环境序列样本的系统发育Kantorovich-Rubinstein度量
The phylogenetic Kantorovich-Rubinstein metric for environmental sequence samples
摘要：
使用现代技术，现在通常通过对从给定环境中大量提取的DNA或RNA进行测序来调查微生物群落。需要采用比较方法，根据这类数据集，说明两个社区的差异程度。UniFrac是一种建立在两个社区之间基于遗传学距离的方法，是这些分析中最常用的工具之一。我们为这种方法提供了一个基础，如果一个等同于一个宏基因组样本与其经验分布的参考系统发育树，那么两个样本之间的加权UniFrac距离只是经典的Kantorovich-Rubinstein（KR）距离之间的相应的经验分布。我们证明，这种KR距离和扩展，它所产生的将不确定性的位置的样本点可以写为一个容易计算的积分树，我们开发$L^p$ Zolotarev型推广的度量，我们展示了零假设“两个社区之间没有差异”的自然排列检验的p值如何可以使用由树索引的高斯过程的泛函来近似。我们与$L^2$的情况下，方差分析型分解，并发现其相关的高斯函数的分布是一个独立的$χ_1^2$随机变量的可计算的线性组合。
英文摘要：
Using modern technology, it is now common to survey microbial communities by sequencing DNA or RNA extracted in bulk from a given environment. Comparative methods are needed that indicate the extent to which two communities differ given data sets of this type. UniFrac, a method built around a somewhat ad hoc phylogenetics-based distance between two communities, is one of the most commonly used tools for these analyses. We provide a foundation for such methods by establishing that if one equates a metagenomic sample with its empirical distribution on a reference phylogenetic tree, then the weighted UniFrac distance between two samples is just the classical Kantorovich-Rubinstein (KR) distance between the corresponding empirical distributions. We demonstrate that this KR distance and extensions of it that arise from incorporating uncertainty in the location of sample points can be written as a readily computable integral over the tree, we develop $L^p$ Zolotarev-type generalizations of the metric, and we show how the p-value of the resulting natural permutation test of the null hypothesis "no difference between the two communities" can be approximated using a functional of a Gaussian process indexed by the tree. We relate the $L^2$ case to an ANOVA-type decomposition and find that the distribution of its associated Gaussian functional is that of a computable linear combination of independent $χ_1^2$ random variables.
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