Geometry of the Kimura 3-parameter model
Geometry of the Kimura 3-parameter model
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Kimura 3 参数模型的几何结构
DOI：
10.1016/j.aam.2007.09.003
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Jesús Fernández
中科院分区：
文献类型：
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作者：
M. Casanellas;Jesús Fernández
木村3参数模型是遗传学中最常用的模型之一。与之相关的仿射代数簇W是复曲面簇。我们研究它的几何，我们证明了它是同构的仿射空间的几何商的有限群，这是完全描述。因此，我们能够研究W的奇点，并证明生物学意义的点是光滑点。然后，我们给出了一个算法，用于构建一组最小生成元的局部化理想在这些点，对于任意数量的叶子n。这导致了一个重大的改进系统发育重建方法的基础上代数几何。
The Kimura 3-parameter model on a tree of n leaves is one of the most used in phylogenetics. The affine algebraic variety W associated to it is a toric variety. We study its geometry and we prove that it is isomorphic to a geometric quotient of the affine space by a finite group, which is completely described. As a consequence, we are able to study the singularities of W and prove that the biologically meaningful points are smooth points. Then we give an algorithm for constructing a set of minimal generators of the localized ideal at these points, for an arbitrary number of leaves n. This leads to a major improvement of phylogenetic reconstruction methods based on algebraic geometry.