Statistical geometry

This was one of the first network   approaches for intraspecific phylogenetics to be developed. In this method,   haplotypes are considered as geometric configurations in the HAPLOTYPE SPACE.   Numerical invariants (some function of the data whose value remains constant)   related to the length of the connections (pairwise differences) among   haplotypes are assigned to the haplotypes and statistical averages of these   invariants are then calculated. Given the value for the invariants, the   optimal network connecting the four haplotypes in each quartet is derived.   Finally, an average quartet geometry representative of the whole data set is constructed   by integrating all the quartet networks. This geometry and the associated   statistics can be used, for example, to deduce the degree of treelikeness of   the data, to detect varying positional substitution rates in sequences or to   estimate the relative temporal order of haplotype divergence. However, they   do not offer an estimate of the sequence genealogy. The statistical geometry incorporates   a model of nucleotide substitution through the estimation of haplotype   distances and its statistical nature allows a reliable assessment of the derived   conclusions.  

统计几何

这是首先发展出来的研究种内系统发育学的网络方法。在这种方法中，单倍型被认为是单倍型空间中的几何构型。将单倍型之间标准化的相互变化数表征为连接长度（成对差异），分配给各个单倍型，然后计算这些标准变化数的统计平均值。考虑单倍型之间标准步数，导出了连接四个单倍型的最优网络。最后，通过对所有四重网络的积分，构造出代表整个数据集的平均四重网络几何。该几何图形和相关的统计数据可用于推断数据的树型程度、检测序列中不同的位置替换率或估计单倍型分化的相对时间顺序。然而，它们没有提供序列谱系的估计。统计几何学通过估计单倍型距离整合了一个核苷酸替代模型，其统计性质允许对得出的结论进行可靠的评估。