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In this work we study the limit distribution of an appropriately normalized cophenetic index of the pure-birth tree conditioned on $n$ contemporary tips. We show that this normalized phylogenetic balance index is a submartingale that…
The reliability of a phylogenetic inference method from genomic sequence data is ensured by its statistical consistency. Bayesian inference methods produce a sample of phylogenetic trees from the posterior distribution given sequence data.…
In mathematical phylogenetics, the time-consistent galled trees provide a simple class of rooted binary network structures that can be used to represent a variety of different biological phenomena. We study the enumerative combinatorics of…
In this paper we give some estimates for nonlinear harmonic measures on trees. In particular, we estimate in terms of the size of a set $D$ the value at the origin of the solution to $ u(x)=F((x,0),\dots,(x,m-1))$ for every…
We provide a logarithmic upper bound for the disentangling number on unordered lists of leaf labeled trees. This results is useful for analyzing phylogenetic mixture models. The proof depends on interpreting multisets of trees as high…
Phylogenetic trees are a central tool in understanding evolution. They are typically inferred from sequence data, and capture evolutionary relationships through time. It is essential to be able to compare trees from different data sources…
Learning from an imbalanced dataset is a tricky proposition. Because these datasets are biased towards one class, most existing classifiers tend not to perform well on minority class examples. Conventional classifiers usually aim to…
We solve a class of optimization problems for (phylogenetic) $X$-trees or their shapes. These problems have recently appeared in different contexts, e.g. in the context of the impact of tree shapes on the size of TBR neighborhoods, but so…
Phylogenomics heavily relies on well-curated sequence data sets that consist, for each gene, exclusively of 1:1-orthologous. Paralogs are treated as a dangerous nuisance that has to be detected and removed. We show here that this severe…
We have developed an alignment-free method that calculates phylogenetic distances using a maximum likelihood approach for a model of sequence change on patterns that are discovered in unaligned sequences. To evaluate the phylogenetic…
Selective inference is considered for testing trees and edges in phylogenetic tree selection from molecular sequences. This improves the previously proposed approximately unbiased test by adjusting the selection bias when testing many trees…
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…
Fixed tree topologies are widely used in phylodynamic analyses to reduce computational burden, yet the consequences of this assumption remain insufficiently understood. Here, we systematically assess the impact of various fixed-topology…
Phylogenetic networks are a type of directed acyclic graph that represent how a set $X$ of present-day species are descended from a common ancestor by processes of speciation and reticulate evolution. In the absence of reticulate evolution,…
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…
The inference of the evolutionary history of a collection of organisms is a problem of fundamental importance in evolutionary biology. The abundance of DNA sequence data arising from genome sequencing projects has led to significant…
Here we introduce a general class of multiple calibration birth-death tree priors for use in Bayesian phylogenetic inference. All tree priors in this class separate ancestral node heights into a set of "calibrated nodes" and "uncalibrated…
Rooted binary perfect phylogenies provide a generalization of rooted binary unlabeled trees in which each leaf is assigned a positive integer value that corresponds in a biological setting to the count of the number of indistinguishable…
We propose a topological learning algorithm for the estimation of the conditional dependency structure of large sets of random variables from sparse and noisy data. The algorithm, named Maximally Filtered Clique Forest (MFCF), produces a…
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…