Related papers: A balance index for phylogenetic trees based on ro…
In phylogenetics, phylogenetic trees are rooted binary trees, whereas phylogenetic networks are rooted arbitrary acyclic digraphs. Edges are directed away from the root and leaves are uniquely labeled with taxa in phylogenetic networks. For…
In mathematical phylogenetics, labeled histories describe the sequences by which sets of labeled lineages coalesce to a shared ancestral lineage. We study labeled histories for at-most-$r$-furcating trees. Consider a rooted leaf-labeled…
A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees. Previous work on this similarity measure is only concerned with the comparison of labeled trees of two…
For a model of molecular evolution to be useful for phylogenetic inference, the topology of evolutionary trees must be identifiable. That is, from a joint distribution the model predicts, it must be possible to recover the tree parameter.…
Graham and Sloane proposed in 1980 a conjecture stating that every tree has a harmonious labelling, a graph labelling closely related to additive base. Very limited results on this conjecture are known. In this paper, we proposed a…
A phylogenetic variety is an algebraic variety parameterized by a statistical model of the evolution of biological sequences along a tree. Understanding this variety is an important problem in the area of algebraic statistics with…
Phylogenetic trees are binary nonplanar trees with labelled leaves, and plane oriented recursive trees are planar trees with an increasing labelling. Both families are enumerated by double factorials. A bijection is constructed, using the…
Phylogenetic diversity is a measure for describing how much of an evolutionary tree is spanned by a subset of species. If one applies this to the (unknown) subset of current species that will still be present at some future time, then this…
The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…
Understanding the evolution of a set of genes or species is a fundamental problem in evolutionary biology. The problem we study here takes as input a set of trees describing {possibly discordant} evolutionary scenarios for a given set of…
The evolutionary relationships among organisms have traditionally been represented using rooted phylogenetic trees. However, due to reticulate processes such as hybridization or lateral gene transfer, evolution cannot always be adequately…
We study distorted metrics on binary trees in the context of phylogenetic reconstruction. Given a binary tree $T$ on $n$ leaves with a path metric $d$, consider the pairwise distances $\{d(u,v)\}$ between leaves. It is well known that these…
The selection of the most suitable evolutionary model to analyze the given molecular data is usually left to biologist's choice. In his famous book, J Felsenstein suggested that certain linear equations satisfied by the expected…
Invariants for complicated objects such as those arising in phylogenetics, whether they are invariants as matrices, polynomials, or other mathematical structures, are important tools for distinguishing and working with such objects. In this…
We consider extremal problems related to decks and multidecks of rooted binary trees (a.k.a. rooted phylogenetic tree shapes). Here, the deck (resp. multideck) of a tree $T$ refers to the set (resp. multiset) of leaf induced binary subtrees…
Trees with labelled leaves and with all other vertices of degree three play an important role in systematic biology and other areas of classification. A classical combinatorial result ensures that such trees can be uniquely reconstructed…
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…
When we apply comparative phylogenetic analyses to genome data, it is a well-known problem and challenge that some of given species (or taxa) often have missing genes. In such a case, we have to impute a missing part of a gene tree from a…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
A probabilistic reconstruction of genealogies in a polyploid population (from 2x to 4x) is investigated, by considering genetic data analyzed as the probability of allele presence in a given genotype. Based on the likelihood of all possible…