BIS2C. Biodiversity and the Tree of Life. 2014. L4. Inferring Phylogenetic Trees

Slides by Jonathan Eisen for BIS2C at UC Davis Spring 2014

Lecture 4

!

Lecture 4: !

Inferring Phylogenetic Trees !!!

BIS 002C Biodiversity & the Tree of Life

Spring 2014 !

Prof. Jonathan Eisen

1


Where we are going and where we have been

• Previous Lecture: !Characters, Traits and States

• Current Lecture: ! Inferring Trees

• Next Lecture: !The Tree of Life

2


Lecture 4: Key Concept

Inferring the phylogenetic history of taxa from analysis of their character traits and states.

3


Lecture 4: Phylogenetic Inference

• General issues

• Case study

• Parsimony inference for case study

• Parsimony informativeness

• Are all changes equal?

• Character conflict

4



• General issues

• Case study





5


Figure 22.5 Constructing a Phylogenetic Tree

6


• Species change over time (i.e., divergence happens)

• Comparison and analysis of the patterns of similarity and differences among species should allow us to infer (some) information on the history of those species

7

Phylogenetic Inference


Table 22.1: Matrix of Traits and States Across 8 Taxa

8


Figure 22.5 Constructing a Phylogenetic Tree

9



• General issues

• Case study





10

Slides by Jonathan Eisen for BIS2C at UC Davis Spring 2014 11

polytomy

Key Concept: Polytomy


Key Concept: Polytomy

12

Polytomies - some nodes have three or more descendant branches - usually reflect uncertainty about phylogenetic relationships. polytomy


Clicker Question

13


Clicker Question

14

How many different rooted trees are there for four taxa?

A. 3 B. 5 C. 8 D. 15

polytomy


Clicker Answer: Rooted Trees for Four Taxa

15



15

H OCG



15

H OCG

H OGC



15

H GCO

H OCG

H OGC



15

H GCO

H OCG

H OGC

H OCG



15

H GCO

H OCG

H OGC

H OCG

H OGC



15

H GCO

H OCG

H OGC

H OCG

H OGC

H CGO



15

H GCO

H OCG

H OGC

H OCG

H OGC

H CGO

G OCH

G OHC

G HCO



15

H GCO

H OCG

H OGC

H OCG

H OGC

H CGO

G OCH

G OHC

G HCO

C OGH

C HGO

C HOG



15

H GCO

H OCG

H OGC

H OCG

H OGC

H CGO

G OCH

G OHC

G HCO

C OGH

C HGO

C HOG

O CGH

O CHG

O HGC


H GCO

H OCG

H OGC

H OCG

H OGC

H CGO

G OCH

G OHC

G HCO

C OGH

C HGO

C HOG

O CGH

O CHG

O HGC

WHICH OF THESE POSSIBLE TREES IS THE BEST MODEL?




polytomy


Key Concept: Unrooted Tree


polytomy

Step 1 - Identify Outgroup


outgroup?


Outgroup: one or more taxa that are not members of the ingroup.

a b c d e h g f

Ingroup

m n

Outgroups

20

Key Concepts: Ingroups and Outgroups

Ingroup: the group of taxa under study


outgroup?


polytomy



outgroup

polytomy



outgroup?

polytomy



outgroup

polytomy


Step 2 - Root with Outgroup


outgroup

polytomy


Step 2 - Root with Outgroup


outgroup

polytomy


Step 2: Consider Possible Trees for Ingroup


polytomy


Possible Tree #1



Possible Tree #2



Possible Tree #3



15 possible trees

31

H GCO

H OCG

H OGC

H OCG

H OGC

H CGO

G OCH

G OHC

G HCO

C OGH

C HGO

C HOG

O CGH

O CHG

O HGC


Narrowed down to three

32

H GCO

H OCG

H OGC

H OCG

H OGC

H CGO

G OCH

G OHC

G HCO

C OGH

C HGO

C HOG

O CGH

O CHG

O HGC


Narrowed down to three

33

H GCO

H OCG

H OGC

H OCG

H OGC

H CGO

G OCH

G OHC

G HCO

C OGH

C HGO

C HOG

O CGH

O CHG

O HGC

WHICH OF THESE

POSSIBLE TREES IS THE BEST MODEL?



• General issues

• Case study





34


Principle of parsimony

The Principle of Parsimony: the simplest of two (or more) competing theories is to be preferred (assuming all else is equal).

