Related papers: Impossibility of phylogeny reconstruction from $k$…
The log-det distance between two aligned DNA sequences was introduced as a tool for statistically consistent inference of a gene tree under simple non-mixture models of sequence evolution. Here we prove that the log-det distance, coupled…
Phylogenetic networks are necessary to represent the tree of life expanded by edges to represent events such as horizontal gene transfers, hybridizations or gene flow. Not all species follow the paradigm of vertical inheritance of their…
We consider the phylogenetic tree reconstruction problem with insertions and deletions (indels). Phylogenetic algorithms proceed under a model where sequences evolve down the model tree, and given sequences at the leaves, the problem is to…
In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of…
Maximum likelihood is one of the most widely used techniques to infer evolutionary histories. Although it is thought to be intractable, a proof of its hardness has been lacking. Here, we give a short proof that computing the maximum…
The general Markov plus invariable sites (GM+I) model of biological sequence evolution is a two-class model in which an unknown proportion of sites are not allowed to change, while the remainder undergo substitutions according to a Markov…
The amount of non-unique sequence (non-singletons) in a genome directly affects the difficulty of read alignment to a reference assembly for high throughput-sequencing data. Although a greater length increases the chance for reads being…
In previous work, we gave asymptotic counting results for the number of tree-child and normal networks with $k$ reticulation vertices and explicit exponential generating functions of the counting sequences for $k=1,2,3$. The purpose of this…
We derive the asymptotic distribution of the total length $L_n$ of a $\operatorname {Beta}(2-\alpha,\alpha)$-coalescent tree for $1<\alpha<2$, starting from $n$ individuals. There are two regimes: If $\alpha\le1/2(1+\sqrt{5})$, then $L_n$…
Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…
Most of major algorithms for phylogenetic tree reconstruction assume that sequences in the analyzed set either do not have any offspring, or that parent sequences can maximally mutate into just two descendants. The graph resulting from such…
Phylogenetic data arising on two possibly different tree topologies might be mixed through several biological mechanisms, including incomplete lineage sorting or horizontal gene transfer in the case of different topologies, or simply…
Applying a method to reconstruct a phylogenetic tree from random data provides a way to detect whether that method has an inherent bias towards certain tree `shapes'. For maximum parsimony, applied to a sequence of random 2-state data, each…
Supertree methods are tree reconstruction techniques that combine several smaller gene trees (possibly on different sets of species) to build a larger species tree. The question of interest is whether the reconstructed supertree converges…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
We introduce new methods for phylogenetic tree quartet construction by using machine learning to optimize the power of phylogenetic invariants. Phylogenetic invariants are polynomials in the joint probabilities which vanish under a model of…
Distance-based approaches in phylogenetics such as Neighbor-Joining are a fast and popular approach for building trees. These methods take pairs of sequences from them construct a value that, in expectation, is additive under a stochastic…
Methods of phylogenetic inference use more and more complex models to generate trees from data. However, even simple models and their implications are not fully understood. Here, we investigate the two-state Markov model on a tripod tree,…
Recombination is a powerful evolutionary process that shapes the genetic diversity observed in the populations of many species. Reconstructing genealogies in the presence of recombination from sequencing data is a very challenging problem,…
Phylogenetic networks provide a more general description of evolutionary relationships than rooted phylogenetic trees. One way to produce a phylogenetic network is to randomly place $k$ arcs between the edges of a rooted binary phylogenetic…