Detecting Recent Positive Selection with a Single Locus Test Bipartitioning the Coalescent Tree

Statistical summaries of unlabelled evolutionary trees

Rooted and ranked phylogenetic trees are mathematical objects that are useful in modelling hierarchical data and evolutionary relationships with applications to many fields such as evolutionary biology and genetic epidemiology. Bayesian phylogenetic inference usually explores the posterior distribution of trees via Markov chain Monte Carlo methods. However, assessing uncertainty and summarizing distributions remains challenging for these types of structures. While labelled phylogenetic trees have been extensively studied, relatively less literature exists for unlabelled trees that are increasingly useful, for example when one seeks to summarize samples of trees obtained with different methods, or from different samples and environments, and wishes to assess the stability and generalizability of these summaries. In our paper, we exploit recently proposed distance metrics of unlabelled ranked binary trees and unlabelled ranked genealogies, or trees equipped with branch lengths, to define the Fréchet mean, variance and interquartile sets as summaries of these tree distributions. We provide an efficient combinatorial optimization algorithm for computing the Fréchet mean of a sample or of distributions on unlabelled ranked tree shapes and unlabelled ranked genealogies. We show the applicability of our summary statistics for studying popular tree distributions and for comparing the SARS-CoV-2 evolutionary trees across different locations during the COVID-19 epidemic in 2020. Our current implementations are publicly available at https://github.com/RSamyak/fmatrix.

Robust detection of natural selection using a probabilistic model of tree imbalance

Neutrality tests such as Tajima's D and Fay and Wu's H are standard implements in the population genetics toolbox. One of their most common uses is to scan the genome for signals of natural selection. However, it is well understood that D and H are confounded by other evolutionary forces-in particular, population expansion-that may be unrelated to selection. Because they are not model-based, it is not clear how to deconfound these tests in a principled way. In this article, we derive new likelihood-based methods for detecting natural selection, which are robust to fluctuations in effective population size. At the core of our method is a novel probabilistic model of tree imbalance, which generalizes Kingman's coalescent to allow certain aberrant tree topologies to arise more frequently than is expected under neutrality. We derive a frequency spectrum-based estimator that can be used in place of D, and also extend to the case where genealogies are first estimated. We benchmark our methods on real and simulated data, and provide an open source software implementation.

Sweeps in time: leveraging the joint distribution of branch lengths

Current methods of identifying positively selected regions in the genome are limited in two key ways: the underlying models cannot account for the timing of adaptive events and the comparison between models of selective sweeps and sequence data is generally made via simple summaries of genetic diversity. Here, we develop a tractable method of describing the effect of positive selection on the genealogical histories in the surrounding genome, explicitly modeling both the timing and context of an adaptive event. In addition, our framework allows us to go beyond analyzing polymorphism data via the site frequency spectrum or summaries thereof and instead leverage information contained in patterns of linked variants. Tests on both simulations and a human data example, as well as a comparison to SweepFinder2, show that even with very small sample sizes, our analytic framework has higher power to identify old selective sweeps and to correctly infer both the time and strength of selection. Finally, we derived the marginal distribution of genealogical branch lengths at a locus affected by selection acting at a linked site. This provides a much-needed link between our analytic understanding of the effects of sweeps on sequence variation and recent advances in simulation and heuristic inference procedures that allow researchers to examine the sequence of genealogical histories along the genome.

Selective Sweeps Under Dominance and Inbreeding

A major research goal in evolutionary genetics is to uncover loci experiencing positive selection. One approach involves finding 'selective sweeps' patterns, which can either be 'hard sweeps' formed by de novo mutation, or 'soft sweeps' arising from recurrent mutation or existing standing variation. Existing theory generally assumes outcrossing populations, and it is unclear how dominance affects soft sweeps. We consider how arbitrary dominance and inbreeding via self-fertilization affect hard and soft sweep signatures. With increased self-fertilization, they are maintained over longer map distances due to reduced effective recombination and faster beneficial allele fixation times. Dominance can affect sweep patterns in outcrossers if the derived variant originates from either a single novel allele, or from recurrent mutation. These models highlight the challenges in distinguishing hard and soft sweeps, and propose methods to differentiate between scenarios.

Adaptation in structured populations and fuzzy boundaries between hard and soft sweeps

Selective sweeps, the genetic footprint of positive selection, have been extensively studied in the past decades, with dozens of methods developed to identify swept regions. However, these methods suffer from both false positive and false negative reports, and the candidates identified with different methods are often inconsistent with each other. We propose that a biological cause of this problem can be population subdivision, and a technical cause can be incomplete, or inaccurate, modeling of the dynamic process associated with sweeps. Here we used simulations to show how these effects interact and potentially cause bias. In particular, we show that sweeps maybe misclassified as either hard or soft, when the true time stage of a sweep and that implied, or pre-supposed, by the model do not match. We call this "temporal misclassification". Similarly, "spatial misclassification (softening)" can occur when hard sweeps, which are imported by migration into a new subpopulation, are falsely identified as soft. This can easily happen in case of local adaptation, i.e. when the sweeping allele is not under positive selection in the new subpopulation, and the underlying model assumes panmixis instead of substructure. The claim that most sweeps in the evolutionary history of humans were soft, may have to be reconsidered in the light of these findings.