An almost infinite sites model.

Motivation: A main challenge in molecular evolution is to find computationally efficient mutation models with flexible assumptions that properly reflect genetic variation. The infinite sites model assumes that each mutation event occurs at a site never previously mutant, i.e.

An estimator for the recombination rate from a continuously observed diffusion of haplotype frequencies.

Recombination is a fundamental evolutionary force, but it is difficult to quantify because the effect of a recombination event on patterns of variation in a sample of genetic data can be hard to discern. Estimators for the recombination rate, which are usually based on the idea of integrating over the unobserved possible evolutionary histories of a sample, can therefore be noisy. Here we consider a related question: how would an estimator behave if the evolutionary history actually was observed? This would offer an upper bound on the performance of estimators used in practice.

EWF: simulating exact paths of the Wright-Fisher diffusion.

Motivation: The Wright-Fisher diffusion is important in population genetics in modelling the evolution of allele frequencies over time subject to the influence of biological phenomena such as selection, mutation and genetic drift. Simulating the paths of the process is challenging due to the form of the transition density. We present EWF, a robust and efficient sampler which returns exact draws for the diffusion and diffusion bridge processes, accounting for general models of selection including those with frequency dependence.

Ongoing Recombination in SARS-CoV-2 Revealed through Genealogical Reconstruction.

The evolutionary process of genetic recombination has the potential to rapidly change the properties of a viral pathogen, and its presence is a crucial factor to consider in the development of treatments and vaccines. It can also significantly affect the results of phylogenetic analyses and the inference of evolutionary rates. The detection of recombination from samples of sequencing data is a very challenging problem and is further complicated for SARS-CoV-2 by its relatively slow accumulation of genetic diversity.

KwARG: parsimonious reconstruction of ancestral recombination graphs with recurrent mutation.

Motivation: The reconstruction of possible histories given a sample of genetic data in the presence of recombination and recurrent mutation is a challenging problem, but can provide key insights into the evolution of a population. We present KwARG, which implements a parsimony-based greedy heuristic algorithm for finding plausible genealogical histories (ancestral recombination graphs) that are minimal or near-minimal in the number of posited recombination and mutation events.

Results: Given an input dataset of aligned sequences, KwARG outputs a list of possible candidate solutions, each comprising a list of mutation and recombination events that could have generated the dataset; the relative proportion of recombinations and recurrent mutations in a solution can be controlled via specifying a set of 'cost' parameters.

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.

A Likelihood-Free Inference Framework for Population Genetic Data using Exchangeable Neural Networks.

An explosion of high-throughput DNA sequencing in the past decade has led to a surge of interest in population-scale inference with whole-genome data. Recent work in population genetics has centered on designing inference methods for relatively simple model classes, and few scalable general-purpose inference techniques exist for more realistic, complex models. To achieve this, two inferential challenges need to be addressed: (1) population data are exchangeable, calling for methods that efficiently exploit the symmetries of the data, and (2) computing likelihoods is intractable as it requires integrating over a set of correlated, extremely high-dimensional latent variables.

Wright-Fisher diffusion bridges.

The trajectory of the frequency of an allele which begins at x at time 0 and is known to have frequency z at time T can be modelled by the bridge process of the Wright-Fisher diffusion. Bridges when x=z=0 are particularly interesting because they model the trajectory of the frequency of an allele which appears at a time, then is lost by random drift or mutation after a time T. The coalescent genealogy back in time of a population in a neutral Wright-Fisher diffusion process is well understood.

A coalescent dual process for a Wright-Fisher diffusion with recombination and its application to haplotype partitioning.

Duality plays an important role in population genetics. It can relate results from forwards-in-time models of allele frequency evolution with those of backwards-in-time genealogical models; a well known example is the duality between the Wright-Fisher diffusion for genetic drift and its genealogical counterpart, the coalescent. There have been a number of articles extending this relationship to include other evolutionary processes such as mutation and selection, but little has been explored for models also incorporating crossover recombination.

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

Human immunodeficiency virus (HIV) is a rapidly evolving pathogen that causes chronic infections, so genetic diversity within a single infection can be very high. High-throughput "deep" sequencing can now measure this diversity in unprecedented detail, particularly since it can be performed at different time points during an infection, and this offers a potentially powerful way to infer the evolutionary dynamics of the intrahost viral population. However, population genomic inference from HIV sequence data is challenging because of high rates of mutation and recombination, rapid demographic changes, and ongoing selective pressures.

TRACTABLE DIFFUSION AND COALESCENT PROCESSES FOR WEAKLY CORRELATED LOCI.

Widely used models in genetics include the Wright-Fisher diffusion and its moment dual, Kingman's coalescent. Each has a multilocus extension but under neither extension is the sampling distribution available in closed-form, and their computation is extremely difficult. In this paper we two new multilocus population genetic models, one a diffusion and the other a coalescent process, which are much simpler than the standard models, but which capture their key properties for large recombination rates.

General triallelic frequency spectrum under demographic models with variable population size.

