The Effects of Population Size Histories on Estimates of Selection Coefficients from Time-Series Genetic Data

Scaling the discrete-time Wright-Fisher model to biobank-scale datasets

The discrete-time Wright-Fisher (DTWF) model and its diffusion limit are central to population genetics. These models can describe the forward-in-time evolution of allele frequencies in a population resulting from genetic drift, mutation, and selection. Computing likelihoods under the diffusion process is feasible, but the diffusion approximation breaks down for large samples or in the presence of strong selection. Existing methods for computing likelihoods under the DTWF model do not scale to current exome sequencing sample sizes in the hundreds of thousands. Here, we present a scalable algorithm that approximates the DTWF model with provably bounded error. Our approach relies on two key observations about the DTWF model. The first is that transition probabilities under the model are approximately sparse. The second is that transition distributions for similar starting allele frequencies are extremely close as distributions. Together, these observations enable approximate matrix-vector multiplication in linear (as opposed to the usual quadratic) time. We prove similar properties for Hypergeometric distributions, enabling fast computation of likelihoods for subsamples of the population. We show theoretically and in practice that this approximation is highly accurate and can scale to population sizes in the tens of millions, paving the way for rigorous biobank-scale inference. Finally, we use our results to estimate the impact of larger samples on estimating selection coefficients for loss-of-function variants. We find that increasing sample sizes beyond existing large exome sequencing cohorts will provide essentially no additional information except for genes with the most extreme fitness effects.

Effect of Ocrelizumab on B- and T-Cell Receptor Repertoire Diversity in Patients With Relapsing Multiple Sclerosis From the Randomized Phase III OPERA Trial

BACKGROUND AND OBJECTIVES

The B cell-depleting anti-CD20 antibody ocrelizumab (OCR) effectively reduces MS disease activity and slows disability progression. Given the role of B cells as antigen-presenting cells, the primary goal of this study was to evaluate the effect of OCR on the T-cell receptor repertoire diversity.

METHODS

To examine whether OCR substantially alters the molecular diversity of the T-cell receptor repertoire, deep immune repertoire sequencing (RepSeq) of CD4+ and CD8+ T-cell receptor β-chain variable regions was performed on longitudinal blood samples. The IgM and IgG heavy chain variable region repertoire was also analyzed to characterize the residual B-cell repertoire under OCR treatment.

RESULTS

Peripheral blood samples for RepSeq were obtained from 8 patients with relapsing MS enrolled in the OPERA I trial over a period of up to 39 months. Four patients each were treated with OCR or interferon β1-a during the double-blind period of OPERA I. All patients received OCR during the open-label extension. The diversity of the CD4+/CD8+ T-cell repertoires remained unaffected in OCR-treated patients. The expected OCR-associated B-cell depletion was mirrored by reduced B-cell receptor diversity in peripheral blood and a shift in immunoglobulin gene usage. Despite deep B-cell depletion, longitudinal persistence of clonally related B-cells was observed.

DISCUSSION

Our data illustrate that the diversity of CD4+/CD8+ T-cell receptor repertoires remained unaltered in OCR-treated patients with relapsing MS. Persistence of a highly diverse T-cell repertoire suggests that aspects of adaptive immunity remain intact despite extended anti-CD20 therapy.

TRIAL REGISTRATION INFORMATION

This is a substudy (BE29353) of the OPERA I (WA21092; NCT01247324) trial. Date of registration, November 23, 2010; first patient enrollment, August 31, 2011.

