phylogeny reconstruction from experimental data dean l. zeller dr. f. f. dragan, advisor kent state...

Phylogeny Reconstruction from Experimental Data

Dean L. ZellerDr. F. F. Dragan, advisor

Kent State UniversityApril 7th, 2006

Phylogeny Reconstruction Slide 2 of 42

“…the great Tree of Life fills with its dead and broken branches the crust of the earth, and covers the surface with its ever-branching and beautiful ramifications.”

Charles Darwin (1809-1882) Father of Evolution

http://www.general-anaesthesia.com/images/samuel-colt.html


Outline

• Goals of research• Evolution trees, phylogenies• Assumptions• Atlas of Evolution Trees• Genetic tests (hypothetical)• Phylogeny reconstruction methods• Future Work


Goals of ResearchSpecific Goals• Create methods of phylogeny reconstruction from

various hypothetical tests.• Make use of and create more adequate evolution

models.• Create “teachable” lessons on bioinformatics suitable

for a mid-level computer science, mathematics, or biology class.

Long Term Goals• Discover methods of phylogeny reconstruction from a

new perspective.• Educate the next generation of computational biologists.


Evolution Tree example


Evolution Tree (theoretical)


Assumptions

• By making simple assumptions, the problem complexity is greatly reduced.

1. Redundant nodes removed2. Multiple splits nodes replaced with

isomorphic approximations3. Only consider isomorphically unique trees


Assumption #1• Redundant nodes are

removed without loss of data.

• It is already assumed the species is slowly changing over time. It does not add to the problem to consider a single point along the way.


Assumption #2

• Multiple split nodes replaced with isomorphic approximations

• Some loss of data, but greatly reduces the problem complexity


Assumption #3• Isomorphically unique trees


Atlas of Evolution Trees (5 leaves) (12)

a b

(122)

c

a b

(1222)

c d

a b

(124)

a b c d

(1224)

e

a b c d

(1242)

e

a b

c d


Atlas of Evolution Trees (6 leaves) (122222)

c d

a b

e f

(12224)

a b

e f

c d

(12242)

a b

e

f

c d

(12422)

a b

e f

c

d

(1244a)

a b

e f

c d

(1244b)

a b

d c

e f


Genetic Tests

• At this point, all tests are purely hypothetical.• Plausible results can be converted from existing

tests.• Binary Two-Species Test (BTST)• Discrete Two-Species Test (DTST)• Continuous Two-Species Test (CTST)• Closer Relative Three-Species Test (CRTST)


Binary Two-Species Test (BTST)

• Returns 1 if species x and y are genetically close to a certain degree, and 0 otherwise.

• Data collected to form a similarity grid and distance graph (k-leaf root).


Reconstruction from BTSTStep 1 – Difference Summary Table

a b c d e f

a 1 1 0 0 0

b 1 0 0 0

c 1 0 0

d 1 1

e 1

f

Step 2 – k-leaf root

Step 3 – phylogeny


Reconstruction from BTST

• Linear time solution exists for k = 3 [Br05a]

• … and k = 4 [Br05b]

• An open problem for k 5– Severely limits analysis capability.


Discrete Two-Species Test (DTST)

• Returns a discrete value (k=2,3,4,…) denoting distance between x and y in tree.

• Test can be converted from existing tests.• Data collected to form a distance grid.• Create distance graphs incrementally.


Reconstruction from DTSTDifference Summary Table

a b c d e f

a 2 3 5 6 6

b 3 5 6 6

c 4 5 5

d 3 3

e 2

f

k 2 k 3

k 4 k 5

k 6


Reconstruction from DTST

Distance 2Direct Neighbors

Distance 3Close relatives

Distance 4Tree complete


Continuous Two Species Test (CTST)• Returns a continuous value d denoting

distance between x and y in tree.

