论文标题
系统对称代数：系统发育中新工具的数学特性
Phylosymmetric algebras: mathematical properties of a new tool in phylogenetics
论文作者
论文摘要
在系统发育学中，对于速率矩阵集以满足矩阵乘法的闭合是有意的，因为这使得找到一组相应的跃迁矩阵，而无需计算矩阵指数。在应用程序中，拥有少量的免费参数也将导致计算时间减少，这也是有利的。我们探讨了一种通过将速率分配给内部树节点和状态为叶子的速率矩阵构建速率矩阵的方法，然后将两个状态之间的变化速率定义为分配给这两个状态的最新共同祖先的速率。我们从线性代数和图理论的角度研究了这些矩阵集的属性，并表明在矩阵乘法下生成的任何速率矩阵集都封闭。然后考虑将分配给内部树节点分配给内部树节点相等的两个速率的后果。该方法可用于开发具有少量参数但传达生物学含义的氨基酸取代的参数化模型。
In phylogenetics it is of interest for rate matrix sets to satisfy closure under matrix multiplication as this makes finding the set of corresponding transition matrices possible without having to compute matrix exponentials. It is also advantageous to have a small number of free parameters as this, in applications, will result in a reduction of computation time. We explore a method of building a rate matrix set from a rooted tree structure by assigning rates to internal tree nodes and states to the leaves, then defining the rate of change between two states as the rate assigned to the most recent common ancestor of those two states. We investigate the properties of these matrix sets from both a linear algebra and a graph theory perspective and show that any rate matrix set generated this way is closed under matrix multiplication. The consequences of setting two rates assigned to internal tree nodes to be equal are then considered. This methodology could be used to develop parameterised models of amino acid substitution which have a small number of parameters but convey biological meaning.
