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Article overview
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Phylogenetic ideals and varieties for the general Markov model | | Elizabeth S. Allman
; John A. Rhodes
; | | Date: |
28 Oct 2004 | | Subject: | Algebraic Geometry; Statistics; Populations and Evolution | math.AG math.ST q-bio.PE | | Abstract: | The general Markov model of the evolution of biological sequences along a tree leads to a parameterization of an algebraic variety. Understanding this variety and the polynomials, called phylogenetic invariants, which vanish on it, is a problem within the broader area of Algebraic Statistics. For an arbitrary trivalent tree, we determine the full ideal of invariants for the 2-state model, establishing a conjecture of Pachter-Sturmfels. For the $kappa$-state model, we reduce the problem of determining a defining set of polynomials to that of determining a defining set for a 3-leaved tree. Along the way, we prove several new cases of a conjecture of Garcia-Stillman-Sturmfels on certain statistical models on star trees, and reduce their conjecture to a family of subcases. | | Source: | arXiv, math.AG/0410604 | | Services: | Forum | Review | PDF | Favorites | |
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