Coalescent Inference Using Serially Sampled, High-Throughput Sequencing Data from Intrahost HIV Infection

Properties of Two-Locus Genealogies and Linkage Disequilibrium in Temporally Structured Samples

Archaeogenetics has been revolutionary, revealing insights into demographic history and recent positive selection. However, most studies to date have ignored the non-random association of genetic variants at different loci (i.e., linkage disequilibrium, LD). This may be in part because basic properties of LD in samples from different times are still not well understood. Here, we derive several results for summary statistics of haplotypic variation under a model with time-stratified sampling: 1) The correlation between the number of pairwise differences observed between time-staggered samples (πΔt) in models with and without strict population continuity; 2) The product of the LD coefficient, D, between ancient and modern samples, which is a measure of haplotypic similarity between modern and ancient samples; and 3) The expected switch rate in the Li and Stephens haplotype copying model. The latter has implications for genotype imputation and phasing in ancient samples with modern reference panels. Overall, these results provide a characterization of how haplotype patterns are affected by sample age, recombination rates, and population sizes. We expect these results will help guide the interpretation and analysis of haplotype data from ancient and modern samples.

A characterisation of the reconstructed birth-death process through time rescaling

The dynamics of a population exhibiting exponential growth can be modelled as a birth-death process, which naturally captures the stochastic variation in population size over time. In this article, we consider a supercritical birth-death process, started at a random time in the past, and conditioned to have n sampled individuals at the present. The genealogy of individuals sampled at the present time is then described by the reversed reconstructed process (RRP), which traces the ancestry of the sample backwards from the present. We show that a simple, analytic, time rescaling of the RRP provides a straightforward way to derive its inter-event times. The same rescaling characterises other distributions underlying this process, obtained elsewhere in the literature via more cumbersome calculations. We also consider the case of incomplete sampling of the population, in which each leaf of the genealogy is retained with an independent Bernoulli trial with probability ψ, and we show that corresponding results for Bernoulli-sampled RRPs can be derived using time rescaling, for any values of the underlying parameters. A central result is the derivation of a scaling limit as ψ approaches 0, corresponding to the underlying population growing to infinity, using the time rescaling formalism. We show that in this setting, after a linear time rescaling, the event times are the order statistics of n logistic random variables with mode log(1∕ψ); moreover, we show that the inter-event times are approximately exponentially distributed.

Coalescence modeling of intrainfection Bacillus anthracis populations allows estimation of infection parameters in wild populations

Bacillus anthracis, the etiological agent of anthrax, is a well-established model organism. For B. anthracis and most other infectious diseases, knowledge regarding transmission and infection parameters in natural systems, in large part, comprises data gathered from closely controlled laboratory experiments. Fatal, natural anthrax infections transmit the bacterium through new host-pathogen contacts at carcass sites, which can occur years after death of the previous host. For the period between contact and death, all of our knowledge is based upon experimental data from domestic livestock and laboratory animals. Here we use a noninvasive method to explore the dynamics of anthrax infections, by evaluating the terminal diversity of B. anthracis in anthrax carcasses. We present an application of population genetics theory, specifically, coalescence modeling, to intrainfection populations of B. anthracis to derive estimates for the duration of the acute phase of the infection and effective population size converted to the number of colony-forming units establishing infection in wild plains zebra (Equus quagga). Founding populations are small, a few colony-forming units, and infections are rapid, lasting roughly between 1 d and 3 d in the wild. Our results closely reflect experimental data, showing that small founding populations progress acutely, killing the host within days. We believe this method is amendable to other bacterial diseases from wild, domestic, and human systems.

Application of deep sequencing methods for inferring viral population diversity

The first deep sequencing method was announced in 2005. Due to an increasing number of sequencing data and a reduction in the costs of each sequencing dataset, this innovative technique was soon applied to genetic investigations of viral genome diversity in various viruses, particularly RNA viruses. These deep sequencing findings documented viral epidemiology and evolution and provided high-resolution data on the genetic changes in viral populations. Here, we review deep sequencing platforms that have been applied in viral quasispecies studies. Further, we discuss recent deep sequencing studies on viral inter- and intrahost evolution, drug resistance, and humoral immune selection, especially in emerging and re-emerging viruses. Deep sequencing methods are becoming the standard for providing comprehensive results of viral population diversity, and their applications are discussed.