Scaling the Discrete-time Wright Fisher model to biobank-scale datasets

The Discrete-Time Wright Fisher (DTWF) model and its large population diffusion limit are central to population genetics. These models describe the forward-in-time evolution of the frequency of an allele in a population and can include the fundamental forces of genetic drift, mutation, and selection. Computing like-lihoods under the diffusion process is feasible, but the diffusion approximation breaks down for large sample sizes or in the presence of strong selection. Unfortunately, existing methods for computing likelihoods under the DTWF model do not scale to current exome sequencing sample sizes in the hundreds of thousands. Here we present an algorithm that approximates the DTWF model with provably bounded error and runs in time linear in the size of the population. Our approach relies on two key observations about Binomial distributions. The first is that Binomial distributions are approximately sparse. The second is that Binomial distributions with similar success probabilities are extremely close as distributions, allowing us to approximate the DTWF Markov transition matrix as a very low rank matrix. Together, these observations enable matrix-vector multiplication in linear (as opposed to the usual quadratic) time. We prove similar properties for Hypergeometric distributions, enabling fast computation of likelihoods for subsamples of the population. We show theoretically and in practice that this approximation is highly accurate and can scale to population sizes in the billions, paving the way for rigorous biobank-scale population genetic inference. Finally, we use our results to estimate how increasing sample sizes will improve the estimation of selection coefficients acting on loss-of-function variants. We find that increasing sample sizes beyond existing large exome sequencing cohorts will provide essentially no additional information except for genes with the most extreme fitness effects.

Allele frequencies and selection coefficients in locally adapted populations

Understanding the role of natural selection in driving evolutionary change requires accurate estimates of the strength of selection acting at the genetic level in the wild. This is challenging to achieve but may be easier in the case of populations in migration-selection balance. When two populations are at equilibrium under migration-selection balance, there exist loci whose alleles are selected different ways in the two populations. Such loci can be identified from genome sequencing by their high values of F_ST. This raises the question of what is the strength of selection on locally-adaptive alleles. To answer this question we analyse a 1-locus 2-allele model of a population distributed between two niches. We show by simulation of selected cases that the outputs from finite-population models are essentially the same as those from deterministic infinite-population models. We then derive theory for the infinite-population model showing the dependence of selection coefficients on equilibrium allele frequencies, migration rates, dominance and relative population sizes in the two niches. An Excel spreadsheet is provided for the calculation of selection coefficients and their approximate standard errors from observed values of population parameters. We illustrate our results with a worked example, with graphs showing the dependence of selection coefficients on equilibrium allele frequencies, and graphs showing how F_ST depends on the selection coefficients acting on the alleles at a locus. Given the extent of recent progress in ecological genomics, we hope our methods may help those studying migration-selection balance to quantify the advantages conferred by adaptive genes.

Bait-ER: A Bayesian method to detect targets of selection in Evolve-and-Resequence experiments

For over a decade, experimental evolution has been combined with high-throughput sequencing techniques. In so-called Evolve-and-Resequence (E&R) experiments, populations are kept in the laboratory under controlled experimental conditions where their genomes are sampled and allele frequencies monitored. However, identifying signatures of adaptation in E&R datasets is far from trivial, and it is still necessary to develop more efficient and statistically sound methods for detecting selection in genome-wide data. Here, we present Bait-ER - a fully Bayesian approach based on the Moran model of allele evolution to estimate selection coefficients from E&R experiments. The model has overlapping generations, a feature that describes several experimental designs found in the literature. We tested our method under several different demographic and experimental conditions to assess its accuracy and precision, and it performs well in most scenarios. Nevertheless, some care must be taken when analysing trajectories where drift largely dominates and starting frequencies are low. We compare our method with other available software and report that ours has generally high accuracy even for trajectories whose complexity goes beyond a classical sweep model. Furthermore, our approach avoids the computational burden of simulating an empirical null distribution, outperforming available software in terms of computational time and facilitating its use on genome-wide data. We implemented and released our method in a new open-source software package that can be accessed at https://doi.org/10.5281/zenodo.7351736.

Dairying, diseases and the evolution of lactase persistence in Europe

In European and many African, Middle Eastern and southern Asian populations, lactase persistence (LP) is the most strongly selected monogenic trait to have evolved over the past 10,000 years1. Although the selection of LP and the consumption of prehistoric milk must be linked, considerable uncertainty remains concerning their spatiotemporal configuration and specific interactions2,3. Here we provide detailed distributions of milk exploitation across Europe over the past 9,000 years using around 7,000 pottery fat residues from more than 550 archaeological sites. European milk use was widespread from the Neolithic period onwards but varied spatially and temporally in intensity. Notably, LP selection varying with levels of prehistoric milk exploitation is no better at explaining LP allele frequency trajectories than uniform selection since the Neolithic period. In the UK Biobank4,5 cohort of 500,000 contemporary Europeans, LP genotype was only weakly associated with milk consumption and did not show consistent associations with improved fitness or health indicators. This suggests that other reasons for the beneficial effects of LP should be considered for its rapid frequency increase. We propose that lactase non-persistent individuals consumed milk when it became available but, under conditions of famine and/or increased pathogen exposure, this was disadvantageous, driving LP selection in prehistoric Europe. Comparison of model likelihoods indicates that population fluctuations, settlement density and wild animal exploitation-proxies for these drivers-provide better explanations of LP selection than the extent of milk exploitation. These findings offer new perspectives on prehistoric milk exploitation and LP evolution.

