Phylogenetic Reconstruction: Parsimony
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1 Phylogenetic Reconstruction: Parsimony nders Gorm Pedersen
2 Trees: terminology
3 Trees: terminology
4 Trees: terminology Reptiles is a non-monophyletic group (unless you include birds)
5 Trees: representations Three different representations of the same tree-topology
6 Trees: representations Two different representations of the same tree-topology (from T. Ryan Gregory, Understanding Evolutionary Trees, Evo Edu Outreach (2008) 1: )
7 Trees: rooted vs. unrooted Early Late rooted tree has a single node (the root) that represents a point in time that is earlier than any other node in the tree. rooted tree has directionality (nodes can be ordered in terms of earlier or later ). In the rooted tree, distance (i.e., number of mutations) between two nodes is represented along the time-axis only (the second axis just helps spread out the leafs)
8 Trees: rooted vs. unrooted Early Late rooted tree has a single node (the root) that represents a point in time that is earlier than any other node in the tree. rooted tree has directionality (nodes can be ordered in terms of earlier or later ). In the rooted tree, distance (i.e., number of mutations) between two nodes is represented along the time-axis only (the second axis just helps spread out the leafs)
9 Trees: rooted vs. unrooted Early Late rooted tree has a single node (the root) that represents a point in time that is earlier than any other node in the tree. rooted tree has directionality (nodes can be ordered in terms of earlier or later ). In the rooted tree, distance (i.e., number of mutations) between two nodes is represented along the time-axis only (the second axis just helps spread out the leafs)
10 Trees: rooted vs. unrooted In unrooted trees there is no directionality: we do not know if a node is earlier or later than another node Distance along branches directly represents node distance
11 Trees: rooted vs. unrooted In unrooted trees there is no directionality: we do not know if a node is earlier or later than another node Distance along branches directly represents node distance
12 Reconstructing a tree using noncontemporaneous data
13 ladistics: group organisms based on shared, derived characters ( synapomorphies )
14 Homology: limb structure Homology: any similarity between characters that is due to their shared ancestry
15 Homology vs. Homoplasy X X X X Homology: similar traits inherited from a common ancestor Homoplasy: similar traits are not directly caused by common ancestry (convergent evolution).
16 Homoplasy: wings
17 Molecular phylogeny B D G G T T G G G G G T T T G G G T T T G T G G T T T T T G DN and protein sequences Homologous characters inferred from alignment. Other molecular data: absence/ presence of restriction sites, DN hybridization data, antibody crossreactivity, etc. (but losing importance due to cheap, efficient sequencing).
18 Morphology vs. molecular data frican white-backed vulture (old world vulture) ndean condor (new world vulture) New and old world vultures seem to be closely related based on morphology. Molecular data indicates that old world vultures are related to birds of prey (falcons, hawks, etc.) while new world vultures are more closely related to storks Similar features presumably the result of convergent evolution
19 Phylogenetic reconstruction Nucleotide position Taxon G G G B G T G T G T D T T T
20 Phylogenetic reconstruction Nucleotide position Taxon G G G B G T G T G T D T T T
21 Parsimony criterion: choose simplest hypothesis Nucleotide position Taxon G G G B G T G T G T D T T T
22 Parsimonious reconstruction G.. B G.. T.. D T.. Nucleotide position Taxon G G G B G T G T G T D T T T
23 Parsimonious reconstruction G.. G.. T.. B G.. T.. T.. D T.. Nucleotide position Taxon G G G B G T G T G T D T T T
24 Parsimonious reconstruction G.. G.. T.. B G.. T.. T.. D T.. Nucleotide position Taxon G G G B G T G T G T D T T T
25 lternative tree: homoplasy G.. G.. G.. T.. B G.. T.. T.. T.. B G.. D T.. D T.. Nucleotide position Taxon G G G B G T G T G T D T T T
26 lternative tree: homoplasy G.. G.. G.. T.. B G.. T.. T.. T.. B G.. D T.. D T.. Nucleotide position Taxon G G G B G T G T G T D T T T T.. T.. T..
27 lternative tree: homoplasy G.. G.. G.. T.. B G.. D T.. T.. T.. B G.. D T.. T.. Nucleotide position Taxon G G G B G T G T G T D T T T T.. T.. T..
28 One character: ssumption of no homoplasy is equivalent to finding shortest tree G... G.. G.. B G... T.. T.. T.. T... B G.. D T... D T.. Nucleotide position Taxon G G G B G T G T G T D T T T T.. T.. T..
29 Phylogenetic reconstruction..g..g..t B..G..T..T D..T Nucleotide position Taxon G G G B G T G T G T D T T T
30 Phylogenetic reconstruction G.G G.G T.T B G.G T.T T.T D T.T Nucleotide position Taxon G G G B G T G T G T D T T T
31 Phylogenetic reconstruction: conflicts B D.G..G. B.T. D.T. Nucleotide position Taxon G G G B G T G T G T D T T T.G..T..T.
