1Inferring trees and estimatingrate matricesStatistics 246 Spring 2006Week 6 Lecture 22What is a tree (in this context)?Typically: labelled, binary, unrooted.Taxa (plural for taxon) at the tips (aka leaves).The topology is usually what counts.A root may be added later.3 Tree topologiesA E C D B FA E D C B FA E C D B FF B D C E AIdentical:Notidentical:4All 3 rooted, binary, tip labelled trees on3 taxa; just 1 if unrooted.A BC BAC C A B515 rooted, binary, tip labelled treeson 4 taxa; just 3 if unrooted.A C B D B C A D C D A B D C A BA B C D B A C D C B A D D B C AA D C B B D C A C A B D D A B CA B C DA C B DA D B C6All trees : >4 taxa• In general, for any strictly bifurcating rooted treewith n species, there are (2n-3)! / 2n-2(n-2)!different topologies. n #trees 5 105 15 213,458,046,676,875 20 8,200,794,532,637,891,559,375• For unrooted trees, it’s only (2n-5)! / 2n-3(n-3)!7Tree inference: some methodsLeast-squares distanceMaximum parsimonyMinimum evolutionMaximum likelihoodObjectivecriterion-basedmethodsUPGMA Neighbor-joiningWPGMASingle linkageComplete linkageClusteringmethods8Building trees: distance methods There are many ways of building trees using distance methods. Allstart by computing the pairwise distances between the sequences tobe at the tips of the tree, usually along the lines we discussed in thelast lecture, i.e. ML distance, using a rate matrix.One of the oldest distance methods, still widely used, though ratherdiscredited in the molecular evolutionary context , is UPGMA. Thisstands for unweighted pair group method with arithmetic means. It iseasy to understand quickly, and so I will describe it verbally. I don’trecommend it. For more details, seehttp://www.icp.ucl.ac.be/~opperd/private/upgma.html9Revisiting Beta-globins10 20 30 40M V H L T P E E K S A V T A L W G K V N V D E V G G E A L G R L L V V Y P W T Q BG-human- . . . . . . . . N . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . BG-macaque- - M . . A . . . A . . . . F . . . . K . . . . . . . . . . . . . . . . . . . . BG-bovine- . . . S G G . . . . . . N . . . . . . I N . L . . . . . . . . . . . . . . . . BG-platypus. . . W . A . . . Q L I . G . . . . . . . A . C . A . . . A . . . I . . . . . . BG-chicken- . . W S E V . L H E I . T T . K S I D K H S L . A K . . A . M F I . . . . . T BG-shark50 60 70 80R F F E S F G D L S T P D A V M G N P K V K A H G K K V L G A F S D G L A H L D BG-human. . . . . . . . . . S . . . . . . . . . . . . . . . . . . . . . . . . . N . . . BG-macaque. . . . . . . . . . . A . . . . N . . . . . . . . . . . . D S . . N . M K . . . BG-bovine. . . . A . . . . . S A G . . . . . . . . . . . . A . . . T S . G . A . K N . . BG-platypus. . . A . . . N . . S . T . I L . . . M . R . . . . . . . T S . G . A V K N . . BG-chicken. Y . G N L K E F T A C S Y G - - - - - . . E . A . . . T . . L G V A V T . . G BG-shark90 100 110 120N L K G T F A T L S E L H C D K L H V D P E N F R L L G N V L V C V L A H H F G BG-human. . . . . . . Q . . . . . . . . . . . . . . . . K . . . . . . . . . . . . . . . BG-macaqueD . . . . . . A . . . . . . . . . . . . . . . . K . . . . . . . V . . . R N . . BG-bovineD . . . . . . K . . . . . . . . . . . . . . . . N R . . . . . I V . . . R . . S BG-platypus. I . N . . S Q . . . . . . . . . . . . . . . . . . . . D I . I I . . . A . . S BG-chickenD V . S Q . T D . . K K . A E E . . . . V . S . K . . A K C F . V E . G I L L K BG-shark130 140K E F T P P V Q A A Y Q K V V A G V A N A L A H K Y HBG-human. . . . . Q . . . . . . . . . . . . . . . . . . . . .BG-macaque. . . . . V L . . D F . . . . . . . . . . . . . R . .BG-bovine. D . S . E . . . . W . . L . S . . . H . . G . . . .BG-platypus. D . . . E C . . . W . . L . R V . . H . . . R . . .BG-chickenD K . A . Q T . . I W E . Y F G V . V D . I S K E . . BG-shark. means same asreference sequence- means deletion10Beta-globins: Uncorrected pairwise distances Distances: between protein sequences. Calculated over: 1 to 147 Below diagonal: observed number of differences Above diagonal: number of differences per 100 amino acids …
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