Working with Trees in the Phyloinformatic Age

William H. Piel

Yale Peabody Museum

Hilmar Lapp

NESCent, Duke University

Dealing with the Growth of Phyloinformatics

• Trees: Too Many– Search, organize, triage, summarize, synthesize

• Review existing methods

• Describe queries for BioSQL phylo extension

• Making generic queries

• Trees: Too Big– Visualizing and manipulating large trees

• Demo PhyloWidget

Searching Stored Tree

• Path Enumerations

• Nested Sets

• Adjacency Lists

• Transitive Closure

A B C D E

0.1

0.1.1 0.1.2

0.2

0.2.1

0.2.1.1 0.2.1.2 0.2.2

0

Dewey system:

Label Path

Root 0

NULL 0.1

A 0.1.1

B 0.1.2

NULL 0.2

NULL 0.2.1

C 0.2.1.1

D 0.2.1.2

E 0.2.2

A B C D E

Find clade for: Z = (<CS+Ds)

Find common pattern starting from left

SELECT * FROM nodesWHERE (path LIKE “0.2.1%”);

• ATreeGrep– Uses special suffix indexing to optimize speed

– Shasha, D., J. T. L. Wang, H. Shan and K. Zhang. 2002. ATreeGrep: Approximate Searching in Unordered Tree. Proceedings of the 14th SSDM, Edinburgh, Scotland, pp. 89-98.

• Crimson– Uses nested subtrees to avoid long strings

– Zheng, Y. S. Fisher, S. Cohen, S. Guo, J. Kim, and S. B. Davidson. 2006. Crimson: A Data Management System to Support Evaluating Phylogenetic Tree Reconstruction Algorithms. 32nd International Conference on Very Large Data Bases, ACM, pp. 1231-1234.

Searching Stored Tree

• Path Enumerations

• Nested Sets

• Adjacency Lists

• Metrics

• Transitive Closure

A B C D E

2

3 5

8

9

10 12 15

1

4 6

7

17

11 13 16

18

14

Depth-first traversal scoring each node with a lef and right ID

Label Left Right

1 18

2 7

A 3 4

B 5 6

8 17

9 14

C 10 11

D 12 13

E 15 16

A B C D E

2

3 5

8

9

10 12 15

1

4 6

7

17

11 13 16

18

14

SELECT * FROM nodesINNER JOIN nodes AS includeON (nodes.left_id BETWEEN include.left_id AND include.right_id)WHERE include.node_id = 5 ;

Minimum Spanning Clade of Node 5

• PhyloFinder

– Duhong Chen et al.

– http://pilin.cs.iastate.edu/phylofinder/

• Mackey, A. 2002. Relational Modeling of Biological Data: Trees and Graphs. Bioinformatics Technology Conference. http://www.oreillynet.com/pub/a/network/2002/11/27/bioconf.html

Searching Stored Tree

• Path Enumerations

• Nested Sets

• Adjacency Lists

• Metrics

• Transitive Closure

A B C D E

1

23 4

5

67 8 9

-

1

-

-

2

1

A

3

2

B

4

2 -

6

5-

5

1

C

7

6

E

9

5

D

8

6

-

1

-

-

2

1

A

3

2

B

4

2

-

6

5

-

5

1

C

7

6

E

9

5

D

8

6

node_label:

node_id:

parent_id:

SQL Query to find parent node of node “D”:

SELECT *FROM nodes AS parent

INNER JOIN nodes AS childON (child.parent_id = parent.node_id)

WHERE child.node_label = ‘D’;

…but this requires an external procedure to navigate the tree.

Searching Stored Tree

• Path Enumerations• Nested Sets• Adjacency Lists• Metrics• Transitive Closure

Searching trees by distance metrics: USim distanceWang, J. T. L., H. Shan, D. Shasha and W. H. Piel. 2005. Fast Structural Search in

Phylogenetic Databases. Evolutionary Bioinformatics Online, 1: 37-46

A B C DA B C D

A B C D

A 0 1 2 3

B 1 0 2 3

C 1 1 0 2

D 1 1 1 0

A B C D

A 0 1 2 2

B 1 0 2 2

C 2 2 0 1

D 2 2 1 0

Searching Stored Tree

• Path Enumerations

• Nested Sets

• Adjacency Lists

• Transitive Closure

Transitive Closure• Finding paths between vertices on a graph• DB2 and Oracle have special functions:

– From EdgeStart With (child_id = A and tree_id = T)Connect By (Prior parent_id = child_id)And (Prior tree_id = tree_id)

• Nakhleh, L., D. Miranker, F. Barbancon, W. H. Piel, and M. Donoghue. 2003. Requirements of phylogenetic databases. Third IEEE Symposium on Bioinformatics and Bioengineering, p. 141-148.

