Class 9: Phylogenetic Trees

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Class 9 Phylogenetic Trees
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The Tree of Life
Daprès Ernst Haeckel, 1891
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Evolution

• Many theories of evolution
• Basic idea
• speciation events lead to creation of different
  species
• Speciation caused by physical separation into
  groups where different genetic variants become
  dominant
• Any two species share a (possibly distant) common
  ancestor

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Phylogenies

• A phylogeny is a tree that describes the sequence
  of speciation events that lead to the forming of
  a set of current day species
• Leafs - current day species
• Nodes - hypothetical most recent common ancestors
• Edges length - time from one speciation to the
  next

Aardvark
Bison
Chimp
Dog
Elephant
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Primate evolution
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• Until mid 1950s phylogenies were constructed by
  experts based on their opinion (subjective
  criteria)
• The Linnaeus classification scheme implicitly
  assumes tree structure
• Since then, focus on objective criteria for
  constructing phylogenetic trees
• Thousands of articles in the last decades
• Important for many aspects of biology
• Classification (systematics)
• Understanding biological mechanisms

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Morphological vs. Molecular

• Classical phylogenetic analysis morphological
  features
• number of legs, lengths of legs, etc.
• Modern biological methods allow to use molecular
  features
• Gene sequences
• Protein sequences
• Analysis based on homologous sequences (e.g.,
  globins) in different species

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Dangers in Molecular Phylogenies

• We have to remember that gene/protein sequence
  can be homologous for different reasons
• Orthologs -- sequences diverged after a
  speciation event
• Paralogs -- sequences diverged after a
  duplication event
• Xenologs -- sequences diverged after a horizontal
  transfer (e.g., by virus)

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Dangers of Paralogues
Gene Duplication
Speciation events
2B
1B
3A
3B
2A
1A
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Dangers of Paralogs

• If we only consider 1A, 2B, and 3A...

Gene Duplication
Speciation events
2B
1B
3A
3B
2A
1A
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Types of Trees

• A natural model to consider is that of rooted
  trees

Common Ancestor
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Types of Trees

• Depending on the model, data from current day
  species does not distinguish between different
  placements of the root

vs
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Types of trees

• Unrooted tree represents the same phylogeny with
  out the root node

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Positioning Roots in Unrooted Trees

• We can estimate the position of the root by
  introducing an outgroup
• a set of species that are definitely distant from
  all the species of interest

Proposed root
Falcon
Aardvark
Bison
Chimp
Dog
Elephant
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Type of Data

• Distance-based
• Input is a matrix of distances between species
• Can be fraction of residue they disagree on, or
  alignment score between them, or
• Character-based
• Examine each character (e.g., residue) separately

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Simple Distance-Based Method

• Input distance matrix between species
• Outline
• Cluster species together
• Initially clusters are singletons
• At each iteration combine two closest clusters
  to get a new one

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UPGMA Clustering

• Let Ci and Cj be clusters, define distance
  between them to be
• When we combine two cluster, Ci and Cj, to form a
  new cluster Ck, then

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Molecular Clock

• UPGMA implicitly assumes that all distances
  measure time in the same way

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3
2
3
4
1
1
4
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Additivity

• A weaker requirement is additivity
• In real tree, distances between species are the
  sum of distances between intermediate nodes

k
c
b
j
a
i
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Consequences of Additivity

• Suppose input distances are additive
• For any three leaves
• Thus

k
c
b
j
a
m
i
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Neighbor Joining

• Can we use this fact to construct trees?
• Let
• where
• Theorem if D(i,j) is minimal (among all pairs of
  leaves), then i and j are neighbors in the tree

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Neighbor Joining

• Set L to contain all leaves
• Iteration
• Choose i,j such that D(i,j) is minimal
• Create new node k, and set
• remove i,j from L, and add k
• Terminatewhen L 2, connect two remaining
  nodes

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Distance Based Methods

• If we make strong assumptions on distances, we
  can reconstruct trees
• In real-life distances are not additive
• Sometimes they are close to additive

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Parsimony

• Character-based method
• Assumptions
• Independence of characters (no interactions)
• Best tree is one where minimal changes take place

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Simple Example

• Suppose we have five species, such that three
  have C and two T at a specified position
• Minimal tree has one evolutionary change

C
T
C
T
C
C
C
T
T ? C
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Another Example

• What is the parsimony score of

A CAGGTA B CAGACA C CGGGTA D TGCACT E TGCGTA
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Evaluating Parsimony Scores

• How do we compute the Parsimony score for a given
  tree?
• Weighted Parsimony
• Each change is weighted by the score c(a,b)

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Evaluating Parsimony Scores

• Dynamic programming on the tree
• Initialization
• For each leaf i set S(i,a) 0 if i is labeled by
  a, otherwise S(i,a) ?
• Iteration
• if k is node with children i and j, then S(k,a)
  minb(S(i,b)c(a,b)) minb(S(j,b)c(a,b))
• Termination
• cost of tree is minaS(r,a) where r is the root

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Example
A CAGGTA B CAGACA C CGGGTA D TGCACT E TGCGTA
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Cost of Evaluating Parsimony

• If there are n nodes, m characters, and k
  possible values for each character, then
  complexity is O(nmk)
• Using this procedure, we can reconstruct most
  parsimonious values at each ancestor node