Phylogenetic Analysis based on two talks by CaroBeth

Phylogenetic Analysis based on two talks, by Caro-Beth Stewart, Ph. D. Department of Biological Sciences University at Albany, SUNY� c. stewart@albany. edu and Tal Pupko, Ph. D. Faculty of Life Science Tel-Aviv University talp@post. tau. ac. il Based on lectures by C-B Stewart, and by Tal Pupko

What is phylogenetic analysis and why should we perform it? Phylogenetic analysis has two major components: 1. Phylogeny inference or “tree building” — the inference of the branching orders, and ultimately the evolutionary relationships, between “taxa” (entities such as genes, populations, species, etc. ) 2. Character and rate analysis — using phylogenies as analytical frameworks for rigorous understanding of the evolution of various traits or conditions of interest Based on lectures by C-B Stewart, and by Tal Pupko

Common Phylogenetic Tree Terminology Terminal Nodes Branches or Lineages A B C D Ancestral Node or ROOT of the Tree Internal Nodes or Divergence Points (represent hypothetical ancestors of the taxa) Based on lectures by C-B Stewart, and by Tal Pupko E Represent the TAXA (genes, populations, species, etc. ) used to infer the phylogeny

Phylogenetic trees diagram the evolutionary relationships between the taxa Taxon B Taxon C Taxon A Taxon D No meaning to the spacing between the taxa, or to the order in which they appear from top to bottom. Taxon E This dimension either can have no scale (for ‘cladograms’), can be proportional to genetic distance or amount of change (for ‘phylograms’ or ‘additive trees’), or can be proportional to time (for ‘ultrametric trees’ or true evolutionary trees). ((A, (B, C)), (D, E)) = The above phylogeny as nested parentheses These say that B and C are more closely related to each other than either is to A, and that A, B, and C form a clade that is a sister group to the clade composed of Based on lectures by C-B Stewart, D and E. If the tree has a time scale, then and E are the most closely related. and by Tal D Pupko

A few examples of what can be inferred from phylogenetic trees built from DNA or protein sequence data: • Which species are the closest living relatives of modern humans? • Did the infamous Florida Dentist infect his patients with HIV? • What were the origins of specific transposable elements? • Plus countless others…. . Based on lectures by C-B Stewart, and by Tal Pupko

Which species are the closest living relatives of modern humans? 14 MYA Humans Gorillas Chimpanzees Bonobos Gorillas Orangutans Humans 0 15 -30 Mitochondrial DNA, most nuclear DNAencoded genes, and DNA/DNA hybridization all show that bonobos and chimpanzees are related more closely to humans than either are to gorillas. MYA 0 The pre-molecular view was that the great apes (chimpanzees, gorillas and orangutans) formed a clade separate from humans, and that humans diverged from the apes at least 15 -30 MYA. Based on lectures by C-B Stewart, and by Tal Pupko

Did the Florida Dentist infect his patients with HIV? Phylogenetic tree of HIV sequences from the DENTIST, his Patients, & Local HIV-infected People: DENTIST Patient C Patient A Patient G Patient B Patient E Patient A DENTIST Yes: The HIV sequences from these patients fall within the clade of HIV sequences found in the dentist. Local control 2 Local control 3 Patient F No Local control 9 Local control 35 Local control 3 Patient D Based on lectures by C-B Stewart, From Ou et al. (1992) and Page & Holmes (1998) and by Tal Pupko No

A few examples of what can be learned from character analysis using phylogenies as analytical frameworks: • When did specific episodes of positive Darwinian selection occur during evolutionary history? • Which genetic changes are unique to the human lineage? • What was the most likely geographical location of the common ancestor of the African apes and humans? • Plus countless others…. . Based on lectures by C-B Stewart, and by Tal Pupko

The number of unrooted trees increases in a greater than exponential manner with number of taxa A B C A C B D D E A B C F D E (2 N - 5)!! = # unrooted trees for N taxa Based on lectures by C-B Stewart, and by Tal Pupko

