Algorithms for phylogeny construction

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1 Algorithms for phylogeny construction A Hybrid Micro-Macroevolutionary Approach to Gene Tree Reconstruction ICE-TCS Inaugural Symposium Bjarni V. Halldórsson April 30,

2 Character based phylogeny 2

3 Has Intelligence? yes no Has Body Hair? no yes 3

4 Genes, genomes Gene - a sequence having functional importance. AACG, CACC, TACT Genome - a sequence containing genes as subsequences TATAACGTTTCTACTCTATTACTCC 4

5 Evolution - changes in the genome Original: TATAACGTTTCTACTCTATTACTCC Mutation: TATAACGTTTCTAATCTCTTACTCC Duplication: TATAACGTTTCTACTCTATTACTCCTCTACTCT Loss: TA-TCTACTCTATTACTCC 5

6 Phylogenies A species phylogeny shows the evolutionary history of a set of species. human monkey mouse A gene phylogeny shows the evolutionary history of a single gene. P 1 human P P P 1 Pmouse P 2 P 1 monkey P 2 human P 2 monkey 6

7 Why are gene phylogenies interesting? The same gene in different species is likely to play the same role. We want to determine the function of a gene in human. Experiments in mouse, yeast or flies are less controversial and take less time than in human. 7

8 Phylogeny construction considering mutations A very large number of algorithms exist for this problem. Character based algorithms (as mentioned before). Distances between the sequences are computed (such as the number of mutations that occured between the sequences). If the phylogeny has the ultrametric property an efficient algorithm can be employed. 8

9 Macroevolutionary phylogeny Input: A rooted species tree, T S with s leaves; a list of multiplicities m 1... m s, where m l is the number of gene family members found in species l; weights c λ and c δ. Output: A rooted gene tree {T G } with s l=1 m l leaves such that the D/L Score of T G is minimal. 2A 1B 2C 1D 2E 1F 2G 9

10 Phylogenies considering only cost of loss If the cost of losing a gene is much higher than the cost of duplication we will construct a phylogeny that minimizes the number of lost genes. All duplications will then take place after the speciations take place. 10

11 4 Duplications 2A 1B 2C 1D 2E 1F 2G A Dupl A F G 1B Dupl Dupl 1D Dupl C C E E G 11

12 Phylogenies considering only cost of duplication If the cost of a duplication is much higher than the cost of a loss we will construct a phylogeny that minimizes the number of duplications. All duplications can then be assumed to occur before any speciation occurs. 12

13 1 Duplication, 3 Losses 2A 1B 2C 1D 2E 1F 2G A Lost A B C Lost E C D E Lost G F G 13

14 Phylogenies considering duplication and loss Reconstruct[T S, {m 1... m s }] Ascend[root(T S )]; Descend[root(T S ), 1]; Construct[root(T S )]; 14

15 Ascend[v] if v is not a leaf: Ascend[l(v)]; Ascend[r(v)]; if v is a leaf: i s.t. 1 i ˆm cost min v [i] c δ max(m v i,0) + c λ max(i m v,0); if v is not a leaf: i, j s.t. 1 i, j ˆm cost v [i, j] c δ max(j i,0) + c λ max(i j,0) + cost min l(v) i cost min v [i] min j {cost v [i, j]}; [j] + costmin r(v) [j]; 15

16 Descend Descend[v, i] if v is a leaf: v.losses max((i m v ),0); v.dups max((m v i),0); v.out 0; else repeat { v.out + + } until ( cost v [i, v.out] == cost min v [i] ); Descend[l(v), v.out]; Descend[r(v), v.out] v.losses max(i v.out,0); v.dups max(v.out i,0) 16

17 Construct Construct[s] g new gene node; g.species s if (s.currdup < s.dups) s.currdup + +; l(g) Construct[s]; r(g) Construct[s]; else if (s.currloss < s.losses) s.currloss + +; else if (s.currspec < s.out) s.currspec + +; if s is not a leaf: l(g) Construct[l(s)]; r(g) Construct[r(s)]; return g; 17

18 2 Duplications, 1 loss 2A 1B 2C 1D 2E 1F 2G Dupl A A 1B 1D Dupl C Lost G F G C E E 18

19 Time Complexity Optimal history can be found in time O(nˆm 2 ). Where n is the number of nodes in the species tree and ˆm is the maximum number of genes drawn from any species. In Ascendleaves of the species tree can be annotated with multiplicities in O(nˆm) time. The cost vector in each node is of length ˆm + 1 and each entry can be computed in time O(ˆm), total O(nˆm 2 ). Descend requires O( ˆm) at each node, total O(n ˆm). Construct inserts duplication and loss nodes in the new tree, which can number in total no more than ˆm per node in T S. Total O(nˆm). 19

20 Extensions Combining duplication and loss cost with cost of mutations. Some edges of a phylogeny tree are well supported by a micro-evolutionary phylogenetic construction algorithms. Edges that are not as well supported can be rearranged minimizing duplication and loss. Consider and display all possible optimal histories. 20

21 Acknowledgements R. Ravi, Carnegie Mellon University Dannie Durand, Carnegie Mellon University A Hybrid Micro-Macroevolutionary Approach to Gene Tree Reconstruction. D. Durand, B. V. Halldorsson, B. Vernot, Proceedings of the Ninth Annual International Conference on Computational Molecular Biology (RECOMB), To Appear. 21

Evolutionary Tree Analysis. Overview

Evolutionary Tree Analysis. Overview CSI/BINF 5330 Evolutionary Tree Analysis Young-Rae Cho Associate Professor Department of Computer Science Baylor University Overview Backgrounds Distance-Based Evolutionary Tree Reconstruction Character-Based