arXiv subjects

Gerard Ribas

Publications and source records attributed to Gerard Ribas.

4 recordsLinked to original sources

arXiv2026

Polynomial encoding of rooted trees with branch lengths

Phylogenetic trees are rooted trees with branch lengths that record genetic divergence or elapsed time, and quantifying differences between them is central to a wide range of evolutionary and epidemiological analyses. Graph-polynomial encodings of rooted trees provide an accurate, interpretable, and computationally efficient way to compare tree shapes, but existing polynomial encodings must be paired with auxiliary structures to study rooted trees with branch lengths. We introduce a bivariate polynomial encoding that incorporates branch lengths directly into a recursive computation from the leaf vertices to the root vertex of a tree. We prove that, for rooted trees with branch lengths and no vertices of degree two, which include all standard phylogenetic trees, two trees have the same polynomial if and only if their underlying unlabeled trees are isomorphic and the branch lengths of corresponding edges are equal. We apply the polynomial encoding to three published HIV-1 phylogenies sampled in different epidemiological settings and show that it accurately separates the three datasets based on their tree topologies and branch lengths, outperforming previous polynomial-based approaches for analyzing rooted trees with branch lengths.

q-bio.PE↗

arXiv2026

A $\mu$-distance for semidirected orchard phylogenetic networks

In evolutionary biology, phylogenetic networks are now widely used to represent the historical relationships between species and population, when this history includes reticulation events such as hybridization, gene flow and admixture between populations. Semidirected phylogenetic networks are appropriate models when the direction of some edges and the root position are not identifiable from data. Comparing semidirected networks is important in many applications. For rooted and directed networks, a $\mu$-representation was originally introduced to distinguish tree-child networks, and has since been extended in two different directions: to the larger class of orchard directed networks by adding an extra component that counts paths to reticulations; and to semidirected networks, through an edge-based variant. However, the latter does not provide a distance between semidirected and orchard networks. We introduce here a new edge-based $\mu$-representation capable of distinguishing distinct orchard binary semidirected networks. For this class, we provide a reconstruction algorithm and therefore obtain a true distance that is computable in polynomial time.

math.CO↗

arXiv2023

Generation of orchard and tree-child networks

Phylogenetic networks are an extension of phylogenetic trees that allow for the representation of reticulate evolution events. One of the classes of networks that has gained the attention of the scientific community over the last years is the class of orchard networks, that generalizes tree-child networks, one of the most studied classes of networks. In this paper we focus on the combinatorial and algorithmic problem of the generation of orchard networks, and also of tree-child networks. To this end, we use that these networks are defined as those that can be recovered by a reversing a certain reduction process. Then, we show how to choose a ``minimum'' reduction process among all that can be applied to a network, and hence we get a unique representation of the network that, in fact, can be given in terms of sequences of pairs of integers, whose length is related to the number of leaves and reticulations of the network. Therefore, the generation of networks is reduced to the generation of such sequences of pairs. Our main result is a recursive method for the efficient generation of all minimum sequences, and hence of all orchard (or tree-child) networks with a given number of leaves and reticulations. An implementation in C of the algorithms described in this paper, along with some computational experiments, can be downloaded from the public repository https://github.com/gerardet46/OrchardGenerator. Using this implementation, we have computed the number of orchard networks with at most 6 leaves and 8 reticulations.

q-bio.PE↗

arXiv2023

Comparison of orchard networks using their extended $μ$-representation

Phylogenetic networks generalize phylogenetic trees in order to model reticulation events. Although the comparison of phylogenetic trees is well studied, and there are multiple ways to do it in an efficient way, the situation is much different for phylogenetic networks. Some classes of phylogenetic networks, mainly tree-child networks, are known to be classified efficiently by their $μ$-representation, which essentially counts, for every node, the number of paths to each leaf. In this paper, we introduce the extended $μ$-representation of networks, where the number of paths to reticulations is also taken into account. This modification allows us to distinguish orchard networks and to define a sound metric on the space of such networks that can, moreover, be computed efficiently. The class of orchard networks, as well as being one of the classes with biological significance (one such network can be interpreted as a tree with extra arcs involving coexisting organisms), is one of the most generic ones (in mathematical terms) for which such a representation can (conjecturally) exist, since a slight relaxation of the definition leads to a problem that is Graph Isomorphism Complete.

q-bio.PE↗