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Building Phylogenies. Human. Human. Chimp. Chimp. Gorilla. Gorilla. ??. Orangutan. Orangutan. Gibbon. Gibbon. Phylogenetic (evolutionary) trees. Describe evolutionary relationships between species. or. Cannot be known with certainty!. Nevertheless, phylogenies can be useful.

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phylogenetic evolutionary trees

Human

Human

Chimp

Chimp

Gorilla

Gorilla

??

Orangutan

Orangutan

Gibbon

Gibbon

Phylogenetic (evolutionary) trees

Describe evolutionary relationships between species

or

Cannot be known with certainty!

Nevertheless, phylogenies can be useful

applications of phylogenetic analysis
Applications of Phylogenetic Analysis
  • Inferring function
    • Closely related sequences occupy neighboring branches of tree
  • Tracking changes in rapidly evolving populations (e.g., viruses)
    • Which genes are under selection?
phyloinformatics
Phyloinformatics
  • Comparative analysis through phylogenies helps to understand biological function
  • Exploit phylogenies for data mining
methods
Methods
  • Distance-based
  • Parsimony
  • Maximum likelihood
distance matrices

a 0

b 6 0

c 7 3 0

d 14 10 9 0

a b c d

0

1

2

3

4

5

6

7

8

Distance Matrices

a

b

c

d

ultrametric matrices

a 0

b 2 0

c 6 6 0

d 10 10 10 0

a b c d

0

1

2

3

4

5

Ultrametric Matrices

a

b

c

d

least squares

Dij= distance between i and j in matrix

dij= distance between i and j in tree

Objetive: Find tree that minimizes

Least Squares
characters

a

0

1

1

1

A

B

C

D

b

0

1

1

1

c

0

0

1

1

d

0

1

1

0

e

0

0

0

1

f

1

0

0

0

Characters

A character can be a morphological trait or a letter in a column of an alignment.

Characters are represented using matrices

parsimony

a

0

1

1

1

A

B

C

D

b

0

1

1

1

c

0

0

1

1

d

0

1

1

0

e

0

0

0

1

f

1

0

0

0

D

A

B

C

Parsimony

Goal: Find the tree with least number of evolutionary changes

a, b

f

c

d

d

e

markov models on trees
Markov models on trees
  • Observed: The species labeling the leaves
  • Hidden: The ancestral states
  • Transition probabilities: The mutation probabilities
  • Assumptions:
    • Only mutations are allowed
    • Sites are independent
    • Evolution at each site occurs according to a Markov process
models of evolution at a site
Models of evolution at a site
  • Transition probability matrix: M = [mij], i, j {A, C, T, G}where mij = Prob(i  j mutation in 1 time unit)
  • Different branches of tree may have different lengths
the probability of an assignment
The probability of an assignment

T

G

T

A

G

C

T

Probability = mTG · mGA · mGG· mTT· mTC· mTT

ancestral reconstruction most likely assignment
Ancestral reconstruction: most likely assignment

X

Y

Z

A

G

C

T

L* = maxX,Y,Z {mXY · mYA · mYG· mXZ· mZC· mZT}