• Data collected to form a distance grid.• Tree reconstructed in ascending order of

closeness.• Highest degree of accuracy required


Reconstruction from CTSTDistance Summary Table

a b c d e f

a 1.96 3.64 7.31 9.07 11.65

b 3.51 7.64 12.34 10.71

c 5.90 8.21 7.99

d 4.73 4.63

e 2.31

f


Reconstruction from CTSTDiff(a,b) 1.96 Make connection Diff(e,f) 2.31 Make connection Diff(b,c) 3.51 Make connection Diff(a,c) 3.64 Connection previously establishedDiff(d,f) 4.63 Make connection Diff(d,e) 4.73 Connection previously establishedDiff(c,d) 5.90 Make connection , STOP -- All species included in tree


Actual CTST data

Bovine Mouse Gibbon Orang Gorilla Chimp HumanBovine 1.67 1.72 1.66 1.52 1.60 1.59Mouse 1.52 1.48 1.45 1.44 1.46Gibbon 0.71 0.60 0.62 0.56Orang 0.46 0.51 0.47Gorilla 0.35 0.31Chimp 0.27Human

Source: [Fe04]


Phylogeny ReconstructionReconstruction from CTST results in the following tree:


CTST Results, part 1• Use the correlation statistical measurement to determine

relationship between data used to create tree and distance data created by tree. (>0.8 is “strong”.)

data distancechimp human 0.27 2gorilla human 0.31 3gorilla chimp 0.35 3orang gorilla 0.46 3orang human 0.47 4orang chimp 0.51 4gorilla human 0.56 5gibbon gorilla 0.60 5gibbon chimp 0.62 5gibbon orang 0.71 3

Correlation: 0.64 (positive relationship exists)

Note: if gibbon orang was 5 instead of 3, the correlation would be 0.93.


CTST Results, part 2• Use the correlation statistical measurement to determine

relationship between remaining data and distance data created by tree.

data distancemouse chimp 1.44 6mouse gorilla 1.45 5mouse human 1.46 6mouse orang 1.48 4mouse gibbon 1.52 3bovine gorilla 1.52 6bovine human 1.59 7bovine chimp 1.60 7bovine orang 1.66 5bovine mouse 1.67 3bovine gibbon 1.72 4

Correlation: -.24 (weak negative relationship)


CTST Conclusions

• Relationship is statistically significant for the lower data values resulting in species close on resulting phylogeny, but is weak for data values further away.

• There are stronger methods of phylogeny reconstruction, but this serves as a good starting point.


Closer Relative Three-Species Test (CRTST)

• Returns one of two possible trees on three species.

• Use the Merge Partial Evolution Trees [Li99] algorithm to reconstruct phylogeny.

• Allows for multiple species evolution.

Type 1 Single source

x y z

Type 2 Split source

x y z


Results from CRTST data

T4

e g h

T2

d c a

T6

e h b

T1

a b d

T8

f g h

T5

e f h

T3

a d f

T7

e f c


Reconstruction from CRTSTStep 1: Merge T1 with T2

In both trees, species a and d share a common ancestor. Species b shares an ancestor with a, and c shares an ancestor with d. LCA(a,d) is further up in the tree than LCA(a,b) and LCA(c,d).

T1

a b d

T2

d c a

+ = T12

a b c d

Step 2: Merge T12 with T3 In T3, species a and f share a common ancestor higher in the tree than a and d. LCA(a,f) is further up in the tree than LCA(a,d).

T3

a d f

+ = T12

a b c d

T123

a b c d f



There are no intersections between the leaves in T123 and T4. Thus there is no evidence indicating these species came from the same ancestor. At this point, they cannot be merged. T4 is set aside and will be visited again.

T123

a b c d f

T4

e g h

Step 4: Merge T123 with T5 In T5, species e and h share a common ancestor higher in the tree than e and f. LCA(e,h) is further up in the tree than LCA(e,f).

+ = T123

a b c d f

T5

e f h a b

T1235

c d e f h



In T6, species e and b share a common ancestor higher in the tree than e and h. LCA(e,b) is further up in the tree than LCA(e,h). Since the connection of b, e, and h was already determined in the last step, there is no change to the tree.

+ = a b

T1235

c d e f h

T6

e h b a b

T12356

c d e f h

Step 6: Merge T12356 with T7 In T7, species e and c share a common ancestor higher in the tree than e and f. LCA(e,c) is further up in the tree than LCA(e,f). Since the connection of c, e, and f was already determined in the last step, there is no change to the tree.

