Distance-Based Methods of Phylogenetics

Chapter 4Distance–Based Methods of Phylogenetics 暨南大學資訊工程學系黃光璿 (HUANG, Guan-Shieng) 2004/03/29

Motivation • Evolution events on genomes: • substitutions • insertions • deletions • rearrangements • We focus on cluster analysis in this chapter.

比較解剖學

蟒蛇與人

Linnaeus • 林奈 • 十八世紀博物學家 • 帶領未受訓練的學生到世界各地蒐集標本, 遠征過程中有三分之一的學生死亡. • 創立「二名法」(binomial system of nomenclature) • 屬名(genus)＋種名(species)

4.2 Advantages of Molecular Phylogenies • fundamental • evolution is defined as genetic changes • molecular clock hypothesis (Chap. 3) • In early days, taxonomists inferred genotypes from phenotypes. • phenotypes(表現型): how organisms looks • genotypes: the genes that gave rise to their physical appearance

And then • behavior (行為) • ultrastructural (超顯微結構) • biochemical characteristics were studied.

傳統研究方法有以下問題無法解決 • convergent evolution • 眼睛：humans, flies, mollusks (軟體動物) • many organisms do not have easily studied phenotypic features • bacteria (細菌) • comparing distantly related organisms • bacteria, worms, mammals • few characteristics in common!

4.3 Phylogenetic Trees

4.3.1 Terminology of Tree Reconstruction • phylogenetic tree, or dendrogram • nodes: taxonomical units • branches • terminal nodes • collected data (I, II, III, IV, V) • internal nodes • inferred ancestors (A, B, C, D) • Newick format • (((I, II), (III, IV)), V)

4.3.2 Rooted and Unrooted Trees

4.3.4 Character and Distance Data • characters (特質) • DNA sequences, protein sequences, color, behavior, response time, …… • distance • overall, pairwise difference • character data  distance data • pheneticist: prefers distance based methods • cladist: prefer character based methods

4.4 Distance Matrix Methods • UPGMA (Unweighted-Pair-Group Method with Arithmetic mean) • Transformed Distance Method • Neighbor’s Relation Method • Neighbor-Joining Method

4.4.3 Neighbor’s Relation Method • Four-point condition dAB+dCD<dAC+dBD dAB+dCD<dAD+dBC holds if the tree is additive.

Given any four points, say A, B, C, D, we have dAB+dCD dAC+dBD dAD+dBC. The smallest indicates how to pair up.

S. Sattath & A. Tversky, 1977 • For any four points, say A, B, C, D, compute dAB+dCD dAC+dBDdAD+dBC. • The smallest should be paired, and wins a score 1 for each pair. • After trying all possible quadruples, the pair wins the highest scores is grouped.

Example

The length of the branches can be determined by the outgroup method.

Theorem • If a matrix is additive, then its phylogenetic tree (unrooted, binary) can be reconstructed correctly and uniquely by the Neighbor’s Relation Method.

4.4.4 Neighbor-Joining Methods

where L:the set of all leaves (7.4)

Theorem • If a matrix is additive, then its phylogenetic tree (unrooted, binary) can be reconstructed correctly and uniquely by the Neighbor-Joining Method.

參考資料及圖片出處 • Fundamental Concepts of BioinformaticsDan E. Krane and Michael L. Raymer, Benjamin/Cummings, 2003. • Biological Sequence Analysis– Probabilistic models of proteins and nucleic acidsR. Durbin, S. Eddy, A. Krogh, G. Mitchison, Cambridge University Press, 1998. • Biology, by Sylvia S. Mader, 8th edition, McGraw-Hill, 2003.

Distance-Based Methods of Phylogenetics