arXiv subjects

Bryan Currie

Publications and source records attributed to Bryan Currie.

4 recordsLinked to original sources

arXiv2026

Identifiability of phylogenetic networks and quintet concordance factors

Several statistical methods of phylogenetic network inference and testing for non-tree-like relationships are based on assessing genomic data through quartet Concordance Factors, the frequencies of 4-taxon topological relationships on gene trees. While such an approach obviates making several undesirable modeling assumptions, it also results in non-identifiability issues for network roots and for small cycles. In this work, an algorithm and accompanying Macaulay2 implementation are provided for computing $n$-tet Concordance Factors on any phylogenetic network. We employ this algorithm on quintet Concordance Factors, summarizing 5-taxon gene trees, to explore identifiability of level-1 networks under the Network Multispecies Coalescent model. We show some additional network features become identifiable that are not through quartets. As identifiability is a necessary prerequisite to inference by any method, this lays a foundation for future inference work.

q-bio.PE↗

arXiv2026

On Agreement Subtrees in Multiple Phylogenetic Trees

Snir and Yuster [Discrete Appl. Math. 347 (2026) 160--171] asked for the least number $h(k)$ such that $k$ unrooted binary phylogenetic trees on the same $h(k)$ leaves always share a common quartet. We give a new upper bound for the $k$-tree version of the Maximum Agreement Subtree problem, namely an upper bound for the number of leaves, on which $k$ unrooted binary phylogenetic trees always share a common induced binary subtree on $n$ leaves, which is a four-times iterated exponential function. For $h(k)$, this implies a four-times iterated exponential upper bound. We also set an exponential lower bound for $h(k)$.

math.CO↗

arXiv2026

Semialgebraic Conditions for Identifying Triangles in Phylogenetic Networks

An important consideration for a model-based method of phylogenetic network inference is the identifiability of the network parameter of the model. A recurring theme in previous works exploring this issue is that it is often difficult to identify the orientation of edges in a triangle of the network. In fact, it has been shown that for some models it is impossible to determine the orientation of triangle edges utilizing the standard algebraic technique of phylogenetic invariants. In this work, we consider one such model with a Jukes-Cantor site-substitution process and no coalescence. We give a complete semialgebraic description of three, 3-leaf Jukes-Cantor phylogenetic network models with embedded triangles. By describing these base cases, we resolve several questions about the identifiability of networks with embedded triangles. We show that for any pair of models, the intersection and set differences of the models are full-dimensional regions of the space of site-pattern probability distributions. Thus, despite being algebraically indistinguishable, these network models are not identical, nor are they identifiable (or generically identifiable). Our results also yield a straightforward biological interpretation--that the signal from a hybridization event may be immediately detectable but decays over time until it is impossible to identify the orientation of edges in the triangle of a network.

q-bio.PE↗

arXiv2024

On the maximum value of the stairs2 index

Measures of tree balance play an important role in different research areas such as mathematical phylogenetics or theoretical computer science. The balance of a tree is usually quantified in a single number, called a balance or imbalance index, and several such indices exist in the literature. Here, we focus on the stairs2 balance index for rooted binary trees, which was first introduced in the context of viral phylogenetics but has not been fully analyzed from a mathematical viewpoint yet. While it is known that the caterpillar tree uniquely minimizes the stairs2 index for all leaf numbers and the fully balanced tree uniquely maximizes the stairs2 index for leaf numbers that are powers of two, understanding the maximum value and maximal trees for arbitrary leaf numbers is an open problem in the literature. In this note, we fill this gap by showing that for all leaf numbers, there is a unique rooted binary tree maximizing the stairs2 index. Additionally, we obtain recursive and closed expressions for the maximum value of the stairs2 index of a rooted binary tree with $n$ leaves.

math.CO↗