• Paths can be precomputed and stored: BioSQL

Dealing with the Growth of Phyloinformatics

• Trees Too Many– Search, organize, triage, summarize, synthesize

• Review existing methods

• Describe queries for BioSQL phylo extension

• Making generic queries

• Trees Too Big– Visualizing and manipulating large trees

• Demo PhyloWidget

BioSQL: http://www.biosql.org/Schema for persistent storage of sequences and features tightly integrated with BioPerl (+ BioPython, BioJava, and BioRuby)• phylodb extension designed at NESCent Hackathon • perl command-line interface by Jamie Estill, GSoC

A B

1

2

3 4

5

C

1

2

1

53

2

4

2

1

3

1

4

CREATE TABLE node_path ( child_node_id integer, parent_node_id integer, distance integer);

Index of all paths from ancestors to descendants

A B

1

2

3 4

5

C

1

2

1

53

2

4

2

1

3

1

4

SELECT pA.parent_node_idFROM node_path pA, node_path pB, nodes nA, nodes nBWHERE pA.parent_node_id = pB.parent_node_idAND pA.child_node_id = nA.node_idAND nA.node_label = 'A'AND pB.child_node_id = nB.node_idAND nB.node_label = 'B';

Find all paths where A and B share a common parent_node_id

A B

1

2

3 4

5

C

1

2

1

53

2

4

2

1

3

1

4

SELECT pA.parent_node_idFROM node_path pA, node_path pB, nodes nA, nodes nBWHERE pA.parent_node_id = pB.parent_node_idAND pA.child_node_id = nA.node_idAND nA.node_label = 'A'AND pB.child_node_id = nB.node_idAND nB.node_label = 'B'ORDER BY pA.distanceLIMIT 1;

…of those paths, select one that has the shortest path

A B

1

2

3 4

5

C

1

2

1

53

2

4

2

1

3

1

4

SELECT pA.parent_node_idFROM node_path pA, node_path pB, nodes nA, nodes nBWHERE pA.parent_node_id = pB.parent_node_idAND pA.child_node_id = nA.node_idAND nA.node_label = 'A'AND pB.child_node_id = nB.node_idAND nB.node_label = 'B'ORDER BY pA.distance DESCLIMIT 1;

…of those paths, select one that has the longest path

SELECT e.parent_id AS parent, e.child_id AS child, ch.node_label, pt.tree_idFROM node_path p, edges e, nodes pt, nodes chWHERE e.child_id = p.child_node_idAND pt.node_id = e.parent_idAND ch.node_id = e.child_idAND p.parent_node_id IN (      SELECT pA.parent_node_id      FROM   node_path pA, node_path pB, nodes nA, nodes nB      WHERE pA.parent_node_id = pB.parent_node_id      AND   pA.child_node_id = nA.node_id      AND   nA.node_label = 'A'      AND   pB.child_node_id = nB.node_id      AND   nB.node_label = 'B')AND NOT EXISTS (    SELECT 1 FROM node_path np, nodes n    WHERE    np.child_node_id = n.node_id    AND n.node_label  = 'C'    AND np.parent_node_id = p.parent_node_id);

Find the maximum spanning clade (i.e. the subtree) for each tree that includes A and B but not C:

Get all ancestors shared by A and B

Exclude thosethat are alsoancestors to C

Return an adjacency list for each subtree

SELECT DISTINCT t.tree_id, t.nameFROM node_path p, nodes ch, trees tWHERE ch.node_id = p.child_node_idAND ch.tree_id = t.tree_idAND p.parent_node_id IN ( SELECT pA.parent_node_id FROM node_path pA, node_path pB, nodes nA, nodes nB WHERE pA.parent_node_id = pB.parent_node_id AND pA.child_node_id = nA.node_id AND nA.node_label = 'A' AND pB.child_node_id = nB.node_id AND nB.node_label = 'B')AND NOT EXISTS ( SELECT 1 FROM node_path np, nodes n WHERE np.child_node_id = n.node_id AND n.node_label = 'C' AND np.parent_node_id = p.parent_node_id);

Find trees that contain a clade that includes A and B but not C:

Get all ancestors shared by A and B

Exclude thosethat are alsoancestors to C

List the set of trees with these ancestors

SELECT qry.tree_id, MIN(qry.name) AS "tree_name"FROM ( SELECT DISTINCT ON (n.node_id) n.node_id, t.tree_id, t.name FROM trees t, nodes n, (SELECT DISTINCT ON (inN.tree_id) inP.parent_node_id FROM nodes inN, node_path inP WHERE inN.node_label IN ('A','B','C') AND inP.child_node_id = inN.node_id GROUP BY inN.tree_id, inP.parent_node_id HAVING COUNT(inP.child_node_id) = 3 ORDER BY inN.tree_id, inP.parent_node_id DESC) AS lca, WHERE n.node_id IN (lca2.parent_node_id) AND t.tree_id = n.tree_id AND NOT EXISTS (SELECT 1 FROM nodes outN, node_path outP WHERE outN.node_label IN ('D','E') AND outP.child_node_id = outN.node_id AND outP.parent_node_id = lca.parent_node_id) AND EXISTS (SELECT c.tree_id FROM trees c, nodes q WHERE q.node_label IN ('D','E') AND q.tree_id = c.tree_id AND c.tree_id = t.tree_id GROUP BY c.tree_id HAVING COUNT(c.tree_id) = 2)) AS qryGROUP BY (qry.tree_id)HAVING COUNT(qry.node_id) = 1;

