Toric geometry of the Cavender-Farris-Neyman model with a molecular clock

نویسندگان

چکیده

We give a combinatorial description of the toric ideal invariants Cavender-Farris-Neyman model with molecular clock (CFN-MC) on rooted binary phylogenetic tree and prove results about polytope associated to this ideal. Key polyhedral structure include that number vertices is Fibonacci number, facets can be described using “cluster” underlying tree, volume equal an Euler zig-zag number. The CFN-MC has quadratic Gröbner basis squarefree initial terms. Finally, we show Ehrhart polynomial these polytopes, therefore Hilbert series ideals, depends only leaves not topology itself. These are analogous classic for without clock. However, new techniques required because assumption destroys fiber product governs group-based models

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ژورنال

عنوان ژورنال: Advances in Applied Mathematics

سال: 2021

ISSN: ['1090-2074', '0196-8858']

DOI: https://doi.org/10.1016/j.aam.2020.102119