Related papers: Rank conditions on phylogenetic networks
Equivariance of linear neural network layers is well studied. In this work, we relax the equivariance condition to only be true in a projective sense. We propose a way to construct a projectively equivariant neural network through building…
Evolutionary relationships between species are usually represented in phylogenies, i.e. evolutionary trees, which are a type of networks. The terminal nodes of these trees represent species, which are made of individuals and populations…
Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of non-treelike evolutionary events, like recombination, hybridization, or lateral gene transfer. In this paper, we present and study a new…
Random forests are decision tree ensembles that can be used to solve a variety of machine learning problems. However, as the number of trees and their individual size can be large, their decision making process is often incomprehensible. In…
Motivated by a recently introduced network growth mechanism that rely on the ranking of node prestige measures [S. Fortunato \emph{et al}., Phys. Rev. Lett. \textbf{96}, 218701 (2006)], a rank-based model for weighted network evolution is…
Reticulate evolution gives rise to complex phylogenetic networks, making their interpretation challenging. A typical approach is to extract trees within such networks. Since Francis and Steel's seminal paper, "Which Phylogenetic Networks…
In biology, a phylogenetic tree is a tool to represent the evolutionary relationship between species. Unfortunately, the classical Schr\"oder tree model is not adapted to take into account the chronology between the branching nodes. In…
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 explore model based techniques of phylogenetic tree inference exercising Markov invariants. Markov invariants are group invariant polynomials and are distinct from what is known in the literature as phylogenetic invariants, although we…
Phylogenetics is a branch of computational biology that studies the evolutionary relationships among biological entities. Its long history and numerous applications notwithstanding, inference of phylogenetic trees from sequence data remains…
We introduce some natural families of distributions on rooted binary ranked plane trees with a view toward unifying ideas from various fields, including macroevolution, epidemiology, computational group theory, search algorithms and other…
Phylogenetic networks are directed acyclic graphs that depict the genomic evolution of related taxa. Reticulation nodes in such networks (nodes with more than one parent) represent reticulate evolutionary events, such as recombination,…
In biodiversity conservation it is often necessary to prioritize the species to conserve. Existing approaches to prioritization, e.g. the Fair Proportion Index and the Shapley Value, are based on phylogenetic trees and rank species…
It is possible to consider stochastic models of sequence evolution in phylogenetics in the context of a dynamical tensor description inspired from physics. Approaching the problem in this framework allows for the well developed methods of…
The general Markov model of the evolution of biological sequences along a tree leads to a parameterization of an algebraic variety. Understanding this variety and the polynomials, called phylogenetic invariants, which vanish on it, is a…
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…
Identifying undocumented or potential future interactions among species is a challenge facing modern ecologists. Recent link prediction methods rely on trait data, however large species interaction databases are typically sparse and…
Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…
A dynamical picture of phylogenetic evolution is given in terms of Markov models on a state space, comprising joint probability distributions for character types of taxonomic classes. Phylogenetic branching is a process which augments the…
A fundamental problem in the study of phylogenetic networks is to determine whether or not a given phylogenetic network contains a given phylogenetic tree. We develop a quadratic-time algorithm for this problem for binary nearly-stable…