32 Phylogenetic reconstruction: conflicts.g..t. B.T..T..T..G. D.T. B D Nucleotide position Taxon G G G B G T G T G T D T T T
33 Phylogenetic reconstruction: conflicts B D G.G T.T B G.G D T.T Nucleotide position Taxon G G G B G T G T G T D T T T T.T T.T T.T
34 Several characters: choose shortest tree (equivalent to fewer assumptions of homoplasy) GGG GTG GGG TGT TTT B GTG TGT TTT TGT B GTG D TTT D TTT Total length of tree: 4 Total length of tree: 5 TTT TTT
35 Maximum Parsimony Maximum parsimony: the best tree is the shortest tree (the tree requiring the smallest number of mutational events) This corresponds to the tree that implies the least amount of homoplasy (convergent evolution, reversals) How do we find the best tree for a given data set?
36 Maximum Parsimony: first approach 1. onstruct list of all possible trees for data set 2. For each tree: determine length, add to list of lengths 3. When finished: select shortest tree from list 4. If several trees have the same length, then they are equally good (equally parsimonious)
37 Maximum Parsimony: problems We need algorithm for constructing list of all possible trees We need algorithm for determining length of given tree Should all mutational events have same cost?
38 onstructing list of all possible unrooted trees 1. onstruct unrooted tree from first three taxa. There is only one way of doing this 2. Starting from (1), construct the three possible derived trees by adding taxon 4 to each internal branch 3. From each of the trees constructed in step (2), construct the five possible derived trees by adding taxon 5 to each internal branch. 4. ontinue until all taxa have been added in all possible locations
39 Maximum Parsimony: problems We need algorithm for constructing list of all possible trees We need algorithm for determining length of given tree Should all mutational events have same cost?
40 lgorithm for determining length of given tree: Fitch G What is the length of this tree? (How many mutational steps are required?)
41 lgorithm for determining length of given tree: Fitch Root the tree at an arbitrary internal node (or internal branch) Visit an internal node x for which no state set has been defined, but where the state sets of x s immediate descendants (y,z) have been defined. If the state sets of y,z have common states, then assign these to x.! If there are no common states, then assign the union of y,z to x, and increase tree length by one. Repeat until all internal nodes have been visited. Note length of current tree.
42 lgorithm for determining length of given tree: Fitch G
43 lgorithm for determining length of given tree: Fitch G
44 lgorithm for determining length of given tree: Fitch G
45 lgorithm for determining length of given tree: Fitch G
46 lgorithm for determining length of given tree: Fitch G Length so far = 0
47 lgorithm for determining length of given tree: Fitch G {, } Length so far = 1
48 lgorithm for determining length of given tree: Fitch G {, } {, G} Length so far = 2
49 lgorithm for determining length of given tree: Fitch G {, G} {, } {,, G} Length so far = 3
50 lgorithm for determining length of given tree: Fitch G {, G} {, } {,, G} {, } Length so far = 3
51 lgorithm for determining length of given tree: Fitch G {, G} {, } {,, G} {, } Length of tree = 3
52 lgorithm for determining length of given tree: Fitch G Length of tree = 3 One possible reconstruction (several others exist)
53 Maximum Parsimony: problems We need algorithm for constructing list of all possible trees We need algorithm for determining length of given tree Should all mutational events have same cost?
54 Mutational events need not have the same cost G G T G T Sankoff algorithm
55 Maximum Parsimony: problems We need algorithm for constructing list of all possible trees We need algorithm for determining length of given tree Should all mutational events have same cost?
56 How many branches are there on an unrooted tree with N tips? B B D There is only one way of constructing the first tree. This tree has 3 tips and 3 branches Each time an extra taxon is added, two branches are created. tree with N tips will therefore have the following number of branches:! n branches! = 3+(N-3)*2!!! = 3+2N-6!!! = 2N-3
57 How many unrooted trees are there? tree with N tips has 2N-3 branches For each tree with N tips, we can therefore construct 2N-3 derived trees (which each have N+1 tips).
58 How many unrooted trees are there? Ntips Ntrees Nbranches = Nderived trees x 3-3 = x 3 2 x 4-3 = x 3 x 5 2 x 5-3 = x 3 x 5 x 7 2 x 6-3 = x 3 x 5 x 7 x 9 2 x 7-3 = x 3 x 5 x 7 x 9 x 11 2 x 8-3 = x 3 x 5 x 7 x 9 x 11 x N trees with n tips = n 1 i=2 (2i 3)
59 Exhaustive search impossible for large data sets No. taxa No. trees , , ,027, ,459, ,729, ,749,310, ,234,143, ,905,853,580,625
60 Branch and bound: shortcut to perfection
61 Heuristic search 1. onstruct initial tree (e.g., sequential addition); determine length 2. onstruct set of neighboring trees by making small rearrangements of initial tree; determine lengths 3. If any of the neighboring trees are better than the initial tree, then select it/them and use as starting point for new round of rearrangements. (Possibly several neighbors are equally good) 4. Repeat steps 2+3 until you have found a tree that is better than all of its neighbors. 5. This tree is a local optimum (not necessarily a global optimum!)
