Herbst Lina, Li Heyang, Steel Mike
Institute of Mathematics and Computer Science, University of Greifswald, Greifswald, Germany.
School of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand.
J Math Biol. 2019 May;78(6):1953-1979. doi: 10.1007/s00285-019-01330-x. Epub 2019 Feb 13.
In phylogenetic studies, biologists often wish to estimate the ancestral discrete character state at an interior vertex v of an evolutionary tree T from the states that are observed at the leaves of the tree. A simple and fast estimation method-maximum parsimony-takes the ancestral state at v to be any state that minimises the number of state changes in T required to explain its evolution on T. In this paper, we investigate the reconstruction accuracy of this estimation method further, under a simple symmetric model of state change, and obtain a number of new results, both for 2-state characters, and r-state characters ([Formula: see text]). Our results rely on establishing new identities and inequalities, based on a coupling argument that involves a simpler 'coin toss' approach to ancestral state reconstruction.
在系统发育研究中，生物学家常常希望根据在进化树T的叶子节点上观察到的状态，来估计进化树T内部顶点v处的祖先离散特征状态。一种简单快速的估计方法——最大简约法——将v处的祖先状态设定为能使解释其在T上的进化所需的T中状态变化数量最小化的任何状态。在本文中，我们在一个简单的对称状态变化模型下，进一步研究这种估计方法的重建准确性，并针对二态特征和r态特征（[公式：见正文]）都获得了一些新结果。我们的结果依赖于基于一种耦合论证建立新的恒等式和不等式，该耦合论证涉及一种更简单的“抛硬币”方法来进行祖先状态重建。
