Ordered Leaf Attachment (OLA) Vectors can Identify Reticulation Events even in Multifurcated Trees
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912595362971648 |
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| author | Markin, Alexey Anderson, Tavis K. |
| author_facet | Markin, Alexey Anderson, Tavis K. |
| contents | Recently, a new vector encoding, Ordered Leaf Attachment (OLA), was introduced that represents $n$-leaf phylogenetic trees as $n-1$ length integer vectors by recording the placement location of each leaf. Both encoding and decoding of trees run in linear time and depend on a fixed ordering of the leaves. Here, we investigate the connection between OLA vectors and the maximum acyclic agreement forest (MAAF) problem. A MAAF represents an optimal breakdown of $k$ trees into reticulation-free subtrees, with the roots of these subtrees representing reticulation events. We introduce a corrected OLA distance index over OLA vectors of $k$ trees, which is easily computable in linear time. We prove that the corrected OLA distance corresponds to the size of a MAAF, given an optimal leaf ordering that minimizes that distance. Additionally, a MAAF can be easily reconstructed from optimal OLA vectors. We expand these results to multifurcated trees: we introduce an $O(kn \cdot m\log m)$ algorithm that optimally resolves a set of multifurcated trees given a leaf-ordering, where $m$ is the size of a largest multifurcation, and show that trees resolved via this algorithm also minimize the size of a MAAF. These results suggest a new approach to fast computation of phylogenetic networks and identification of reticulation events via random permutations of leaves. Additionally, in the case of microbial evolution, a natural ordering of leaves is often given by the sample collection date, which means that under mild assumptions, reticulation events can be identified in polynomial time on such datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ordered Leaf Attachment (OLA) Vectors can Identify Reticulation Events even in Multifurcated Trees Markin, Alexey Anderson, Tavis K. Populations and Evolution Data Structures and Algorithms Combinatorics 05C05, 68R10, 92B10 F.2.2; G.2.1; G.2.2 Recently, a new vector encoding, Ordered Leaf Attachment (OLA), was introduced that represents $n$-leaf phylogenetic trees as $n-1$ length integer vectors by recording the placement location of each leaf. Both encoding and decoding of trees run in linear time and depend on a fixed ordering of the leaves. Here, we investigate the connection between OLA vectors and the maximum acyclic agreement forest (MAAF) problem. A MAAF represents an optimal breakdown of $k$ trees into reticulation-free subtrees, with the roots of these subtrees representing reticulation events. We introduce a corrected OLA distance index over OLA vectors of $k$ trees, which is easily computable in linear time. We prove that the corrected OLA distance corresponds to the size of a MAAF, given an optimal leaf ordering that minimizes that distance. Additionally, a MAAF can be easily reconstructed from optimal OLA vectors. We expand these results to multifurcated trees: we introduce an $O(kn \cdot m\log m)$ algorithm that optimally resolves a set of multifurcated trees given a leaf-ordering, where $m$ is the size of a largest multifurcation, and show that trees resolved via this algorithm also minimize the size of a MAAF. These results suggest a new approach to fast computation of phylogenetic networks and identification of reticulation events via random permutations of leaves. Additionally, in the case of microbial evolution, a natural ordering of leaves is often given by the sample collection date, which means that under mild assumptions, reticulation events can be identified in polynomial time on such datasets. |
| title | Ordered Leaf Attachment (OLA) Vectors can Identify Reticulation Events even in Multifurcated Trees |
| topic | Populations and Evolution Data Structures and Algorithms Combinatorics 05C05, 68R10, 92B10 F.2.2; G.2.1; G.2.2 |
| url | https://arxiv.org/abs/2509.16405 |