35


The Principle of Parsimony: the simplest of two (or more) competing theories is to be preferred (assuming all else is equal). !

Applied to character state reconstruction: !To choose among two (or more) character state

reconstruction theories for a given tree, select the one requiring the fewest changes or ‘steps’.

36

Parsimony Character State Reconstruction


+++

37

Pattern 1 Pattern 2 Pattern 3

Which pattern is the most plausible?




+++Pattern1: 7 Steps Pattern2: 2 Steps Pattern3: 6 Steps

38



+++

39


Pattern1: 7 Steps Pattern2: 2 Steps Pattern3: 6 Steps



Parsimony Phylogenetic Tree Inference

The Principle of Parsimony: the simplest of two (or more) competing theories is to be preferred (assuming all else is equal). !

Applied to phylogenetic inference: ! To choose among two (or more) phylogenetic

trees, select the one requiring the fewest total number of steps for all characters

40


Revised Steps for Parsimony Phylogenetic Inference

41

1. Root the tree with outgroup

2. Draw possible trees.

3. For each character count the minimum number of steps required on each tree.

4. Sum over all characters to get the “score” (number of steps) for each tree.

5. The most parsimonious tree(s) is/are the one(s) with lowest score.


A data matrix shows the character states in the taxa under consideration

morphology DNA sequences

Characters 1 2 3 4 5 6 7 8 9 10… Taxa Orang 1 0 1 0 0 0 A C C T… Chimp 0 1 1 0 0 1 G C C T… Gorilla 0 1 0 1 1 2 G T C T… Human 0 1 0 1 1 2 G T T T…

A Data Matrix

42


! ! ! Characters! ! ! 1!2!3!4!5!6!7!8!9! Taxa!Orang! ! C!T!G!G!A!C!C!C!T! Chimp! ! C!T!A!G!C!T!C!C!C! Gorilla! C!T!G!G!C!C!A!C!T! Human! ! T!T!A!G!C!T!A!C!T

Data matrix: Nine characters of DNA data



H C GO C G HO C G HO

Tree 1 Tree 2 Tree 3

Data matrix: Nine characters of DNA data



Which Tree Requires Fewest Total # of Steps?





Tree 1


Tree 2 Tree 3


T C CC C C TC C C TC



!48

• How do we decide which pattern is the most plausible?

+++Pattern1: 7 Steps

Character state reconstruction

Pattern2: 2 Steps Pattern3: 6 Steps


! ! ! Characters! ! ! 1!2!3!4!5!6!7!8!9! Taxa!Orang! ! C!T!G!G!A!C!C!C!T! Chimp! ! C!T!A!G!C!T!C!C!C! Gorilla! C!T!G!G!C!C!A!C!T! Human! ! T!T!A!G!C!T!A!C!T! Tree 1!! 1 ! Tree 2!! 1! Tree 3!! 1


Tree 1 Tree 2 Tree 3C

CC

C

CC

C

CC





CC

C

CC

C

CC





CC

C

CC

C

CC





CC

C

CC

C

CC







T T TT T T TT T T TT



! ! ! Characters! ! ! 1!2!3!4!5!6!7!8!9! Taxa!Orang! ! C!T!G!G!A!C!C!C!T! Chimp! ! C!T!A!G!C!T!C!C!C! Gorilla! C!T!G!G!C!C!A!C!T! Human! ! T!T!A!G!C!T!A!C!T! Tree 1!! 1!0 ! Tree 2!! 1!0! Tree 3!! 1!0









A A GG A G AG A G AG









Tree 1 Tree 2 Tree 3G





G

G





GA

G





GA

G





GA

G





GA

G G





GA

G GG





GA

G GG

G





GA

G GG

G





GA

G GG

G





GA

G





GA

G G





GA

G GA





GA

G GA

A





GA

G GA

A





GA

G GA

A





GA

G GA

A





GA

G GA

A

G





GA

G GA

A

GG





GA

G GA

A

GG

G





GA

G GA

A

GG

G





GA

G GA

A

GG

G





GA

G GA

A





GA

G GA

A

G





GA

G GA

A

GA





GA

G GA

A

GA

A





GA

G GA

A

GA

A





GA

G GA

A

GA

A


! ! ! Characters! ! ! 1!2!3!4!5!6!7!8!9! Taxa!Orang! ! C!T!G!G!A!C!C!C!T! Chimp! ! C!T!A!G!C!T!C!C!C! Gorilla! C!T!G!G!C!C!A!C!T! Human! ! T!T!A!G!C!T!A!C!T! Tree 1!! 1!0!1 ! Tree 2!! 1!0!2! Tree 3!! 1!0!2

H C GO C G HO A G AG



! ! ! Characters! ! ! 1!2!3!4!5!6!7!8!9! Taxa!Orang! ! C!T!G!G!A!C!C!C!T! Chimp! ! C!T!A!G!C!T!C!C!C! Gorilla! C!T!G!G!C!C!A!C!T! Human! ! T!T!A!G!C!T!A!C!T! Tree 1!! 1!0 1!0!! Tree 2!! 1!0!2!0!! Tree 3!! 1!0!2!0!




