Convex hull analysis of evolutionary and phylogenetic relationships between biological groups

Kun Tian Tsinghua University Xin Zhao Tsinghua University Stephen S.-T. Yau Tsinghua University

Data Analysis, Bio-Statistics, Bio-Mathematics mathscidoc:1904.42005

Comparing DNA and protein sequence groups plays an important role in biological evolutionary relationship research. Despite many methods available for sequence comparison, only a few can be used for group comparison. In this study, we propose a novel approach using convex hulls. We use statistical information contained within the sequences to represent each sequence as a point in high dimensional space. We find that the points belonging to one biological group are located in a different region of space than points belonging to other biological groups. To be more precise, the convex hull of the points from one group are disjoint from the convex hulls of points from other groups. This finding allows us to do phylogenetic analysis for groups in an efficient way. Five different theorems are presented for checking whether two convex hulls intersect or are disjoint. Test results for datasets related to HRV, HPV, Ebolavirus, PKC and protein phosphatase domains demonstrate that our method performs well and provides a new tool for studying group phylogeny. More significantly, the convex analysis presents a new way to search for sequences belonging to a biological group by examining points within the group’s convex hull.
Convex hull, Group comparison, Phylogenetic analysis, Center point, Disjoint
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@inproceedings{kunconvex,
  title={Convex hull analysis of evolutionary and phylogenetic relationships between biological groups},
  author={Kun Tian, Xin Zhao, and Stephen S.-T. Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190427223944504880283},
}
Kun Tian, Xin Zhao, and Stephen S.-T. Yau. Convex hull analysis of evolutionary and phylogenetic relationships between biological groups. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190427223944504880283.
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