Slides from my defense talk, April 14, 2014

1. Estimating phylogenetic trees from
discrete morphological data
Thesis Defense
April M. Wright
April 14, 2015
Supervising Professor: David M. Hillis
1

2. 2
Bayesian Analysis
Using a Simple
Likelihood Model
Outperforms
Parsimony for
Estimation of
Phylogeny from
Discrete
Morphological Data
Modeling character
change heterogeneity
through the use of
priors
Use of an
Automated
Method for
Partitioning
Morphological
Data
"Bayes' Theorem MMB 01" by mattbuck, PartitionFinder logo by Ainsley Seago

3. Why Morphology?
3

4. Why Morphology?
● Estimates put > 99% of biota that has ever existed as extinct
4

5. Why Morphology?
● Estimates put > 99% of biota that has ever existed as extinct
● Probably, we won’t wring DNA from a stone
5

6. Why Morphology?
● Estimates put > 99% of biota that has ever existed as extinct
● Probably, we won’t wring DNA from a stone
● Inclusion of fossils acknowledged to improve phylogenetic trees
(Huelsenbeck 1991, Wiens 2001 & 2004), divergence dating (Heath, Stadler and Huelsenbeck
2012) and comparative method estimates (Slater and Harmon 2012)
6

7. Image:WikimediaCommons

8. Image:WikimediaCommons
● Smaller
● Selection bias
● Sequence data sets large
● Take the whole sequence

9. Image:WikimediaCommons
● Smaller
● Selection bias
● Morphology has to be
interpreted
● Sequence data sets large
● Take the whole sequence
● Characters have more
clearly-defined properties

10. ● Smaller
● Selection bias
● Morphology has to be
interpreted
Char. 1 Char. 2 Char. 3 Char. 4 Char. 5 Char. 6 Char. 7 Char. 8 Char. 9
Species 1 0 1 1 0 1 1 0 1 0
Species 2 1 0 1 0 0 0 1 1 0
Species 3 1 0 1 0 0 1 0 0 0
Species 4 0 0 0 1 1 0 0 0 1
Species 5 0 0 0 1 0 1 1 0 0

11. Image:WikimediaCommons
● Smaller
● Morphology has to be
interpreted
● ...not so much
● DNA data sets large
● Clearly-defined properties
● Explicit, well-developed
models for sequence
evolution

12. Likelihood models
● Given a model and data, how likely is a tree?
12

13. Likelihood models
● Given a model and data, how likely is a tree?
Devoniantimes.org 13

14. Chapter One: Bayesian Analysis Using a Simple
Likelihood Model Outperforms Parsimony for Estimation of
Phylogeny from Discrete Morphological Data
14

15. Likelihood models
● There is one practical published model for
phylogenetic estimation from discrete
morphological data, Mk
15

16. Likelihood models
● There is one practical published model for
phylogenetic estimation from discrete
morphological data, Mk
○ Like all methods, Mk has assumptions
16

17. Likelihood models
● There is one practical published model for
phylogenetic estimation from discrete
morphological data, Mk
○ Like all methods, Mk has assumptions
■ Change can occur at any instant along a branch
■ Change is symmetrical between states
17

18. Likelihood models
● There is one practical published model for
phylogenetic estimation from discrete
morphological data, Mk
○ Like all methods, Mk has assumptions
■ Change can occur at any instant along a branch
■ Change is symmetrical between states
● This model is statistically consistent
18

19. Likelihood models
● There is one practical published model for
phylogenetic estimation from discrete
morphological data, Mk
○ Like all methods, Mk has assumptions
■ Change can occur at any instant along a branch
■ Change is symmetrical between states
● This model is statistically consistent
○ Caveat: As long as the assumptions hold
○ Also, we don't have infinite data 19

20. Does a parametric approach (Mk)
outperform non-parametric approach
(parsimony) when model assumptions are
violated?
20

21. An example
Image: Nobu Tamura
21

22. ● Full data set
Char. 1 Char. 2 Char. 3 Char. 4 Char. 5 Char. 6 Char. 7 Char. 8 Char. 9
Species 1
(Fossil)
0 1 1 0 1 1 0 1 0
Species 2
(Fossil)
1 1 1 0 0 0 1 1 0
Species 3 1 0 1 0 0 1 0 0 0
Species 4 0 0 0 1 1 0 0 0 1
Species 5 0 0 0 1 0 1 1 0 0

23. ● Random missing data
○ Most studies have looked at random missing data
Char. 1 Char. 2 Char. 3 Char. 4 Char. 5 Char. 6 Char. 7 Char. 8 Char. 9
Species 1
(Fossil)
0 1 1 ? 1 1 0 1 0
Species 2
(Fossil)
1 ? 1 0 0 ? 1 ? 0
Species 3 1 0 1 ? 0 1 ? 0 0
Species 4 0 0 ? 1 1 ? 0 0 ?
Species 5 0 0 ? 1 0 1 1 0 0

