Related papers: Computing phylogenetic invariants for time-reversi…
Phylogenetics is the study of the evolutionary relationships between organisms. One of the main challenges in the field is to take biological data for a group of organisms and to infer an evolutionary tree, a graph that represents these…
Estimating phylogenetic trees is an important problem in evolutionary biology, environmental policy and medicine. Although trees are estimated, their uncertainties are discarded by mathematicians working in tree space. Here we explicitly…
Linear neural network layers that are either equivariant or invariant to permutations of their inputs form core building blocks of modern deep learning architectures. Examples include the layers of DeepSets, as well as linear layers…
The Dollo model for reconstructing evolutionary trees from binary characters has been proposed as a generalization of the infinite sites model, also known as the Perfect Phylogeny. In particular, the Dollo model is considered more realistic…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
By invoking the concept of twisted Poincar\' e symmetry of the algebra of functions on a Minkowski space-time, we demonstrate that the noncommutative space-time with the commutation relations $[x_\mu,x_\nu]=i\theta_{\mu\nu}$, where…
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.…
Markov chains are a common framework for individual-based state and time discrete models in ecology and evolution. Their use, however, is largely limited to systems with a low number of states, since the transition matrices involved pose…
Mixed-effects models are among the most commonly used statistical methods for the exploration of multispecies data. In recent years, also Joint Species Distribution Models and Generalized Linear Latent Variale Models have gained in…
Phylogenetic networks can represent evolutionary events that cannot be described by phylogenetic trees. These networks are able to incorporate reticulate evolutionary events such as hybridization, introgression, and lateral gene transfer.…
We deal with germs of diffeomorphisms that are reversible under an involution. We establish that this condition implies that, in general, both the family of reversing symmetries and the group of symmetries are not finite, in contrast with…
The reconstruction of phylogenies from DNA or protein sequences is a major task of computational evolutionary biology. Common phenomena, notably variations in mutation rates across genomes and incongruences between gene lineage histories,…
The evolution of molecular and phenotypic traits is commonly modelled using Markov processes along a phylogeny. This phylogeny can be a tree, or a network if it includes reticulations, representing events such as hybridization or admixture.…
A common problem in phylogenetics is to try to infer a species phylogeny from gene trees. We consider different variants of this problem. The first variant, called Unrestricted Minimal Episodes Inference, aims at inferring a species tree…
The branching structure of biological evolution confers statistical dependencies on phenotypic trait values in related organisms. For this reason, comparative macroevolutionary studies usually begin with an inferred phylogeny that describes…
We introduce an extension of finite mixture models by incorporating skew-normal distributions within a Hidden Markov Model framework. By assuming a constant transition probability matrix and allowing emission distributions to vary according…
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.…
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…
We present quadrature schemes to calculate matrices, where the so-called modified Hilbert transformation is involved. These matrices occur as temporal parts of Galerkin finite element discretizations of parabolic or hyperbolic problems when…
The use of unitary invariant subspaces of a Hilbert space $\mathcal{H}$ is nowadays a recognized fact in the treatment of sampling problems. Indeed, shift-invariant subspaces of $L^2(\mathbb{R})$ and also periodic extensions of finite…