Find trees that contain a clade that includes (A, B, C) but not D or E:

Get all ancestorsof A, B, C from alltrees that have A, B, C

Exclude thosethat are alsoancestors to D, E

But make sure thatthe tree still contains D, E

Number of clades that each tree must satisfy

Number of ingroups that share node

Number of non-ingroups that must be in tree

SELECT t.tree_id, t.name FROM trees t INNER JOIN (SELECT DISTINCT ON (inN.tree_id) inP.parent_node_id, inN.tree_id FROM nodes inN, node_path inP WHERE inN.node_label IN ('A','B','C') AND inP.child_node_id = inN.node_id GROUP BY inN.tree_id, inP.parent_node_id HAVING COUNT(inP.child_node_id) = 3 ORDER BY inN.tree_id, inP.parent_node_id DESC) AS lca USING (tree_id) WHERE NOT EXISTS ( SELECT 1 FROM nodes outN, node_path outP WHERE outN.node_label IN ('D','E') AND outP.child_node_id = outN.node_id AND outP.parent_node_id = lca.parent_node_id) AND EXISTS ( SELECT c.tree_id FROM trees c, nodes q WHERE q.node_label IN ('D','E') AND q.tree_id = c.tree_id AND c.tree_id = t.tree_id GROUP BY c.tree_id HAVING COUNT(c.tree_id) = 2);

Here's a faster, cleaner version:

Matching a whole tree means querying for all clades

A B C D E

1

23 4

5

67 8 9

(A, B) but not C, D, E(C, D) but not A, B, E(C, D, E) but not A, B

Dealing with the Growth of Phyloinformatics

• Trees Too Many– Search, organize, triage, summarize, synthesize

• Review existing methods

• Describe queries for BioSQL phylo extension

• Making generic queries

• Trees Too Big– Visualizing and manipulating large trees

• Demo PhyloWidget

Sus scrofa

Hippopotamus

Balaenoptera

Equus caballus

Felis catus

Balaenoptera

Hippopotamus

Sus scrofa

Equus caballus

Felis catus

(((Sus_scrofa, Hippopotamus),Balaenoptera),Equus_caballus)vs

((Sus_scrofa, (Hippopotamus,Balaenoptera)),Equus_caballus)

Mining trees for interesting, general, relationship questions:

Sus scrofa

Hippopotamus

Balaenoptera

Equus caballus

Felis catus

Sus celebensis

Hippopotamus

Balaenoptera

Equus asinus

Felis catus

Even if with perfectly-resolved OTUs, you will still fail to hit relevant trees:

Step 1: for each clade all trees in database, run a stem query on a classification tree (e.g. NCBI)

A B C D E

1

23 4

5

67 8 9

Stem Queries:Node 2: (>A, B - C, D, E)Node 3: (>A - B, C, D, E)Node 4: (>B - A, C, D, E)Node 5: (>C, D, E - A, B)Node 6: (>C, D - A, B, E)Node 7: (>C - A, B, D, E)Node 8: (>D - A, B, C, E)Node 9: (>E - A, B, C, D)

Step 2: label each node with an NCBI taxon id (if there is a match)

Step 3: do the same for the query tree

Gorilla gorilla

Homo sapiens

Pan troglodytes

Macaca sinica

Macaca nigra

Rename nodes according to their deepest stem query…

Hominoidea

Cercopithecoidea

Gorilla

Homo

Pan

Macaca sinica

Macaca nigra

Pongo pygmaeus

Macaca irus

Hominoidea

Cercopithecoidea

Dealing with the Growth of Phyloinformatics

• Trees Too Many– Search, organize, triage, summarize, synthesize

• Review existing methods

• Describe queries for BioSQL phylo extension

• Making generic queries

• Trees Too Big– Visualizing and manipulating large trees

• Demo PhyloWidget

PhyloWidget• Greg Jordan

– Google Summer of Code student– Nick Goldman's group, EBI

• Java Applet– Uses the Processing graphics library

• Originally as a graphical phylogenetic query and display tool for TreeBASE, BioSQL, etc

• Can be used for:– Manipulating, visualizing large trees– Building supertrees through pruning & grafting

Thanks