24. An example
Image: Nobu Tamura
24

25. An example
Image: Nobu Tamura
25

26. An example
Image: Nobu Tamura
26

27. ● Some types of characters are more likely to be missing
from fossil taxa
● Missing characters may be more likely to fall into certain
rate classes
Char. 1 Char. 2 Char. 3 Char. 4 Char. 5 Char. 6 Char. 7 Char. 8 Char. 9
Species 1
(Fossil)
0 1 1 0 ? ? ? ? ?
Species 2
(Fossil)
1 0 1 0 ? ? ? ? ?
Species 3 1 0 1 0 0 0 1 1 0
Species 4 0 0 0 1 0 1 0 0 0
Species 5 0 0 0 1 0 1 1 0 0

28. Missing data
● In these conditions, some model
assumptions have been violated
● Given these model violations, is it preferable
to use parsimony?
28

29. A simulation framework
Pyron 2011
29

30. A simulation framework
● Simulate characters along the tree from the
previous slide
30

31. A simulation framework
● Simulate characters
○ 350 & 1000 character data sets
31

32. A simulation framework
● Simulate characters
○ 350 & 1000 character data sets
● Estimate topology using the Mk model and
parsimony
32

33. Rate heterogeneity
● Different rates of character evolution
○ Low rates of change mean each character is likely to
have changed rarely, if at all
○ High rates mean there are likely reversals and
parallel evolution in the data
33

34. Fast Medium Slow
Char. 1 Char. 2 Char. 3 Char. 4 Char. 5 Char. 6 Char. 7 Char. 8 Char. 9
Species 1
(Fossil)
? ? ? 0 1 1 0 1 0
Species 2
(Fossil)
? ? ? 0 0 0 1 1 0
Species 3 1 0 1 0 0 1 0 0 0
Species 4 0 0 0 1 1 0 0 0 1
Species 5 0 0 0 1 0 1 1 0 0
34

35. Reminder
Image: Nobu Tamura
35

36. Rate heterogeneity
● Diversity of rate classes can be helpful for
resolving different regions of phylogenetic
trees
○ Likelihood models account for superimposed
changes
36

37. Rate heterogeneity
● Diversity of rate classes can be helpful for
resolving different regions of phylogenetic
trees
○ Likelihood models account for superimposed
changes
○ In analysis, rate heterogeneity is often modeled as
gamma-distributed
37

38. Results
All nodes wrong
All nodes right
38

39. Comparison of methods
39

40. PercentageTopologicalError
Average Evolutionary Rate 40

41. PercentageTopologicalError
41

42. 42

43. Summary - Chapter One
Does a parametric approach (Mk)
outperform non-parametric approach
(parsimony) when model assumptions are
violated?
43

44. Summary - Chapter One
Does a parametric approach (Mk) outperform
non-parametric approach (parsimony) when
model assumptions are violated?
Yes
44

45. Summary - Chapter One
Caveats: We’ve really only looked at one type
of model violation here
There are other reasons you might use
parsimony, or might think the contrast of
likelihood and parsimony methods is telling you
something interesting
45

46. Chapter Two: Modeling character change
heterogeneity through the use of priors
46

47. Model Assumptions
● Change is symmetrical between states
47

48. Model Assumptions
● Change is symmetrical between states
○ We know this is not always true
48

49. Wright, Lyons, Brandley and Hillis, in review 49

50. Model Assumptions
● Change is symmetrical between states
○ We know this is not always true
What if we could relax this assumption?
50

51. Relaxing this assumption
● In Bayesian estimation, we can put priors on
the parameters in our analyses
51

52. Relaxing this assumption
● In Bayesian estimation, we can put priors on
the parameters in our analyses
● Transition probabilities are the product of
exchangeabilities and frequencies
52

53. Relaxing this assumption
53

54. Relaxing this assumption
Probability of G to T change
54

55. Relaxing this assumption
Probability of G to T change (exchangeability)
55

56. Relaxing this assumption
Probability of G to T change (exchangeability)
Equilibrium frequency of T
56

57. Relaxing this assumption
Probability of G to T change (exchangeability)
Equilibrium frequency of T
.75 * 0 = 0
57

58. Relaxing this assumption
Probability of G to T change (exchangeability)
Equilibrium frequency of T
.75 * .25 = 0.1875
58

59. Relaxing this assumption
Probability of G to T change (exchangeability)
Equilibrium frequency of T
.75 * .25 = 0.1875
59

60. 60

61. 61

62. 62
0 1

63. 63
0 1
0 1

64. 64

65. 65

66. 66

67. 67

68. Empirical Datasets
● 206 datasets
○ 5 to 279 taxa
○ 11 to 364 characters
○ Biased towards vertebrates
68

69. Empirical Datasets
● 206 datasets
○ 5 to 279 taxa
○ 11 to 364 characters
○ Biased towards vertebrates
● Modeled character change asymmetry
according to the 6 distributions
69

70. 70

71. Empirical Datasets
Which priors best match empirical data?
Does using the best-fit prior matter to
phylogenetic inference?
71

72. Simulations
● Simulated data according to 4 distributions
○ Modeled the data according to each of the four
distributions
72

73. 73

74. Simulations
● Simulated data according to 4 distributions
○ Modeled the data according to each of the four
distributions
○ One generating model, 3 misspecified models
74

