EntoGene 606 Distance Methods I

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Ento/Gene 606Distance Methods I
(Another Place, by Chris Howells)
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Phenetics or Numerical Taxonomy
Joseph Camin (1970s)
Robert Sokal (1964)

• Peter Sneath
• (1959)

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Phenetics

• Hypotheses of phylogenetic relationships are
  unnecessary to the process of classification
• In fact, they interfere with the process by
  introducing uncertainty and subjective decisions

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Paul Ehrlich (1965)

• Into which group of taxonomists do you wish to be
  classified in
• Members of the old school, who would like to
  see a pinch of phylogenetic specialization mixed
  into their basic data (presumably for sentimental
  reasons)
• or
• Those who wish to look forward

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Phenetic Methods

• Group taxa based on overall similarity
• Do not distinguish between ancestral and derived
  similarity
• One common methodology
• Compute pairwise distances between taxa
• Cluster similar taxa together using clustering
  algorithms

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Why use phenetic methods?

• Some types of data can only be compared using
  distances
• Immunological distances
• DNA annealing/melting points
• Distance methods are fast
• Analyze large data sets

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Measures of Distance (Dissimilarity)

• Continuous, quantitative characters
• DNA sequence data
• Allozymes, microsatellites, RFLP, AFLP, etc.

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Properties of an ideal distance measure1.
Symmetry

• Dij Dji
• Distance from i to j is same as distance computed
  from j to I

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Properties of an ideal distance measure2.
Distinguishability

• If Dij gt 0, then i is not the same as j
• If Dij 0, then i is the same as j

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Properties of an ideal distance measure 3.
Satisfies Triangle Inequality

• Dik lt Dij Djk

Why is this important?
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3. Triangle Inequality

• Distance measures that satisfy triangle
  inequality are called Metrics
• Failure of triangle inequality implies that the
  distance measure is generating negative distances
• Negative distances are an artifact of the way in
  which distance is computed

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Neis unbiased genetic distance

• Pairwise distances between O.T.U.s based on
  allele frequencies

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Neis Genetic Distance

• Estimated accumulated number of allele
  substitutions per locus
• 0 all alleles in identical frequencies in both
  populations
• 1 alleles have been replaced at each locus

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Neis genetic distance(Hillis, 1984, Systematic
Zoology 33238-240)

• Assumes all loci evolving at equal rates
• Hillis (1984) published correction for this
  assumption
• Assumes all loci in genetic equilibrium
• Is not a metric distance in some cases!

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Other Measures of Genetic Distance

• Rogers
• Acts as a metric
• Microsatellites
• Stepwise mutation model
• Infinite alleles model
• RFLP data

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DNA distances

• Uncorrected P apparent substitutions
• total nucleotides

1 a c g t t c g a c g 2 a c a t t c g a c g 3
a c a c c c g a c g
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DNA distances

• Uncorrected P apparent substitutions
• total nucleotides

1 a c g t t c g a c g 2 a c a t t c g a c g 3
a c a c c c g a c g
P12 1/10 0.10 P13 3/10 0.30
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Saturation of gene sequences
A a g t c t c c a g g t g c a c g t c t t
B a g t c c c c a g g t g c a c g t c t t
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Saturation of gene sequences
A a g t c t c c a g g t g c a c g t c t t
B a g t c c c c a g g t g c a c g t c t t
C a g t c t c c a g g t g c a c g t c t t
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Saturation of gene sequences
A a g t c t c c a g g t g c a c g t c t t
B a g t c c c c a g g t g c a c g t c t t
C a g t c t c c a g g t g c a c g t c t t
D a g t c a c c a g g t g c a c g t c t t
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A
B
t gt c
C
D
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A
B
t gt c c gt t
C
D
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A
B
t gt c c gt t t gt a
C
D
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Page and Holmes (1998) Molecular Evolution
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Page and Holmes (1998) Molecular Evolution
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• (Galewski et al. BMC Evol. Biol 2006 680)

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Corrected DNA distances

• Jukes/Cantor - 3/4 ln (1- 4/3 D)
• Assumes equal rates of substitution between all
  nucleotides
• Assumes equal nucleotide frequencies
• One correction to overall distance

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Kimura 2-Parameter Distance(K2P)

• Two rates of substitutions, for transitions and
  transversions

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Generalized Time Reversable Distance(GTR)

• Six different substitution rates
• Backward rates are same as forward rates

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Substitution rates

• All rates equal (essentially the Jukes-Cantor
  model)
• Transitions have different rate than
  transversions
• Two different kinds of transversions (this gives
  us three rates)
• Maximally, all types of substitutions are allowed
  to have their own rate
• But note that substitution rates are not
  independent of base frequencies in the data!

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Base Frequences

• For example, insect mtDNA is A-T rich
• much more adenine and thymine
• much less cytosine and guanine
• What does this do to frequencies of base changes?

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Base Frequences

• For example, insect mtDNA is A-T rich
• much more adenine and thymine
• much less cytosine and guanine
• What does this do to frequencies of base changes?

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Base Frequences

• For example, insect mtDNA is A-T rich
• much more adenine and thymine
• much less cytosine and guanine
• What does this do to frequencies of base changes?