Inferring evolutionary relationships between the taxa requires rooting the tree: B To root a tree mentally, imagine that the tree is made of string. Grab the string at the root and tug on it until the ends of the string (the taxa) fall opposite the root: Root D Unrooted tree A A Note that in this rooted tree, taxon A is no more closely related to taxon B than it is to C or D. C B C D Rooted tree Root Based on lectures by C-B Stewart, and by Tal Pupko

Now, try it again with the root at another position: B C Root Unrooted tree D A A B C D Rooted tree Root Note that in this rooted tree, taxon A is most closely related to taxon B, and together they are equally distantly related to taxa C and D. Based on lectures by C-B Stewart, and by Tal Pupko

An unrooted, four-taxon tree theoretically can be rooted in five different places to produce five different rooted trees A The unrooted tree 1: 4 1 B Rooted tree 1 a 2 Rooted tree 1 b C 5 D 3 Rooted tree 1 c Rooted tree 1 d Rooted tree 1 e B A A C D A B B D C C A A D D D B B These trees show five different evolutionary relationships among the taxa! Based on lectures by C-B Stewart, and by Tal Pupko

There are two major ways to root trees: By outgroup: Uses taxa (the “outgroup”) that are known to fall outside of the group of interest (the “ingroup”). Requires some prior knowledge about the relationships among the taxa. The outgroup can either be species (e. g. , birds to root a mammalian tree) or previous gene duplicates (e. g. , a-globins to root b-globins). outgroup By midpoint or distance: Roots the tree at the midway point A between the two most distant taxa in the tree, as determined by branch 10 lengths. Assumes that the taxa are evolving in a clock-like manner. This assumption is built into some of the distance-based tree building methods. Based on lectures by C-B Stewart, and by Tal Pupko d (A, D) = 10 + 3 + 5 = 18 Midpoint = 18 / 2 = 9 C 3 B 2 2 5 D

Each unrooted tree theoretically can be rooted anywhere along any of its branches C A D B A C B A B x = D E C F D E (2 N - 3)!! = # unrooted trees for N taxa Based on lectures by C-B Stewart, and by Tal Pupko

Molecular phylogenetic tree building methods: Are mathematical and/or statistical methods for inferring the divergence order of taxa, as well as the lengths of the branches that connect them. There are many phylogenetic methods available today, each having strengths and weaknesses. Most can be classified as follows: COMPUTATIONAL METHOD Characters Distances DATA TYPE Optimality criterion Clustering algorithm PARSIMONY MAXIMUM LIKELIHOOD MINIMUM EVOLUTION UPGMA LEAST SQUARES NEIGHBOR-JOINING Based on lectures by C-B Stewart, and by Tal Pupko

Types of data used in phylogenetic inference: Character-based methods: Use the aligned characters, such as DNA or protein sequences, directly during tree inference. Taxa Species Species A B C D E Characters ATGGCTATTCTTATAGTACG ATCGCTAGTCTTATATTACA TTCACTAGACCTGTGGTCCA TTGACCAGACCTGTGGTCCG TTGACCAGTTCTCTAGTTCG Distance-based methods: Transform the sequence data into pairwise distances (dissimilarities), and then use the matrix during tree building. Species Species A B C D E A ---0. 23 0. 87 0. 73 0. 59 B 0. 20 ---0. 59 1. 12 0. 89 C 0. 50 0. 40 ---0. 17 0. 61 D 0. 45 0. 55 0. 15 ---0. 31 E 0. 40 0. 50 0. 40 0. 25 ---- Based on 2 -parameter lectures by distance C-B Stewart, Example 2: Kimura and by Talof. Pupko (estimate of the true number substitutions between taxa) Example 1: Uncorrected “p” distance (=observed percent sequence difference)

Computational methods for finding optimal trees: Exact algorithms: "Guarantee" to find the optimal or "best" tree for the method of choice. Two types used in tree building: Exhaustive search: Evaluates all possible unrooted trees, choosing the one with the best score for the method. Branch-and-bound search: Eliminates the parts of the search tree that only contain suboptimal solutions. Heuristic algorithms: Approximate or “quick-and-dirty” methods that attempt to find the optimal tree for the method of choice, but cannot guarantee to do so. Heuristic searches often operate by “hill-climbing” methods. Based on lectures by C-B Stewart, and by Tal Pupko

