Invariants for level-1 phylogenetic networks under the Cavendar-Farris-Neyman model

Joseph Cummings; Benjamin Hollering; Christopher Manon

doi:10.1016/j.aam.2023.102633

Invariants for level-1 phylogenetic networks under the Cavendar-Farris-Neyman model

Joseph Cummings, Benjamin Hollering, Christopher Manon

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Phylogenetic networks model evolutionary phenomena that trees fail to capture such as horizontal gene transfer and hybridization. The same Markov models used for sequence evolution on trees can also be extended to networks and similar problems, such as determining if the network parameter is identifiable or finding the invariants of the model, can be studied. This paper focuses on finding the invariants of the Cavendar-Farris-Neyman (CFN) model on level-1 phylogenetic networks by reducing the problem to finding invariants of sunlet networks, which are level-1 networks consisting of a single cycle with leaves at each vertex. We determine all quadratic invariants for sunlet networks, and conjecture these generate the full sunlet ideal.

Original language	English
Article number	102633
Journal	Advances in Applied Mathematics
Volume	153
DOIs	https://doi.org/10.1016/j.aam.2023.102633
State	Published - Feb 2024

Bibliographical note

Publisher Copyright:
© 2023 Elsevier Inc.

Funding

Joseph Cummings was partially supported by Simons Collaboration Grant (587209) and the US National Science Foundation (DMS 2101911).Benjamin Hollering was partially supported by the US National Science Foundation (DMS 1615660).Christopher Manon was partially supported by Simons Collaboration Grant (587209) and the US National Science Foundation (DMS 2101911).

Funders	Funder number
Simons Collaboration	587209
National Science Foundation Arctic Social Science Program	DMS 1615660, DMS 2101911

Keywords

Algebraic variety
Group-based model
Markov model
Phylogenetic invariant
Phylogenetic network
Torus action

ASJC Scopus subject areas

Applied Mathematics

Access to Document

10.1016/j.aam.2023.102633

Cite this

@article{7bdc16ad734948358db77fa6d3662a82,

title = "Invariants for level-1 phylogenetic networks under the Cavendar-Farris-Neyman model",

abstract = "Phylogenetic networks model evolutionary phenomena that trees fail to capture such as horizontal gene transfer and hybridization. The same Markov models used for sequence evolution on trees can also be extended to networks and similar problems, such as determining if the network parameter is identifiable or finding the invariants of the model, can be studied. This paper focuses on finding the invariants of the Cavendar-Farris-Neyman (CFN) model on level-1 phylogenetic networks by reducing the problem to finding invariants of sunlet networks, which are level-1 networks consisting of a single cycle with leaves at each vertex. We determine all quadratic invariants for sunlet networks, and conjecture these generate the full sunlet ideal.",

keywords = "Algebraic variety, Group-based model, Markov model, Phylogenetic invariant, Phylogenetic network, Torus action",

author = "Joseph Cummings and Benjamin Hollering and Christopher Manon",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier Inc.",

year = "2024",

month = feb,

doi = "10.1016/j.aam.2023.102633",

language = "English",

volume = "153",

}

TY - JOUR

T1 - Invariants for level-1 phylogenetic networks under the Cavendar-Farris-Neyman model

AU - Cummings, Joseph

AU - Hollering, Benjamin

AU - Manon, Christopher

PY - 2024/2

Y1 - 2024/2

N2 - Phylogenetic networks model evolutionary phenomena that trees fail to capture such as horizontal gene transfer and hybridization. The same Markov models used for sequence evolution on trees can also be extended to networks and similar problems, such as determining if the network parameter is identifiable or finding the invariants of the model, can be studied. This paper focuses on finding the invariants of the Cavendar-Farris-Neyman (CFN) model on level-1 phylogenetic networks by reducing the problem to finding invariants of sunlet networks, which are level-1 networks consisting of a single cycle with leaves at each vertex. We determine all quadratic invariants for sunlet networks, and conjecture these generate the full sunlet ideal.

AB - Phylogenetic networks model evolutionary phenomena that trees fail to capture such as horizontal gene transfer and hybridization. The same Markov models used for sequence evolution on trees can also be extended to networks and similar problems, such as determining if the network parameter is identifiable or finding the invariants of the model, can be studied. This paper focuses on finding the invariants of the Cavendar-Farris-Neyman (CFN) model on level-1 phylogenetic networks by reducing the problem to finding invariants of sunlet networks, which are level-1 networks consisting of a single cycle with leaves at each vertex. We determine all quadratic invariants for sunlet networks, and conjecture these generate the full sunlet ideal.

KW - Algebraic variety

KW - Group-based model

KW - Markov model

KW - Phylogenetic invariant

KW - Phylogenetic network

KW - Torus action

UR - https://www.scopus.com/pages/publications/85174955616

UR - https://www.scopus.com/inward/citedby.url?scp=85174955616&partnerID=8YFLogxK

U2 - 10.1016/j.aam.2023.102633

DO - 10.1016/j.aam.2023.102633

M3 - Article

AN - SCOPUS:85174955616

SN - 0196-8858

VL - 153

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

M1 - 102633

ER -

Invariants for level-1 phylogenetic networks under the Cavendar-Farris-Neyman model

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this