneously. We find lower and upper bounds on the invasion probability of the parasites in terms of survival probabilities of branching processes with cooperation. Furthermore, we characterize the asymptotic invasion time. An important ingredient of the proofs is a comparison with infection dynamics of cooperative parasites in host populations structured according to a complete graph, i.e. in well-mixed host populations. For these infection processes we can show that invasion probabilities are asymptotically equal to survival probabilities of branching processes with cooperation. Furthermore, we build in the proofs on techniques developed in [BP22], where an analogous invasion process has been studied for host populations structured according to a configuration model. We substantiate our results with simulations

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 approximately 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 u(b), 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. (c) 2013 Elsevier Inc. All rights reserved

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

For a class of Cannings models we prove Haldane’s formula, π(sN)∼2sNρ2, 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 sN∼N−b and 0<b<1/2. Here, sN is the selective advantage of an individual carrying the beneficial type, and ρ2 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