Detecting and Quantifying Natural Selection at Two Linked Loci from Time Series Data of Allele Frequencies with Forward-in-Time Simulations

Recent advances in DNA sequencing techniques have made it possible to monitor genomes in great detail over time. This improvement provides an opportunity for us to study natural selection based on time serial samples of genomes while accounting for genetic recombination effect and local linkage information. Such time series genomic data allow for more accurate estimation of population genetic parameters and hypothesis testing on the recent action of natural selection. In this work, we develop a novel Bayesian statistical framework for inferring natural selection at a pair of linked loci by capitalising on the temporal aspect of DNA data with the additional flexibility of modeling the sampled chromosomes that contain unknown alleles. Our approach is built on a hidden Markov model where the underlying process is a two-locus Wright-Fisher diffusion with selection, which enables us to explicitly model genetic recombination and local linkage. The posterior probability distribution for selection coefficients is computed by applying the particle marginal Metropolis-Hastings algorithm, which allows us to efficiently calculate the likelihood. We evaluate the performance of our Bayesian inference procedure through extensive simulations, showing that our approach can deliver accurate estimates of selection coefficients, and the addition of genetic recombination and local linkage brings about significant improvement in the inference of natural selection. We also illustrate the utility of our method on real data with an application to ancient DNA data associated with white spotting patterns in horses.

Estimation of Natural Selection and Allele Age from Time Series Allele Frequency Data Using a Novel Likelihood-Based Approach

Temporally spaced genetic data allow for more accurate inference of population genetic parameters and hypothesis testing on the recent action of natural selection. In this work, we develop a novel likelihood-based method for jointly estimating selection coefficient and allele age from time series data of allele frequencies. Our approach is based on a hidden Markov model where the underlying process is a Wright-Fisher diffusion conditioned to survive until the time of the most recent sample. This formulation circumvents the assumption required in existing methods that the allele is created by mutation at a certain low frequency. We calculate the likelihood by numerically solving the resulting Kolmogorov backward equation backward in time while reweighting the solution with the emission probabilities of the observation at each sampling time point. This procedure reduces the two-dimensional numerical search for the maximum of the likelihood surface, for both the selection coefficient and the allele age, to a one-dimensional search over the selection coefficient only. We illustrate through extensive simulations that our method can produce accurate estimates of the selection coefficient and the allele age under both constant and nonconstant demographic histories. We apply our approach to reanalyze ancient DNA data associated with horse base coat colors. We find that ignoring demographic histories or grouping raw samples can significantly bias the inference results.

Clonal reconstruction from time course genomic sequencing data

BACKGROUND

Bacterial cells during many replication cycles accumulate spontaneous mutations, which result in the birth of novel clones. As a result of this clonal expansion, an evolving bacterial population has different clonal composition over time, as revealed in the long-term evolution experiments (LTEEs). Accurately inferring the haplotypes of novel clones as well as the clonal frequencies and the clonal evolutionary history in a bacterial population is useful for the characterization of the evolutionary pressure on multiple correlated mutations instead of that on individual mutations.

RESULTS

In this paper, we study the computational problem of reconstructing the haplotypes of bacterial clones from the variant allele frequencies observed from an evolving bacterial population at multiple time points. We formalize the problem using a maximum likelihood function, which is defined under the assumption that mutations occur spontaneously, and thus the likelihood of a mutation occurring in a specific clone is proportional to the frequency of the clone in the population when the mutation occurs. We develop a series of heuristic algorithms to address the maximum likelihood inference, and show through simulation experiments that the algorithms are fast and achieve near optimal accuracy that is practically plausible under the maximum likelihood framework. We also validate our method using experimental data obtained from a recent study on long-term evolution of Escherichia coli.

