Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.1/22

Transcription

1 Lecture 30. Phylogeny methods, part 2 (Searching tree space) Joe elsenstein epartment of Genome Sciences and epartment of iology Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.1/22

2 ll possible trees a b a c b a c b c a b etc. etc. a d c b a c b d d a c b a b c d a d c b orming all 4-species trees by adding the next species in all possible places Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.2/22

3 The number of rooted bifurcating trees: (2n 3) = (2n 3)!/ ( (n 2)! 2 n 2) Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.3/22

4 which is: species number of trees , ,135 2,027, ,45, ,72, ,74,310, ,234,143, ,05,853,580, ,458,046,676, ,10,283,353,62, ,88,783,62,510, ,332,65,870,762,850, ,643,05,476,6,771, ,200,74,532,637,81,55, Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.4/22

5 Rooting an unrooted tree Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.5/22

6 global maximum is not easy to find end up here but global maximum is here if start here Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.6/22

7 a subtree S T U V is rearranged by dissolving the connections to an interior branch: Is@ S T U V and reforming them in one of the two possible alternative ways: S T S T U V U V Nearest-neighbor interchange (NNI) rearrangement of a tree (the triangles are subtrees) Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.7/22

8 all 15 trees, connected by NNIs Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.8/22

9 with parsimony scores Lecture 30. Phylogeny methods, part 2 (Searching tree space) p./22

10 Subtree pruning and regrafting (SPR) rearrangement G H I J K L M reak each branch, remove a subtree G H K L I J M G H K L G H K L I J M * Here is the result: dd it in, attaching to one (*) of the other branches Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.10/22

11 Tree bisection and reconnection (TR) rearrangement G H I J K L M L reak each branch, separate the subtrees I J M G H K Here is that result: G K L H J I M onnect a branch of one to a branch of another I J M G H K L Lecture 30. Phylogeny methods, part 2 (Searching tree space) p./22

12 Greedy search by sequential addition 8 7 Greedy search by addition of species in a fixed order (,,,, ) in the best place each time. Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.12/22

13 S U Goloboff s time-saving trick G G H R H K L V Z S U V Z M R Goloboff s economy in computing scores of rearranged trees Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.13/22

14 Star decomposition Star decomposition" search for best tree can happen in multiple ways Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.14/22

15 isk-covering isk covering" assembly of a tree from overlapping estimated subtrees Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.15/22

16 Shortest Hamiltonian path problem (a) (b) (c) (d) Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.16/22

17 Search tree for this problem (1,2,3,4,5,6,7,8,10,) (1,2,3,4,5,6,7,,10,8) (1,2,3,4,5,6,7,10,,8) (1,2,3,4,5,6,7,8,,10) (1,2,3,4,5,6,7,,8,10) (1,2,3,4,5,6,7,10,8,) add 10 add add add 310 add 8 add add 3 add 8 add add 10 add 8 add 10 add 8 add add 8 add 10 add etc. etc. add 3 add 4 add 5 etc. etc. etc. add 2 add 3 add 4 add 5 etc. etc. add 1 add 2 add 3 start Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.17/22

18 Search tree of trees Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.18/22

19 same, with parsimony scores in place of trees Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.1/22

20 Some references amin, J. H. and R. R. Sokal method for deducing branching sequences in phylogeny. volution 1: [arly parsimony paper includes rearrangement of trees] avalli-sforza, L. L. and. W.. dwards Phylogenetic analysis: models and estimation procedures. merican Journal of Human Genetics 1: also volution 21: [Includes counting and tree shapes] arris, J. S Methods for computing Wagner trees. Systematic Zoology 1: [arly parsimony algorithms paper is one of first to mention sequential addition strategy] elsenstein, J The number of evolutionary trees. Systematic Zoology 27: (orrection, vol. 30, p. 122, 181) [Review of counting tip-labelled trees, recursion for counting multifurcating case] oulds, L. R. and R. L. Graham The Steiner problem in phyloge ny is NP-complete. dvances in pplied Mathematics 3: [Parsimony is NP-hard] Graham, R. L. and L. R. oulds Unlikelihood that minimal phylogenies for a realistic biological study can be constructed in reasonable computat ional time. Mathematical iosciences 60: [... and more] Hendy, M.. and. Penny ranch and bound algorithms to determine minimal evolutionary trees. Mathematical iosciences 60: [Introduced branch-and-bound for phylogenies] Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.20/22

21 continued Huson,., S. Nettles, L. Parida, T. Warnow, and S. Yooseph. 18. The disk-covering method for tree reconstruction. pp in Proceedings of lgorithms and xperiments (LX8), Trento, Italy, eb. -, 18, ed. R. attiti and.. ertossi. [ isk-covering method for long stringy trees] Maddison,. R. 11. The discovery and importance of multiple islands of most-parsimonious trees. Systematic Zoology 40: [iscusses heuristic search strategy involving ties, multiple starts] Saitou, N., and M. Nei The neighbor-joining method: a new method for reconstructing phylogenetic trees. Molecular iology and volution 4: [irst mention of star-decomposition search for best trees, sort of] Strimmer, K., and. von Haeseler. 16. Quartet puzzling: a quartet maximum likelihood method for reconstructing tree topologies. Molecular iology and volution 13: [ssembles trees out of quartets] Swofford,. L. and G. J. Olsen. 10. Phylogeny reconstruction. hapter, Pp in Molecular Systematics, ed.. M. Hillis and. Moritz. Sinauer ssociates, Sunderland, Massachusetts. [Review that discusses strategies, names SPR and TR rearrangement methods] Waterman, M. S. and T.. Smith On the similarity of dendrograms. Journal of Theoretical iology 73: [efines NNIs. Uses them to get a distance between trees.] Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.21/22

22 How it was done This projection produced using the prosper style in LaTeX, using Latex to make a.dvi file, using dvips to turn this into a Postscript file, using ps2pdf to mill it into a P file, and displaying the slides in dobe crobat Reader. Result: nice slides using freeware. Lecture 30. Phylogeny methods, part 2 (Searching tree space) p.22/22