Phylodynamic Inference across Epidemic Scales

Within-host genetic diversity and large transmission bottlenecks confound phylodynamic inference of epidemiological dynamics. Conventional phylodynamic approaches assume that nodes in a time-scaled pathogen phylogeny correspond closely to the time of transmission between hosts that are ancestral to the sample. However, when hosts harbor diverse pathogen populations, node times can substantially pre-date infection times. Imperfect bottlenecks can cause lineages sampled in different individuals to coalesce in unexpected patterns. To address realistic violations of standard phylodynamic assumptions we developed a new inference approach based on a multi-scale coalescent model, accounting for nonlinear epidemiological dynamics, heterogeneous sampling through time, non-negligible genetic diversity of pathogens within hosts, and imperfect transmission bottlenecks. We apply this method to HIV-1 and Ebola virus (EBOV) outbreak sequence data, illustrating how and when conventional phylodynamic inference may give misleading results. Within-host diversity of HIV-1 causes substantial upwards bias in the number of infected hosts using conventional coalescent models, but estimates using the multi-scale model have greater consistency with reported number of diagnoses through time. In contrast, we find that within-host diversity of EBOV has little influence on estimated numbers of infected hosts or reproduction numbers, and estimates are highly consistent with the reported number of diagnoses through time. The multi-scale coalescent also enables estimation of within-host effective population size using single sequences from a random sample of patients. We find within-host population genetic diversity of HIV-1 p17 to be 2Nμ=0.012 (95% CI 0.0066-0.023), which is lower than estimates based on HIV envelope serial sequencing of individual patients.

Recent advances in understanding HIV evolution

The human immunodeficiency virus (HIV) evolves rapidly owing to the combined activity of error-prone reverse transcriptase, recombination, and short generation times, leading to extensive viral diversity both within and between hosts. This diversity is a major contributing factor in the failure of the immune system to eradicate the virus and has important implications for the development of suitable drugs and vaccines to combat infection. This review will discuss the recent technological advances that have shed light on HIV evolution and will summarise emerging concepts in this field.

Exceptional Heterogeneity in Viral Evolutionary Dynamics Characterises Chronic Hepatitis C Virus Infection

The treatment of HCV infection has seen significant progress, particularly since the approval of new direct-acting antiviral drugs. However these clinical achievements have been made despite an incomplete understanding of HCV replication and within-host evolution, especially compared with HIV-1. Here, we undertake a comprehensive analysis of HCV within-host evolution during chronic infection by investigating over 4000 viral sequences sampled longitudinally from 15 HCV-infected patients. We compare our HCV results to those from a well-studied HIV-1 cohort, revealing key differences in the evolutionary behaviour of these two chronic-infecting pathogens. Notably, we find an exceptional level of heterogeneity in the molecular evolution of HCV, both within and among infected individuals. Furthermore, these patterns are associated with the long-term maintenance of viral lineages within patients, which fluctuate in relative frequency in peripheral blood. Together, our findings demonstrate that HCV replication behavior is complex and likely comprises multiple viral subpopulations with distinct evolutionary dynamics. The presence of a structured viral population can explain apparent paradoxes in chronic HCV infection, such as rapid fluctuations in viral diversity and the reappearance of viral strains years after their initial detection.

Our knowledge of HCV within-host evolution is substantially limited, which is surprising given that highly successful therapies against the virus have been developed. Key aspects of HCV infection, such as rapid fluctuations in viral diversity and the reappearance of viral strains years after their initial detection, remain unexplained. To better understand this problem, we analyse viral sequences from HCV-infected patients sampled over several years. Our findings suggest that the replication dynamics during chronic HCV infection are distinct from those of HIV-1, and dominated by the co-circulation of multiple viral strains. Although a major difference between the two chronic-infecting viruses is the level of recombination, our results indicate that HCV within-host evolution is most likely to be shaped by a structured viral population. Crucially, our study shows that HCV sampled from blood does not fully represent the within-host viral population at that time. This may have important implications for HCV treatment, especially in patients that have seemingly cleared the virus, as well as for molecular epidemiology studies investigating HCV transmission.

Two-Locus Likelihoods Under Variable Population Size and Fine-Scale Recombination Rate Estimation

Two-locus sampling probabilities have played a central role in devising an efficient composite-likelihood method for estimating fine-scale recombination rates. Due to mathematical and computational challenges, these sampling probabilities are typically computed under the unrealistic assumption of a constant population size, and simulation studies have shown that resulting recombination rate estimates can be severely biased in certain cases of historical population size changes. To alleviate this problem, we develop here new methods to compute the sampling probability for variable population size functions that are piecewise constant. Our main theoretical result, implemented in a new software package called LDpop, is a novel formula for the sampling probability that can be evaluated by numerically exponentiating a large but sparse matrix. This formula can handle moderate sample sizes ([Formula: see text]) and demographic size histories with a large number of epochs ([Formula: see text]). In addition, LDpop implements an approximate formula for the sampling probability that is reasonably accurate and scales to hundreds in sample size ([Formula: see text]). Finally, LDpop includes an importance sampler for the posterior distribution of two-locus genealogies, based on a new result for the optimal proposal distribution in the variable-size setting. Using our methods, we study how a sharp population bottleneck followed by rapid growth affects the correlation between partially linked sites. Then, through an extensive simulation study, we show that accounting for population size changes under such a demographic model leads to substantial improvements in fine-scale recombination rate estimation.