Models of Molecular Evolution
Bret Larget
Departments of Botany and of Statistics
University of WisconsinMadison
September 15, 2007
Genetics 875 (Fall 2009)
Molecular Evolution
September 15, 2009
1 / 14
Molecular Evolution
Features
Features of Molecular E
Lecture Outline: Trees
1. Nomenclature
Phylogeny A phylogeny is a tree that shows the evolutionary relationships among a group of organisms.
Taxon A taxon is a generic name for a taxonomic group. Examples are species, but also populations, genera, familie
Lecture Outline: Assessing Uncertainty with the Bootstrap
1. The Bootstrap
The bootstrap was introduced to the world by Brad Efron, chair of the Department of Statistics at Stanford
University, in 1979.
The bootstrap is one of the most widely used new m
Genetics 629
Solutions to Homework #2
Exam on September 22, 2011
1. Create your own fully resolved unrooted tree with n = 8 taxa.
There will be many different answers depending on your choice. I will answer for this unrooted tree:
(1,2),3),(4,5),(6,7),8);
Lecture Outline: Molecular Evolution (part 1)
1. Features of Molecular Evolution
(a) Possible multiple changes on edges
(b) Transition/transversion bias
(c) Nonuniform base composition
(d) Rate variation across sites
(e) Dependence among sites
(f) Codon
Lecture Outline: Phylogeny Reconstruction using Distance Methods
1. Summary of Models of Molecular Evolution
(a) The standard form for the rate matrix of a timereversible continuoustime Markov model of DNA substitution
is the following, where the base o
Homework #2
Genetics 629
Quiz on September 22, 2011
Trees Recall the following formula:
There are 1 3 (2n 5) (2n 5)! u(n) unrooted binary tree topologies with n leaves (n > 2).
There are 1 3 (2n 3) (2n 3)! r(n) rooted binary tree topologies with n leave
Phylogenetic Trees
Bret Larget
Departments of Botany and of Statistics
University of WisconsinMadison
September 8, 2011
Genetics/Botany 629 (Fall 2011)
Phylogenetic Trees
September 7, 2011
1 / 13
A Brief History
Darwin
Phylogenetics and Darwin
In 1837, sh
Molecular Evolution
Bret Larget
Departments of Botany and of Statistics
University of WisconsinMadison
September 15, 2011
Molecular Evolution
1 / 13
Features of Molecular Evolution
1
Possible multiple changes on edges
2
Transition/transversion bias
3
Non
Maximum Likelihood and the Bootstrap
Bret Larget
Departments of Botany and of Statistics
University of WisconsinMadison
September 29, 2011
ML+Bootstrap
1 / 17
Principle of Maximum Likelihood
Given parameters and data X
The function f (X  ) is the probabi
Lecture Outline: Parsimony
1. Concepts
(a) The method of maximum parsimony prefers the tree that is consistent with the most parsimonious or simplest
explanation. For aligned DNA sequences, this is interpreted as the tree that requires the fewest nucleoti
Genetics 629
Solution to Homework #2
Exam on October 8, 2009
Distance Methods
A
0
10
6
4
A
B
C
D
B
10
0
12
8
C
6
12
0
6
D
4
8
6
0
1. Apply the UPGMA algorithm to the matrix to nd the UPGMA tree.
Solution: ( (A:2,D:2):1,C:3):2,B:5);
2. Assume that the rst
Maximum Parsimony
Bret Larget
Departments of Botany and of Statistics
University of WisconsinMadison
September 10, 2009
Genetics 875 (Fall 2009)
Parsimony
September 10, 2009
1/7
Maximum Parsimony
Denition
The maximum parsimony tree is the tree that best t
Lecture Outline: Phylogeny Reconstruction using Distance Methods
1. Summary of Models of Molecular Evolution
(a) The standard form for the rate matrix of a timereversible continuoustime Markov model of DNA substitution
is the following, where the base o
Distance Methods
Bret Larget
Departments of Botany and of Statistics
University of WisconsinMadison
September 22, 2009
Genetics/Botany 629 (Fall 2009)
Distance Methods
October 6, 2009
1 / 12
UPGMA
UPGMA is an acronym for Unweighted PairGroup Method with
Lecture Outline: Molecular Evolution (part 1)
1. Features of Molecular Evolution
(a) Possible multiple changes on edges
(b) Transition/transversion bias
(c) Nonuniform base composition
(d) Rate variation across sites
(e) Dependence among sites
(f) Codon
Lecture Outline: Phylogeny Reconstruction using Maximum Likelihood
1. Principle of Maximum Likelihood
(a) In a typical statistical model, given parameters , the probability of observing data X is f (X  ). (Both X and
can be multidimensional.)
(b) Keepi
Maximum Likelihood
Bret Larget
Departments of Botany and of Statistics
University of WisconsinMadison
September 24, 2009
Genetics 629 (Fall 2009)
Maximum Likelihood
October 6, 2009
1/8
Principle of Maximum Likelihood
Given parameters and data X
The functi
Genetics 629
Solutions to Homework #1
Exam on September 22, 2009
1. Create your own fully resolved unrooted tree with n = 8 taxa.
There will be many different answers depending on your choice. I will answer for this unrooted tree:
(1,2),3),(4,5),(6,7),8);
Notes for Exam 2
Genetics 629
Exam on October 8, 2009
Distance Methods
1. Be able to apply the UPGMA algorithm to nd a tree from a distance matrix. (You do not need to memorize the algorithm.)
2. Be able to nd the last three edge lengths when combining th
Bayesian Phylogenetics
Bret Larget
Departments of Botany and of Statistics
University of WisconsinMadison
October 1, 2009
Genetics 629 (Fall 2009)
Bayesian Phylogenetics
October 6, 2009
1 / 13
History
Reverend Thomas Bayes
Who was Bayes?
The Reverand Thom
Bayesian Phylogenetics
Bret Larget
Departments of Botany and of Statistics
University of WisconsinMadison
October 6, 2011
Bayesian Phylogenetics
1 / 27
Who was Bayes?
The Reverand Thomas Bayes was born in London in 1702.
He was the son of one of the rst N
Maximum Parsimony
Bret Larget
Departments of Botany and of Statistics
University of WisconsinMadison
September 13, 2011
Parsimony
1/6
Maximum Parsimony
Denition
The maximum parsimony tree is the tree that best ts the data in the
sense that it can explain
Genetics 629
Solution to Homework #2
Quiz on October 6, 2011
Distance Methods
A
0
10
6
4
A
B
C
D
B
10
0
12
8
C
6
12
0
6
D
4
8
6
0
1. Apply the UPGMA algorithm to the matrix to nd the UPGMA tree.
Solution: ( (A:2,D:2):1,C:3):2,B:5);
2. Assume that the rst
Genetics 629
Solutions to Homework #2
Exam on September 22, 2011
1. Create your own fully resolved unrooted tree with n = 8 taxa.
There will be many different answers depending on your choice. I will answer for this unrooted tree:
(1,2),3),(4,5),(6,7),8);
Genetics/Botany 629
Quiz 2
October 8, 2009
Name:
This matrix displays pairwise distances among three species.
A
B
C
A
0
4
6
B
4
0
8
C
6
8
0
1. (10 points) Find the UPGMA tree and neighborjoining trees associated with the distance matrix. Draw
each tree t
Genetics/Botany 629
Quiz1
September 22, 2009
Name:
+++