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Base Frequencies

• We can assume they are all equal
• We can count them in the data matrix
• But this will not include the base frequencies at
  all the internal nodes of the tree (HTUs) once
  it is constructed
• We can build the tree, step by step, changing the
  estimates of base frequencies as we go

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Substitution Rate Models

• GTR general time reversible
• JC Jukes Cantor
• Relax each assumption to move to the model below

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Matrix of Distances
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Clustering Methods

• Visualize as much information as possible in
  matrix of distances or assocations in 2
  dimensional scheme
• Order O.T.U.s into connected groups

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Clustering Methods
B
C
A
E
G
D
F

• Divisive Methods
• Start with all O.T.U.s in one group
• Divide into two groups
• Continue until only individuals are left

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Clustering Methods
B
C
A
E
G
D
F

• Divisive Methods
• Start with all O.T.U.s in one group
• Divide into two groups
• Continue until only individuals are left

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Clustering Methods
B
C
A
E
G
D
F

• Divisive Methods
• Start with all O.T.U.s in one group
• Divide into two groups
• Continue until only individuals are left

G
F
C
A
B
E
D
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Clustering Methods
B
C
A
E
G
D
F

• Divisive Methods
• Start with all O.T.U.s in one group
• Divide into two groups
• Continue until only individuals are left

G
F
C
A
B
E
D
C
A
D
(etc.)
D
C
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Clustering Methods
B
C
A
E
G
D
F

• Agglomerative Methods
• Start with individual O.T.U.s
• Join two most similar O.T.U.s to form 1st
  cluster
• Find which O.T.U. is most similar to cluster
• Join to form second cluster

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Clustering Methods
B
C
A
E
G
D
F

• Agglomerative Methods
• Start with individual O.T.U.s
• Join two most similar O.T.U.s to form 1st
  cluster
• Find which O.T.U. is most similar to cluster
• Join to form second cluster

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Clustering Methods
B
A
E
G
F

• Agglomerative Methods
• Start with individual O.T.U.s
• Join two most similar O.T.U.s to form 1st
  cluster
• Find which O.T.U. is most similar to cluster, or
  which two O.T.U.s are most similar to each other
• Join to form second cluster

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Clustering Methods
B
F

• Agglomerative Methods
• Start with individual O.T.U.s
• Join two most similar O.T.U.s to form 1st
  cluster
• Find which O.T.U. is most similar to cluster, or
  which two O.T.U.s are most similar to each other

?
A
G
E
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Clustering Methods
B
F

• Agglomerative Methods
• Start with individual O.T.U.s
• Join two most similar O.T.U.s to form 1st
  cluster
• Find which O.T.U. is most similar to cluster, or
  which two O.T.U.s are most similar to each other
• Join to form second cluster

G
A
E
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• Agglomerative Methods
• Start with individual O.T.U.s
• Join two most similar O.T.U.s to form 1st
  cluster
• Find which O.T.U. is most similar to cluster, or
  which two O.T.U.s are most similar to each other
• Join to form second cluster
• Continue until all O.T.U.s have been clustered

B
F
?
A
G
E
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• Agglomerative Methods
• Start with individual O.T.U.s
• Join two most similar O.T.U.s to form 1st
  cluster
• Find which O.T.U. is most similar to cluster, or
  which two O.T.U.s are most similar to each other
• Join to form second cluster
• Continue until all O.T.U.s have been clustered

A
C
D
F
E
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• Agglomerative Methods
• Start with individual O.T.U.s
• Join two most similar O.T.U.s to form 1st
  cluster
• Find which O.T.U. is most similar to cluster, or
  which two O.T.U.s are most similar to each other
• Join to form second cluster
• Continue until all O.T.U.s have been clustered

A
E
C
D
F
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• Hierarchical
• Members of lower level cluster also members of
  higher level clusters
• Non-Overlapping
• An O.T.U. is a member of only one cluster at a
  particular level of similarity or distance

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Agglomerative Clustering Methods

• Start with distance or association matrix
• Each method has rule to join most similar
  O.T.U.s to form clusters
• Each method has rules to determine distance of
  unclustered O.T.U.s to existing clusters
• Each methods has rules to determine distance
  between two clusters

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Single Linkage or Nearest Neighbor Method

• D a (b,c) min (Dab, Dac)
• D (a,b)(c,d) min (Dac, Dbc, Dad, Dbd)

B
A
D
C
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Single Linkage or Nearest Neighbor Method

• D a (b,c) min (Dab, Dac)
• D (a,b)(c,d) min (Dac, Dbc, Dad, Dbd)

B
B
E
A
D
D
C
F
C
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Complete Linkage or Furthest Neighbor Method

• D a (b,c) max (Dab, Dac)
• D (a,b)(c,d) max (Dac, Dbc, Dad, Dbd)

B
A
D
C
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Complete Linkage or Furthest Neighbor Method

• D a (b,c) max (Dab, Dac)
• D (a,b)(c,d) max (Dac, Dbc, Dad, Dbd)

B
B
E
A
D
D
C
F
C
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Averaging methods

• D a (b,c) average (Dab, Dac)
• D (a,b)(c,d) average (Dac, Dbc, Dad, Dbd)

B
A
D
C
Da(b,c,d) 1/3(DabDacDad)
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Averaging Methods

• D a (b,c) average (Dab, Dac)
• D (a,b)(c,d) average (Dac, Dbc, Dad, Dbd)

B
B
E
A
D
D
C
F
C
D(e,f)(b,c,d) 1/6(DebDecDedDfbDfcDfd)
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UPGMA clustering

• Unweighted Pair Group Method using arithmetic
  Averages
• Agglomerative method
• Computes distances between clusters and between
  clusters and O.T.U. as averages

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E
F
A
C
D
B
G
E
F
A
C
D
B
G
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Dendrogram or Phenogram

• Graphical display of clustering algorithm
• Branch lengths of clusters in units of similarity
  or distance