论文标题
在随机根和无根的系统发育树的樱桃和干草叉分布上
On cherry and pitchfork distributions of random rooted and unrooted phylogenetic trees
论文作者
论文摘要
树状统计对于研究介导系统发育树的进化机制很重要。为了迈向根系和未根的树之间桥接形状统计的一步，我们介绍了一项比较研究，该研究对两种被称为樱桃和干草叉数量的子树统计数据，与可分类的布置（PDA）和Yule-Harding-Kingman（YHK）模型。基于对樱桃数量和干草叉数量的联合分布的递归公式，这表明在这两个模型下，樱桃分布都是根系和无根树的对数孔。此外，樱桃的平均数量和无根树的干草叉数量分别收敛于YHK模型下的生根树的樱桃，而PDA模型的限制差距为1/4。最后，两种模型的根樱桃分布与未根树的樱桃分布之间的总变化距离。我们的结果表明，对涉及根和无根的树木形状进行统计分析需要谨慎。
Tree shape statistics are important for investigating evolutionary mechanisms mediating phylogenetic trees. As a step towards bridging shape statistics between rooted and unrooted trees, we present a comparison study on two subtree statistics known as numbers of cherries and pitchforks for the proportional to distinguishable arrangements (PDA) and the Yule-Harding-Kingman (YHK) models. Based on recursive formulas on the joint distribution of the number of cherries and that of pitchforks, it is shown that cherry distributions are log-concave for both rooted and unrooted trees under these two models. Furthermore, the mean number of cherries and that of pitchforks for unrooted trees converge respectively to those for rooted trees under the YHK model while there exists a limiting gap of 1/4 for the PDA model. Finally, the total variation distances between the cherry distributions of rooted and those of unrooted trees converge for both models. Our results indicate that caution is required for conducting statistical analysis for tree shapes involving both rooted and unrooted trees.