62 Heuristic search: hill-climbing
63 Heuristic search: local vs. global optimum
64 Types of rearrangement I: nearest neighbor interchange (NNI) Original tree Two neighbors per internal branch: tree with n tips has 2(n-3) neighbors (For example, a tree with 20 tips has 34 neighbbors)
65 Types of rearrangement II: subtree pruning and regrafting (SPR)
66 Types of rearrangement III: tree bisection and reconnection (TBR)
67 lgorithm for determining length of given tree: Sankoff G G T
68 Sankoff: length of subtrees starting at terminal node G 0 G T
69 Sankoff: length of subtrees starting at terminal node G 0
70 Sankoff: length of subtrees starting at terminal node 0 G 0
71 Sankoff: length of subtrees starting at terminal node G 0 0 0
72 Sankoff: length of subtrees starting at terminal node G
73 Sankoff: length of subtrees starting at terminal node G
74 Sankoff: minimal length of possible subtrees starting at internal node? G 0 0???? 0 0 0
75 Sankoff: minimal length of possible subtrees having nucleotide at internal node 0 S 0 S = min i [cost i + S left, i ] + min j [cost j + S right, j ] cost = 0, cost = cost G = cost T = 1
76 Sankoff: minimal length of possible subtrees having nucleotide at internal node 0 0? Nt on left branch ost 0 S = min i [cost i + S left, i ] + min j [cost j + S right, j ] G T
77 Sankoff: minimal length of possible subtrees having nucleotide at internal node 0 0? Nt on left branch S = min i [cost i + S left, i ] + min j [cost j + S right, j ] G T ost 0 +
78 Sankoff: minimal length of possible subtrees having nucleotide at internal node 0 0? Nt on left branch S = min i [cost i + S left, i ] + min j [cost j + S right, j ] G T ost 0 + =
79 Sankoff: minimal length of possible subtrees having nucleotide at internal node 0 1? Nt on left branch ost 0 + = = 1 S = min i [cost i + S left, i ] + min j [cost j + S right, j ] G T
80 Sankoff: minimal length of possible subtrees having nucleotide at internal node 0 1? Nt on left branch ost 0 + = = 1 S = min i [cost i + S left, i ] + min j [cost j + S right, j ] G T 1 + =
81 Sankoff: minimal length of possible subtrees having nucleotide at internal node 0 1? Nt on left branch ost 0 + = = 1 S = min i [cost i + S left, i ] + min j [cost j + S right, j ] G T 1 + = 1 + =
82 Sankoff: minimal length of possible subtrees having nucleotide at internal node 0 1? Nt on left branch ost 0 + = = 1 S = min i [cost i + S left, i ] + min j [cost j + S right, j ] G T 1 + = 1 + =
83 Sankoff: minimal length of possible subtrees having nucleotide at internal node S 0 0 Nt on left branch ost = 0 G T S = 1 + min j [cost j + S right, j ]
84 Sankoff: minimal length of possible subtrees having nucleotide at internal node S 0 1 Nt on left branch ost = = G T S = 1 + min j [cost j + S right, j ]
85 Sankoff: minimal length of possible subtrees having nucleotide at internal node S 0 1 Nt on left branch ost = = G 1 + = T S = 1 + min j [cost j + S right, j ]
86 Sankoff: minimal length of possible subtrees having nucleotide at internal node S 0 1 Nt on left branch ost = = G 1 + = T 1 + = S = 1 + min j [cost j + S right, j ]
87 Sankoff: minimal length of possible subtrees having nucleotide at internal node S 0 0 Nt on left branch ost = = G 1 + = T 1 + = S = 1 + min j [cost j + S right, j ]
88 Sankoff: minimal length of possible subtrees having nucleotide at internal node S = min i [cost i + S left, i ] + min j [cost j + S right, j ] S = = 1
89 Sankoff: minimal length of possible subtrees having nucleotide at internal node G
90 Sankoff: minimal length of possible subtrees having nucleotide at internal node S = = 1
91 Sankoff: minimal length of possible subtrees having nucleotide G at internal node S G = = 2
92 Sankoff: minimal length of possible subtrees having nucleotide T at internal node S T = = 2
93 Sankoff: minimal length of all possible subtrees starting at internal node G
94 Sankoff: minimal length of possible subtrees starting at all internal nodes G
95 Sankoff: smallest possible length of tree = 3 G
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