! ! ! Characters! ! ! 1!2!3!4!5!6!7!8!9! Taxa!Orang! ! C!T!G!G!A!C!C!C!T! Chimp! ! C!T!A!G!C!T!C!C!C! Gorilla! C!T!G!G!C!C!A!C!T! Human! ! T!T!A!G!C!T!A!C!T! Tree 1!! 1!0 1!0!1! Tree 2!! 1!0!2!0!1! Tree 3!! 1!0!2!0!1

H C GO C G HO C G GO



! ! ! Characters! ! ! 1!2!3!4!5!6!7!8!9! Taxa!Orang! ! C!T!G!G!A!C!C!C!T! Chimp! ! C!T!A!G!C!T!C!C!C! Gorilla! C!T!G!G!C!C!A!C!T! Human! ! T!T!A!G!C!T!A!C!T! Tree 1!! 1!0 1!0!1!1! Tree 2!! 1!0!2!0!1!2! Tree 3!! 1!0!2!0!1!2




! ! ! Characters! ! ! 1!2!3!4!5!6!7!8!9! Taxa!Orang! ! C!T!G!G!A!C!C!C!T! Chimp! ! C!T!A!G!C!T!C!C!C! Gorilla! C!T!G!G!C!C!A!C!T! Human! ! T!T!A!G!C!T!A!C!T! Tree 1!! 1!0 1!0!1!1!2! Tree 2!! 1!0!2!0!1!2!1! Tree 3!! 1!0!2!0!1!2!2




! ! ! Characters! ! ! 1!2!3!4!5!6!7!8!9! Taxa!Orang! ! C!T!G!G!A!C!C!C!T! Chimp! ! C!T!A!G!C!T!C!C!C! Gorilla! C!T!G!G!C!C!A!C!T! Human! ! T!T!A!G!C!T!A!C!T! Tree 1!! 1!0 1!0!1!1!2!0! Tree 2!! 1!0!2!0!1!2!1!0! Tree 3!! 1!0!2!0!1!2!2!0




! ! ! Characters! ! ! 1!2!3!4!5!6!7!8!9! Taxa!Orang! ! C!T!G!G!A!C!C!C!T! Chimp! ! C!T!A!G!C!T!C!C!C! Gorilla! C!T!G!G!C!C!A!C!T! Human! ! T!T!A!G!C!T!A!C!T! Tree 1!! 1!0 1!0!1!1!2!0!1!! ! Tree 2!! 1!0!2!0!1!2!1!0!1! Tree 3!! 1!0!2!0!1!2!2!0!1




! ! ! Characters! ! ! 1!2!3!4!5!6!7!8!9! Taxa!Orang! ! C!T!G!G!A!C!C!C!T! Chimp! ! C!T!A!G!C!T!C!C!C! Gorilla! C!T!G!G!C!C!A!C!T! Human! ! T!T!A!G!C!T!A!C!T! Tree 1!! 1!0 1!0!1!1!2!0!1!7!! ! Tree 2!! 1!0!2!0!1!2!1!0!1!8! Tree 3!! 1!0!2!0!1!2!2!0!1!9









• General issues

• Case study





69


Key Concept: Parsimony Informativeness

• Not all traits are useful in determining which tree is most parsimonious

• Parsimony-uninformative characters do not provide any differentiation among trees in parsimony analysis

70






• No variation = not informative

72







• All taxa the same except one = non informative

74







































Simple rule for determining which characters in a data matrix are parsimony-informative? !Must be at least two states, each present in at least two taxa

78

Traits seen across taxa: Example 1: AACC Example 2: AAAGG Example 3: AACGGG Example 4: GGGCCC



Clicker

79


How Many of These Characters are Parsimony Informative

80

! ! ! Characters! ! ! 1!2!3!4!5!6!7!8!9! Taxa!Orang! ! C!T!G!G!A!C!C!C!T! Chimp! ! T!A!G!A!C!T!A!C!C! Gorilla! C!A!G!A!C!T!C!C!C! Human! ! T!T!A!G!C!T!A!C!T!