Exact searches become increasingly difficult, and eventually impossible, as the number of taxa increases: A B C A C B D D E A B C D F E (2 N - 5)!! = # unrooted trees for N taxa Based on lectures by C-B Stewart, and by Tal Pupko

Heuristic search algorithms are input order dependent and can get stuck in local minima or maxima Search for global minimum local minimum Rerunning heuristic searches using different input orders of taxa can help find global minima or maxima Search for global maximum GLOBAL MAXIMUM local maximum GLOBAL MAXIMUM GLOBAL MINIMUM Based on lectures by C-B Stewart, and by Tal Pupko

Classification of phylogenetic inference methods COMPUTATIONAL METHOD Characters Distances DATA TYPE Optimality criterion Clustering algorithm PARSIMONY MAXIMUM LIKELIHOOD MINIMUM EVOLUTION UPGMA LEAST SQUARES NEIGHBOR-JOINING Based on lectures by C-B Stewart, and by Tal Pupko

Parsimony methods: Optimality criterion: The ‘most-parsimonious’ tree is the one that requires the fewest number of evolutionary events (e. g. , nucleotide substitutions, amino acid replacements) to explain the sequences. Advantages: • Are simple, intuitive, and logical (many possible by ‘pencil-and-paper’). • Can be used on molecular and non-molecular (e. g. , morphological) data. • Can tease apart types of similarity (shared-derived, shared-ancestral, homoplasy) • Can be used for character (can infer the exact substitutions) and rate analysis. • Can be used to infer the sequences of the extinct (hypothetical) ancestors. Disadvantages: • Are simple, intuitive, and logical (derived from “Medieval logic”, not statistics!) • Can be fooled by high levels of homoplasy (‘same’ events). • Can become positively misleading in the “Felsenstein Zone”: [See Stewart (1993) for a simple explanation of parsimony analysis, and Swofford et al. (1996) for a detailed explanation of various parsimony methods. ] Based on lectures by C-B Stewart, and by Tal Pupko

Branch and Bound Tal Pupko, Tel-Aviv University Based on lectures by C-B Stewart, and by Tal Pupko

There are many trees. . , We cannot go over all the trees. We will try to find a way to find the best tree. There approximate solutions… But what if we want to make sure we find the global maximum. There is a way more efficient than just go over all possible tree. It is called BRANCH AND BOUND and is a general technique in computer science, that can be applied to phylogeny. Based on lectures by C-B Stewart, and by Tal Pupko

BRANCH AND BOUND To exemplify the BRANCH AND BOUND (BNB) method, we will use an example not connected to evolution. Later, when the general BNB method is understood, we will see how to apply this method to finding the MP tree. We will present the traveling salesperson path problem (TSP). Based on lectures by C-B Stewart, and by Tal Pupko

THE TSP PROBLEM (especially adapted to israel). A guard has to visit n check-points whose location on a map is known. The problem is to find the shortest path that goes through all points exactly once (no need to come back to starting point). Naïve approach: (say for 5 points). You have 5 starting points. For each such starting point you have 4 “next steps”. For each such combination of starting point and first step, you have 3 possible second steps, etc. All together we have 5*4*3*2*1 Based on lectures by C-B Stewart, Possible solutions = and 5! by. Tal Pupko

THE TSP TREE 1 2 3 2 4 5 1 3 3 4 5 245 1 2 145 45 25 24 54 52 42 4 4 5 125 1 2 124 Based on lectures by C-B Stewart, and by Tal Pupko 5 3 5 1 2 3 4

THE SHP NAÏVE APPROACH Each solution can be represented as a permutation: (1, 2, 3, 4, 5) (1, 2, 3, 5, 4) (1, 2, 4, 3, 5) (1, 2, 4, 5, 3) (1, 2, 5, 3, 4) … We can go over the list and find the one giving the highest score. Based on lectures by C-B Stewart, and by Tal Pupko

