Related papers: Impossibility of phylogeny reconstruction from $k$…
Phylogenetics is now fundamental in life sciences, providing insights into the earliest branches of life and the origins and spread of epidemics. However, finding suitable phylogenies from the vast space of possible trees remains…
We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the…
The inference of phylogenetic networks, which model complex evolutionary processes including hybridization and gene flow, remains a central challenge in evolutionary biology. Until now, statistically consistent inference methods have been…
The last decade brought a significant increase in the amount of data and a variety of new inference methods for reconstructing the detailed evolutionary history of various cancers. This brings the need of designing efficient procedures for…
Phylogenetic trees are the fundamental mathematical representation of evolutionary processes in biology. They are also objects of interest in pure mathematics, such as algebraic geometry and combinatorics, due to their discrete geometry.…
A major task of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on a tree. Given samples from the leaves of the Markov chain, the goal is to reconstruct…
Diffusion processes on trees are commonly used in evolutionary biology to model the joint distribution of continuous traits, such as body mass, across species. Estimating the parameters of such processes from tip values presents challenges…
We introduce a notion of finite sampling consistency for phylogenetic trees and show that the set of finitely sampling consistent and exchangeable distributions on n leaf phylogenetic trees is a polytope. We use this polytope to show that…
This paper extends the semiconservative quasispecies equations to account for arbitrary post-replication lesion repair efficiency. Such an extension could be an important tool for understanding processes such as cancer development and stem…
Consider a population that is expanding in two-dimensional space. Suppose we collect data from a sample of individuals taken at random either from the entire population, or from near the outer boundary of the population. A quantity of…
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$…
Species trees represent the historical divergences of populations or species, while gene trees trace the ancestry of individual gene copies sampled within those populations. In cases involving rapid speciation, gene trees with topologies…
Tree trace reconstruction aims to learn the binary node labels of a tree, given independent samples of the tree passed through an appropriately defined deletion channel. In recent work, Davies, R\'acz, and Rashtchian used combinatorial…
The stationary distribution of allele frequencies under a variety of Wright--Fisher $k$-allele models with selection and parent independent mutation is well studied. However, the statistical properties of maximum likelihood estimates of…
Background: With the fast development of next generation sequencing technologies, increasing numbers of genomes are being de novo sequenced and assembled. However, most are in fragmental and incomplete draft status, and thus it is often…
Null models of binary phylogenetic trees are useful for testing hypotheses on real world phylogenies. In this paper we consider phylogenies as binary trees without edge lengths together with a sampling measure and encode them as algebraic…
How do phylogenetic reconstruction algorithms go astray when they return incorrect trees? This simple question has not been answered in detail, even for maximum parsimony (MP), the simplest phylogenetic criterion. Understanding MP has…
A major problem for inferring species trees from gene trees is that evolutionary processes can sometimes favour gene tree topologies that conflict with an underlying species tree. In the case of incomplete lineage sorting, this phenomenon…
Classification of gene trees is an important task both in the analysis of multi-locus phylogenetic data, and assessment of the convergence of Markov Chain Monte Carlo (MCMC) analyses used in Bayesian phylogenetic tree reconstruction. The…
Comparative analyses of phylogenetic trees typically require identical taxon sets, however, in practice, trees often include distinct but overlapping taxa. Pruning non-shared leaves discards phylogenetic signal, whereas tree completion can…