A. 1 B. 3 C. 5 D. 7


How Many of These Characters are Parsimony Informative

81

! ! ! Characters! ! ! 1!2!3!4!5!6!7!8!9! Taxa!Orang! ! C!T!G!G!A!C!C!C!T! Chimp! ! T!A!G!A!C!T!A!C!C! Gorilla! C!A!G!A!C!T!C!C!C! Human! ! T!T!A!G!C!T!A!C!T!

A. 1 B. 3 C. 5 D. 7



82








83

1. Ignore parsimony uninformative characters








• General issues

• Case study





84


pyrimidines

purines

A G

T C

Transitions and transversions

85


transitions

pyrimidines

purines

A G

T C


86

transitions


transitions

transversions

pyrimidines

purines

A G

T C


87

transitions


!Transitions: changes from one purine to another purine (A↔G) or from one pyrimidine to another pyrimidine (C↔T) !Transversions: changes from a purine to a pyrimidine or vice-versa (A↔C, A↔T, G↔C, G↔T)

For many molecular data sets it has been found that transitions are more likely to occur than transversions.


88

! ! ! Characters! ! ! 1!2!3!4!5!6!7!8!9! Taxa!Orang! ! C!T!G!G!A!C!C!C!T! Chimp! ! C!T!A!G!C!T!C!C!C! Gorilla! C!T!G!G!C!C!A!C!T! Human! ! T!T!A!G!C!T!A!C!T! !Score! ! ! ! ! ! ! ! ! ! ! Total ! Tree2! ! 1 0 2 0! 1!2 1!0!1! 5! ! Tree1! ! 1 0 1 0! 1!1!2!0!1! 4! Tree3! ! 1 0 2 0! 1!2!2!0!1! 6

89


90

Transitions vs. transversions


91

What if transversions counted 2x transitions?


92

What if transversions counted 3x transitions?



• General issues

• Case study





93

94

Informative characters

! ! ! Characters! ! ! 1!2!3!4!5!6!7!8!9! Taxa!Orang! ! C!T!G!G!A!C!C!C!T! Chimp! ! C!T!A!G!C!T!C!C!C! Gorilla! C!T!G!G!C!C!A!C!T! Human! ! T!T!A!G!C!T!A!C!T! !Score!Tree1! ! 1 0 2 0! 1!2 1!0!1! !! Tree2! ! 1 0 1 0! 1!1!2!0!1! Tree3! ! 1 0 2 0! 1!2!2!0!1

95

Two characters support Tree 2


96

One character supports Tree 1



Ket Concept: Likelihood methods

• Rather than searching for trees with the fewest changes, likelihood based methods assign trees probabilities

• The probabilities that are calculated do not favor one reconstruction 100% over others

• They are based on a probabilistic model of evolution of characters.

• Longer branches have higher probabilities of changes occurring on them

• Probabilities of different types of changes can be accounted for readily

103


Kinds of Phylogenetic Trees

104

A B C D

A

BC

D

A B C D

Units of character divergence

Units of time

Cladogram Phylogram Chronogram

Different kinds of trees

Only the relative branching order is depicted. No meaning to branch lengths.

Branch length is proportional to the amount of character change

Branch length is proportional to time

!105

Hidden assumptions in analysis so far

• Hidden assumptions in analysis

!106

Assumption I

• Hidden assumptions in analysis ! All types of characters treated equally

!107

Character examples

# Character Character States

1 Wings present, absent

2 Eye color red, white, brown

3 Leg length short, long

4 # antennal segments

11, 12

5 Nucleotide site (DNA)

adenine, thymine, guanine, cytosine

!108

Hidden assumptions in analysis so far

• Hidden assumptions in analysis ! All types of characters treated equally ! All types of changes treated equally

!109

Assumption III

• Hidden assumptions in analysis ! All types of characters treated equally ! All types of changes treated equally ! Changes on all branches treated equally

!110

Assumption III

• Why might some branches be different from others?

• Rates of evolution are not uniform across taxa. Some lineages (e.g., HIV) evolve much more rapidly than others (e.g., humans)

• Perhaps changes in lineages that evolve rapidly should count “less” since they are more common?

BIS2C. Biodiversity and the Tree of Life. 2014. L4. Inferring Phylogenetic Trees

Science