THE SHP NAÏVE APPROACH However, for 15 points, for example, there are 1, 307, 674, 368, 000 The rate of increase of the number of solutions is too fast for this to be practical. Based on lectures by C-B Stewart, and by Tal Pupko

A TSP GREEDY HEURISTIC Start from a random point. Go to the closest point. Go to its closest point, etc. This approach doesn’t work so well… (but a reasonably close heuristic, based on simulated annealing, will be presented in a couple of lectures. ) Based on lectures by C-B Stewart, and by Tal Pupko

BNB SOLUTION TO SHP 1 2 3 2 4 5 1 Shortest path found so far = 15 3 3 4 5 245 1 2 145 45 25 24 54 52 42 4 4 5 125 1 2 124 Based on lectures by C-B Stewart, and by Tal Pupko 5 3 5 1 2 3 Score here already 16: no point in expanding the rest of the subtree 4

Back to finding the MP tree Finding the MP tree is NP-Hard (will see shortly)… BNB helps, though it is still exponential… Based on lectures by C-B Stewart, and by Tal Pupko

The MP search tree 1 3 4 is added to branch 1. 2 1 4 1 1 3 4 3 3 4 2 5 is added to branch 2. There are 5 branches 2 Based on lectures by C-B Stewart, and by Tal Pupko 2

The MP search tree 30 4 is added to branch 1. 55 43 52 54 52 53 58 61 56 59 39 61 69 Based on lectures by C-B Stewart, and by Tal Pupko 53 51 42 47 47

MP-BNB 30 4 is added to branch 1. 55 43 52 54 52 53 58 61 56 59 39 61 69 Best (minimum) value = 52 Based on lectures by C-B Stewart, and by Tal Pupko 53 51 42 47 47

MP-BNB 30 4 is added to branch 1. 55 43 52 54 52 53 58 61 56 59 39 61 69 Best record = 52 Based on lectures by C-B Stewart, and by Tal Pupko 53 51 42 47 47

MP-BNB 30 4 is added to branch 1. 55 43 52 54 52 53 58 61 56 59 39 61 69 Best record = 52 Based on lectures by C-B Stewart, and by Tal Pupko 53 51 42 47 47

MP-BNB 30 43 52 54 52 53 55 58 39 53 Best record = 52 Based on lectures by C-B Stewart, and by Tal Pupko 51 42 47 47

MP-BNB 30 43 52 54 52 53 55 58 39 53 Best record = 52 Based on lectures by C-B Stewart, and by Tal Pupko 51 42 47 47

MP-BNB 30 43 52 54 52 53 55 58 39 53 Best record = 52 Based 51 on lectures by C-B Stewart, and by Tal Pupko 51 42 47 47

MP-BNB 30 43 52 54 52 53 55 58 39 53 Best record = 52 Based 51 on 42 lectures by C-B Stewart, and by Tal Pupko 51 42 47 47

MP-BNB 30 43 52 54 52 53 55 58 39 53 Best record = 52 Based 51 on 42 lectures by C-B Stewart, and by Tal Pupko 51 42 47 47

MP-BNB 30 43 52 54 52 53 55 58 39 53 Best record = 52 Based 51 on 42 lectures by C-B Stewart, and by Tal Pupko 51 42 47 47

MP-BNB 30 43 52 54 52 53 55 58 39 53 Total # trees visited: 14 Based on lectures by C-B Stewart, and by Tal Pupko 51 42 47 Best TREE. MP score = 42 47

Order of Evaluation Matters The bound after searching this subtree will be 42. 30 Evaluate all 3 first 43 55 39 53 Total tree visited: 9 Based on lectures by C-B Stewart, and by Tal Pupko 51 42 47 47

And Now Maximum Parsimony is Computationally Intractable Felsenstein’s Dynamic Programming Algorithm for tiny maximum likelihood and more, time permitting Based on lectures by C-B Stewart, and by Tal Pupko