Lewitus Eric, Morlon Helene
Institut de Biologie (IBENS), École Normale Supérieure, Paris, France;
Syst Biol. 2016 May;65(3):495-507. doi: 10.1093/sysbio/syv116. Epub 2015 Dec 12.
Phylogenetic trees are central to many areas of biology, ranging from population genetics and epidemiology to microbiology, ecology, and macroevolution. The ability to summarize properties of trees, compare different trees, and identify distinct modes of division within trees is essential to all these research areas. But despite wide-ranging applications, there currently exists no common, comprehensive framework for such analyses. Here we present a graph-theoretical approach that provides such a framework. We show how to construct the spectral density profile of a phylogenetic tree from its Laplacian graph. Using ultrametric simulated trees as well as non-ultrametric empirical trees, we demonstrate that the spectral density successfully identifies various properties of the trees and clusters them into meaningful groups. Finally, we illustrate how the eigengap can identify modes of division within a given tree. As phylogenetic data continue to accumulate and to be integrated into various areas of the life sciences, we expect that this spectral graph-theoretical framework to phylogenetics will have powerful and long-lasting applications.
系统发育树在生物学的许多领域都至关重要，从群体遗传学、流行病学到微生物学、生态学以及宏观进化。总结树的属性、比较不同的树以及识别树内不同的分裂模式的能力对于所有这些研究领域都是必不可少的。但是，尽管有广泛的应用，目前对于此类分析尚无通用、全面的框架。在此，我们提出一种图论方法来提供这样一个框架。我们展示了如何从其拉普拉斯图构建系统发育树的谱密度轮廓。使用超度量模拟树以及非超度量经验树，我们证明谱密度成功识别了树的各种属性并将它们聚类为有意义的组。最后，我们说明了特征间隙如何识别给定树内的分裂模式。随着系统发育数据不断积累并被整合到生命科学的各个领域，我们预计这种用于系统发育学的谱图论框架将有强大且持久的应用。