+++

+++


+
++
+
+
+
Nicotiana
(N)
A
C
A
G
A
A
Zea
(Z)
A
C
A
A
A
A
Amborella
(A)
A
A
A
G
A
A
Pinus
(P)
A
A
A
G
T
A
Welwitschia (W)
A
A
A
A
G
A
Adiantum
G
C
G
G
A
G
(O)
The rst sever
Genetics/Botany 629
Solution to Quiz 2
October 8, 2009
This matrix displays pairwise distances among three species.
A
B
C
A
0
4
6
B
4
0
8
C
6
8
0
1. (10 points) Find the UPGMA tree and neighborjoining trees associated with the distance matrix. Draw
each
Genetics/Botany 629
Solution to Quiz 1
+++

+++

+++


+
++
+
+
+
September 22, 2009
Nicotiana
(N)
A
C
A
G
A
A
Zea
(Z)
A
C
A
A
A
A
Amborella
(A)
A
A
A
G
A
A
Pinus
(P)
A
A
A
G
T
A
Welwitschia (W)
A
A
A
A
G
A
Adiantum
G
C
G
G
A
G
(O)
The rs
Lecture Outline: Phylogeny Reconstruction using Maximum Likelihood
1. Principle of Maximum Likelihood
(a) In a typical statistical model, given parameters , the probability of observing data X is f (X  ). (Both X and
can be multidimensional.)
(b) Keepi