It is becoming routine to obtain data sets on DNA sequence variation across several thousands of chromosomes, providing unprecedented opportunity to infer the underlying biological and demographic forces. Such data make it vital to study summary statistics that offer enough compression to be tractable, while preserving a great deal of information. One well-studied summary is the site frequency spectrum-the empirical distribution, across segregating sites, of the sample frequency of the derived allele.

High-precision and high-accuracy rovibrational spectroscopy of molecular ions.

We present a versatile new instrument capable of measuring rovibrational transition frequencies of molecular ions with sub-MHz accuracy and precision. A liquid-nitrogen cooled positive column discharge cell, which can produce large column densities of a wide variety of molecular ions, is probed with sub-Doppler spectroscopy enabled by a high-power optical parametric oscillator locked to a moderate finesse external cavity. Frequency modulation (heterodyne) spectroscopy is employed to reduce intensity fluctuations due to the cavity lock, and velocity modulation spectroscopy permits ion-neutral discrimination.

Genome-wide fine-scale recombination rate variation in Drosophila melanogaster.

Estimating fine-scale recombination maps of Drosophila from population genomic data is a challenging problem, in particular because of the high background recombination rate. In this paper, a new computational method is developed to address this challenge. Through an extensive simulation study, it is demonstrated that the method allows more accurate inference, and exhibits greater robustness to the effects of natural selection and noise, compared to a well-used previous method developed for studying fine-scale recombination rate variation in the human genome.

Genealogy-based methods for inference of historical recombination and gene flow and their application in Saccharomyces cerevisiae.

Genetic exchange between isolated populations, or introgression between species, serves as a key source of novel genetic material on which natural selection can act. While detecting historical gene flow from DNA sequence data is of much interest, many existing methods can be limited by requirements for deep population genomic sampling. In this paper, we develop a scalable genealogy-based method to detect candidate signatures of gene flow into a given population when the source of the alleles is unknown.

Stopping-time resampling and population genetic inference under coalescent models.

To extract full information from samples of DNA sequence data, it is necessary to use sophisticated model-based techniques such as importance sampling under the coalescent. However, these are limited in the size of datasets they can handle efficiently. Chen and Liu (2000) introduced the idea of stopping-time resampling and showed that it can dramatically improve the efficiency of importance sampling methods under a finite-alleles coalescent model.

PADÉ APPROXIMANTS AND EXACT TWO-LOCUS SAMPLING DISTRIBUTIONS.

For population genetics models with recombination, obtaining an exact, analytic sampling distribution has remained a challenging open problem for several decades. Recently, a new perspective based on asymptotic series has been introduced to make progress on this problem. Specifically, closed-form expressions have been derived for the first few terms in an asymptotic expansion of the two-locus sampling distribution when the recombination rate is moderate to large.

The effect of recurrent mutation on the frequency spectrum of a segregating site and the age of an allele.

The sample frequency spectrum of a segregating site is the probability distribution of a sample of alleles from a genetic locus, conditional on observing the sample to be polymorphic. This distribution is widely used in population genetic inferences, including statistical tests of neutrality in which a skew in the observed frequency spectrum across independent sites is taken as a signature of departure from neutral evolution. Theoretical aspects of the frequency spectrum have been well studied and several interesting results are available, but they are usually under the assumption that a site has undergone at most one mutation event in the history of the sample.

Inference from samples of DNA sequences using a two-locus model.

Performing inference on contemporary samples of DNA sequence data is an important and challenging task. Computationally intensive methods such as importance sampling (IS) are attractive because they make full use of the available data, but in the presence of recombination the large state space of genealogies can be prohibitive. In this article, we make progress by developing an efficient IS proposal distribution for a two-locus model of sequence data.

AN ASYMPTOTIC SAMPLING FORMULA FOR THE COALESCENT WITH RECOMBINATION.

Ewens sampling formula (ESF) is a one-parameter family of probability distributions with a number of intriguing combinatorial connections. This elegant closed-form formula first arose in biology as the stationary probability distribution of a sample configuration at one locus under the infinite-alleles model of mutation. Since its discovery in the early 1970s, the ESF has been used in various biological applications, and has sparked several interesting mathematical generalizations.

Closed-form two-locus sampling distributions: accuracy and universality.

Sampling distributions play an important role in population genetics analyses, but closed-form sampling formulas are generally intractable to obtain. In the presence of recombination, there is no known closed-form sampling formula that holds for an arbitrary recombination rate. However, we recently showed that it is possible to obtain useful closed-form sampling formulas when the population-scaled recombination rate rho is large.

IMPORTANCE SAMPLING AND THE TWO-LOCUS MODEL WITH SUBDIVIDED POPULATION STRUCTURE.

The diffusion-generator approximation technique developed by De Iorio and Griffiths (2004a) is a very useful method of constructing importance sampling proposal distributions. Being based on general mathematical principles, the method can be applied to various models in population genetics. In this paper we extend the technique to the neutral coalescent model with recombination, thus obtaining novel sampling distributions for the two-locus model.