CONCLUSION

We developed efficient algorithms to reconstruct the clonal evolution history from time course genomic sequencing data. Our algorithm can also incorporate clonal sequencing data to improve the reconstruction results when they are available. Based on the evaluation on both simulated and experimental sequencing data, our algorithms can achieve satisfactory results on the genome sequencing data from long-term evolution experiments.

AVAILABILITY

The program (ClonalTREE) is available as open-source software on GitHub at https://github.com/COL-IU/ClonalTREE.

Quantifying Selection with Pool-Seq Time Series Data

Allele frequency time series data constitute a powerful resource for unraveling mechanisms of adaptation, because the temporal dimension captures important information about evolutionary forces. In particular, Evolve and Resequence (E&R), the whole-genome sequencing of replicated experimentally evolving populations, is becoming increasingly popular. Based on computer simulations several studies proposed experimental parameters to optimize the identification of the selection targets. No such recommendations are available for the underlying parameters selection strength and dominance. Here, we introduce a highly accurate method to estimate selection parameters from replicated time series data, which is fast enough to be applied on a genome scale. Using this new method, we evaluate how experimental parameters can be optimized to obtain the most reliable estimates for selection parameters. We show that the effective population size (N_e) and the number of replicates have the largest impact. Because the number of time points and sequencing coverage had only a minor effect, we suggest that time series analysis is feasible without major increase in sequencing costs. We anticipate that time series analysis will become routine in E&R studies.

Inferring Fitness Effects from Time-Resolved Sequence Data with a Delay-Deterministic Model

A broad range of approaches have considered the challenge of inferring selection from time-resolved genome sequence data. Models describing deterministic changes in allele or haplotype frequency have been highlighted as providing accurate and computationally...

A common challenge arising from the observation of an evolutionary system over time is to infer the magnitude of selection acting upon a specific genetic variant, or variants, within the population. The inference of selection may be confounded by the effects of genetic drift in a system, leading to the development of inference procedures to account for these effects. However, recent work has suggested that deterministic models of evolution may be effective in capturing the effects of selection even under complex models of demography, suggesting the more general application of deterministic approaches to inference. Responding to this literature, we here note a case in which a deterministic model of evolution may give highly misleading inferences, resulting from the nondeterministic properties of mutation in a finite population. We propose an alternative approach that acts to correct for this error, and which we denote the delay-deterministic model. Applying our model to a simple evolutionary system, we demonstrate its performance in quantifying the extent of selection acting within that system. We further consider the application of our model to sequence data from an evolutionary experiment. We outline scenarios in which our model may produce improved results for the inference of selection, noting that such situations can be easily identified via the use of a regular deterministic model.

Assessing the Relationship of Ancient and Modern Populations

Sequencing DNA from deceased individuals can inform whether the individuals that currently live in a location are descended from individuals that.....

Genetic material sequenced from ancient samples is revolutionizing our understanding of the recent evolutionary past. However, ancient DNA is often degraded, resulting in low coverage, error-prone sequencing. Several solutions exist to this problem, ranging from simple approach, such as selecting a read at random for each site, to more complicated approaches involving genotype likelihoods. In this work, we present a novel method for assessing the relationship of an ancient sample with a modern population, while accounting for sequencing error and postmortem damage by analyzing raw reads from multiple ancient individuals simultaneously. We show that, when analyzing SNP data, it is better to sequence more ancient samples to low coverage: two samples sequenced to 0.5× coverage provide better resolution than a single sample sequenced to 2× coverage. We also examined the power to detect whether an ancient sample is directly ancestral to a modern population, finding that, with even a few high coverage individuals, even ancient samples that are very slightly diverged from the modern population can be detected with ease. When we applied our approach to European samples, we found that no ancient samples represent direct ancestors of modern Europeans. We also found that, as shown previously, the most ancient Europeans appear to have had the smallest effective population sizes, indicating a role for agriculture in modern population growth.