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arXiv2026

Identifiability of a Simple Model of Lateral Gene Transfer

In evolutionary biology, factors like lateral gene transfer complicate the tree of life, making inference of a species tree more difficult. The phenomenon of lateral gene transfer allows genetic material to be passed between organisms as opposed to inheritance, causing the tree for a particular gene to differ from the species tree. In this work, we define a model of lateral gene transfer on site patterns. In the case where lateral gene transfer is restricted to occur only between closely related species, we show that the unrooted topology of the species tree is identifiable from SNP data on the taxa. Our proof involves showing a connection between our lateral gene transfer model and graphical models on a related tree, and uses ranks of flattenings to identify splits in the tree. We also report on results of using the singular value decomposition on flattening matrices to identify the unrooted topology in simulated data.

q-bio.PE↗

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.

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