+ = a b

T12356

c d e f h

T7

e f c a b

T123567

c d e f h



Species f, g, and h all share the same common ancestor. Since the connection of f and h was already determined in the last step, g is added as a child to LCA(f,h).

+ = a b

T123567

c d e f h

T8

f g h a b

T1235678

c d e f g h

Step 8: Merge T1235678 with T4 Species e, g, and h all share the same common ancestor. Since the connection of e, g, and h has already been determined, there is no change to the tree.

+ = T4

e g h a b

T1235678

c d e f g h a b

T12345678

c d e f g h


Literature Review of Related Methods

• Additive and Ultrametric Trees [Wu04]

• Minimum Increment Evolution Tree (MEIT) [Wu04]

• Evolutionary Tree Insertion with Minimum Increment (ETIMI) [Wu04]

• Maximum Homeomorphic Agreement Subtree (MHT) [Ga97]

• Maximum Agreement Subtree (MAST) [Ga97]

• Maximum Inferred Consensus Tree (MICT) [Li99] • Maximum Inferred Local Consensus Tree (MILCT) [Li99] • Balanced Randomized Tree Splitting (BRTS) [Ka99] • Merging Partial Evolution Trees (MPET) [Li99]


Atlas of Distance Graphs• Inspired by An Atlas of Graphs [Re99]

• Elegant yet simple way to analyze graphs and trees

• Apply same style to phylogenies and distance graphs.


Atlas of Distance Graphs (12)

a b

ab

a b

(122)

c

a b

ab c

a

b

abc c

a

b

(1222)

c d

a b

ab d

a b

c

abcd d

a b

c

k=2

k=2 k=3

abc, cd d

a b

c

k=2 k=3 k=4


Atlas of Distance Graphs (124)

a b c d

abcd d

a b

c

ab

d

a

b

c

e

abcde d

a

b

c

e

k=2

ab, cd d

a b

c

ab, cd d

a b

c

k=3 k=4

abc, cd, ef d

a

b

c

e

abcd, cde d

a

b

c

e

k=2 k=3 k=4 k=5


Distance Graph Simulator

ab

d

f

g

h c

i

eGraph complete

k = 2k = 3k = 4k = 5k = 6k = 7k = 8


Class Assignments

• Assignment 1 – Drawing Trees• Assignment 2 – Phylogenetic Distance Graphs• Assignment 3 – Phylogeny Reconstruction

(Tested on CS10051 students, Spring 2006)


Future Work

• Additional bioinformatics class assignments• Atlas of Phylogenetic Distance Graphs• Implement the Phylogeny Reconstruction

Simulator using NetworkX• Remove redundant node and isomorphic

approximation assumptions• Apply to all nodes in tree instead of just the

leaves


References[Br05a] Brandstädt, A., V.B. Le, and R. Sritharan (2005). “Structure and Linear Time Recognition of

4-Leaf Powers”, Unpublished manuscript.[Br05b] Brandstädt, A. and V. B. Le (2005). “Structure and Linear Time Recognition of 3-Leaf

Powers”, Unpublished manuscript. [Fe04] J. Felsenstein (2004). Inferring Phylogenies, Sinauer Associates, Inc.[Ga97] L. Gąsieniec, J. Jansson, A. Lingas, and A. Östlin (1997), “On the complexity of computing

evolutionary trees,” Proceedings of Computing and Combinatonics Third Annual International Conference COCOON ’97, Shanghai, China, pp. 134 to 145, Aug 97.

[Ka99] Y. Kao, A. Lingas, and A. Östlin (1999), “Balanced Randomized Tree Splitting with Applications to Evolutionary Tree Constructions,” Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science, Trier, Germany, pp. 184 to 196, March 1999.

[Li99] A. Lingas, H. Olsson, and A. Östlin (1999), “Efficient Merging, Construction, and Maintenance of Evolutionary Trees,” Proceedings of the 26th International Colloquium on Automata, Languages, and Programming (ICALP) ’99, Prague, Chech Republic, pp. 544 to 553, July 1999.

[Re99] Read, R.C. and R.J. Wilson (1999). An Atlas of Graphs, Oxford Science Publications.[Wu04] Wu, B.Y. and K.M. Chao (2004). Spanning Trees and Optimization Problems. Chapman &

Hall/CRC.

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