Convex hull analysis of evolutionary and phylogenetic relationships between biological groups

• Published in: Journal of theoretical biology Vol. 456; pp. 34 - 40
• Main Authors: Tian, Kun, Zhao, Xin, Yau, Stephen S.-T.
• Format: Journal Article
• Language: English
• Published: England Elsevier Ltd 07.11.2018
• Subjects: Algorithms; Biological Evolution; Center point; Convex hull; Disjoint; Ebolavirus - genetics; Genome, Viral - genetics; Group comparison; Humans; Numerical Analysis, Computer-Assisted; Papillomaviridae - genetics; Phylogenetic analysis; Phylogeny; Protein Kinase C - genetics; Rhinovirus - genetics; Sequence Analysis, DNA - methods; Sequence Analysis, Protein - methods; Phylogenetic analysis; Disjoint; Convex hull; Group comparison; Center point
• ISSN: 0022-5193; 1095-8541
• DOI: 10.1016/j.jtbi.2018.07.035

•We propose a novel approach using convex hulls to study the evolutionary of biological groups.•Each sequence is represented by a vector point containing statistics information.•The convex hulls formed from the vector points of different groups are disjoint.•Five different theorems are presented for checking whether two hulls intersect.•The classification performs well together with reasonable phylogenetic trees. 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.