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The method of multivariable Mendelian randomization uses genetic variants to instrument multiple exposures, to estimate the effect that a given exposure has on an outcome conditional on all other exposures included in a linear model.…

Methodology · Statistics 2024-08-20 Ashish Patel , James Lane , Stephen Burgess

In this paper we propose a method and discuss its computational implementation as an integrated tool for the analysis of viral genetic diversity on data generated by high-throughput sequencing. Most methods for viral diversity estimation…

In phylogenomics, species-tree methods must contend with two major sources of noise; stochastic gene-tree variation under the multispecies coalescent model (MSC) and finite-sequence substitutional noise. Fast agglomerative methods such as…

Populations and Evolution · Quantitative Biology 2025-07-11 Georgios Aliatimis , Ruriko Yoshida , Burak Boyaci , James A. Grant

We consider species tree estimation under a standard stochastic model of gene tree evolution that incorporates incomplete lineage sorting (as modeled by a coalescent process) and gene duplication and loss (as modeled by a branching…

Probability · Mathematics 2020-07-15 Max Hill , Brandon Legried , Sebastien Roch

Phylogenetic species trees typically represent the speciation history as a bifurcating tree. Speciation events that simultaneously create more than two descendants, thereby creating polytomies in the phylogeny, are possible. Moreover, the…

Populations and Evolution · Quantitative Biology 2018-02-08 Erfan Sayyari , Siavash Mirarab

Kingman's coalescent is a random tree that arises from classical population genetic models such as the Moran model. The individuals alive in these models correspond to the leaves in the tree and the following two laws of large numbers…

Probability · Mathematics 2014-06-24 Andrej Depperschmidt , Peter Pfaffelhuber , Annika Scheuringer

When an advantageous mutation occurs in a population, the favorable allele may spread to the entire population in a short time, an event known as a selective sweep. As a result, when we sample $n$ individuals from a population and trace…

Probability · Mathematics 2007-05-23 Rick Durrett , Jason Schweinsberg

The multispecies coalescent model describes the generation of gene trees from a rooted metric species tree, and thus provides a framework for the inference of species trees from sampled gene trees. We prove that the STAR method of Liu et…

Populations and Evolution · Quantitative Biology 2012-04-20 Elizabeth S. Allman , James H. Degnan , John A. Rhodes

Consider a random permutation of $\{1, \ldots, \lfloor n^{t_2}\rfloor\}$ drawn according to the Ewens measure with parameter $t_1$ and let $K(n, t)$ denote the number of its cycles, where $t\equiv (t_1, t_2)\in\mathbb [0, 1]^2$. Next,…

Probability · Mathematics 2021-06-21 Helmut Pitters

We investigate the $\Lambda$-Seed-Bank-Wright-Fisher process, a model describing allele frequency dynamics in populations exhibiting both skewed offspring distributions and dormancy. By performing a change of measure, we condition this…

We investigate the infinitely many demes limit of the genealogy of a sample of individuals from a subdivided population subject to sporadic mass extinction events. By exploiting a separation of timescales property of Wright's island model,…

Probability · Mathematics 2009-01-29 Jesse E. Taylor , Amandine Veber

Distances between sequences based on their $k$-mer frequency counts can be used to reconstruct phylogenies without first computing a sequence alignment. Past work has shown that effective use of k-mer methods depends on 1) model-based…

Populations and Evolution · Quantitative Biology 2017-05-22 Chris Durden , Seth Sullivant

As researchers collect increasingly large molecular data sets to reconstruct the Tree of Life, the heterogeneity of signals in the genomes of diverse organisms poses challenges for traditional phylogenetic analysis. A class of phylogenetic…

Populations and Evolution · Quantitative Biology 2015-09-11 Liang Liu , Zhenxiang Xi , Shaoyuan Wu , Charles Davis , Scott V. Edwards

In population genetics, there is often interest in inferring selection coefficients. This task becomes more challenging if multiple linked selected loci are considered simultaneously. For such a situation, we propose a novel generalized…

Methodology · Statistics 2025-12-17 Ritabrata Dutta , Yuehao Xu , Sherman Khoo , Francesca Basini , Andreas Futschik

We consider a system of interacting Fisher-Wright diffusions with seed-bank. Individuals live in colonies and are subject to resampling and migration as long as they are active. Each colony has a structured seed-bank into which individuals…

Probability · Mathematics 2020-04-30 Andreas Greven , Frank den Hollander , Margriet Oomen

We consider a multi-colony version of the Wright-Fisher model with seed-bank that was recently introduced by Blath et al. Individuals live in colonies and change type via resampling and mutation. Each colony contains a seed-bank that acts…

Probability · Mathematics 2016-10-07 Giulia Pederzani , Frank den Hollander

We consider the evolution of an asexually reproducing population in an uncorrelated random fitness landscape in the limit of infinite genome size, which implies that each mutation generates a new fitness value drawn from a probability…

Populations and Evolution · Quantitative Biology 2009-11-13 Su-Chan Park , Joachim Krug

Variation in a sample of molecular sequence data informs about the past evolutionary history of the sample's population. Traditionally, Bayesian modeling coupled with the standard coalescent, is used to infer the sample's bifurcating…

Applications · Statistics 2024-10-22 Julie Zhang , Julia A. Palacios

We propose a new hierarchy of semidefinite programming relaxations for inference problems. As test cases, we consider the problem of community detection in block models. The vertices are partitioned into $k$ communities, and a graph is…

Data Structures and Algorithms · Computer Science 2020-09-22 Jess Banks , Sidhanth Mohanty , Prasad Raghavendra

The increasing availability of population-level allele frequency data across one or more related populations necessitates the development of methods that can efficiently estimate population genetics parameters, such as the strength of…

Computation · Statistics 2017-11-09 Jeffrey J. Gory , Radu Herbei , Laura S. Kubatko