75. 75
Zheng 2009

76. 76

77. Simulations
● Simulated data according to 4 distributions
○ Modeled the data according to each of the four
distributions
○ One generating model, 3 misspecified models
● Also simulated missing data
77

78. Simulations
● Estimated trees according to each of the 4
values of alpha
● Used Bayes Factor model selection to
choose the best-fit value
● Used Robinson-Foulds distance to assess
topological correctness
78

79. Simulations
Can we detect the generating value of alpha
among misspecified values of alpha?
Does using the correct alpha result in a more
correct tree?
79

80. Empirical - Results
80

81. 81

82. 82

83. 83

84. Empirical Datasets
Which priors best match empirical data?
About half: best fit is the α = ∞ prior
Strength of support for different values of α
varies
84

85. Empirical Datasets
Does using the best-fit prior matter to
phylogenetic inference?
85

86. 86

87. Empirical Datasets
Does using the best-fit prior matter to
phylogenetic inference?
Variable.
87

88. Simulated Datasets
Can we detect the generating value of α among
misspecified values of α?
88

89. 89

90. Simulated Data
Can we detect the generating value of α among
misspecified values of α?
Yes.
90

91. Simulated Data
Does using the best-fit α result in a more
correct tree?
91

92. ScaledRobinson-FouldsDistancetoTrueTree
ZhengTrees8-Taxon
92

93. 93

94. 94

95. Simulations
Does using the best-fit alpha result in a more
correct tree?
No missing data: Yes.
95

96. 96

97. Analytical Model
97

98. Simulations
Does using the best-fit α result in a more
correct tree?
Yes, and the importance of doing so is greater
when the problem is harder
98

99. Chapter Two: Conclusions
● Appropriate fit of α parameter improves
phylogenetic estimation
● Bayes Factor model selection performs well
at choosing the best-fit value of α among a
set of α values
99

100. Chapter Three: Use of an Automated Method for
Partitioning Morphological Data
100

101. Partitioning
● Refers to breaking a dataset into smaller
subsets that can be analyzed under different
phylogenetic models
101

102. Partitioning
● Refers to breaking a dataset into smaller
subsets that can be analyzed under different
phylogenetic models
○ Well-explored in a molecular context
102

103. Partitioning
● Refers to breaking a dataset into smaller
subsets that can be analyzed under different
phylogenetic models
○ Well-explored in a molecular context (Brown and Lemmon
2007)
○ Often, partition schemes are tested as a stage in
model-fitting
103

104. Partitioning
● Less well-explored in morphology
104

105. Partitioning
● Less well-explored in morphology
○ Clarke and Middleton (2008) is one of the few
explorations of partitioning in a likelihood context for
morphology
105

106. Partitioning
● Less well-explored in morphology
○ Clarke and Middleton (2008) is one of the few
explorations of partitioning in a likelihood context for
morphology
○ Used anatomical subregion partitioning
106

107. Partitioning
● Less well-explored in morphology
○ Clarke and Middleton (2008) is one of the few
explorations of partitioning in a likelihood context for
morphology
○ Used anatomical subregion partitioning
○ Found improved model fit and different topology with
partitioned data
107

108. Partitioning
● Less well-explored in morphology
○ Clarke and Middleton (2008) is one of the few
explorations of partitioning in a likelihood context for
morphology
○ Used anatomical subregion partitioning
○ Found improved model fit and different topology with
partitioned data
108

109. PartitionFinder Morphology
● Adaptation of technology for partitioning of
genome-scale information
109

110. PartitionFinder Morphology
● Adaptation of technology for partitioning of
genome-scale information
○ But we don’t have genome-scale information
110

111. 111

112. PartitionFinder Morphology
● Estimate a phylogenetic tree from the
unpartitioned data matrix
112

113. PartitionFinder Morphology
● Estimate a phylogenetic tree from the
unpartitioned data matrix
● Fit parameters of the evolutionary model to
the whole dataset as a single set of sites
113

114. PartitionFinder Morphology
● Estimate a phylogenetic tree from the
unpartitioned data matrix
● Fit parameters of the evolutionary model to
the whole dataset as a single set of sites
● Calculate the score of the data given this
model according to an information theoretic
criterion (AIC, BIC or AICc)
114

115. PartitionFinder Morphology
● Generate rates of evolution for each site in
the dataset
115

116. PartitionFinder Morphology
● Generate rates of evolution for each site in
the dataset
● Use k-means clustering to split the subset in
two based on these rates
116

117. PartitionFinder Morphology
● Generate rates of evolution for each site in
the dataset
● Use k-means clustering to split the subset in
two based on these rates
● Fit parameters of the model for these new
subsets
117

118. PartitionFinder Morphology
● Calculate the score of this new partitioned
data matrix according to the same
information theoretic criterion used in step 3.
118

119. PartitionFinder Morphology
● Calculate the score of this new partitioned
data matrix according to the same
information theoretic criterion used in step 3.
● If smaller subsets are supported by this
criterion, continue to divide them, repeating
steps 5-7. If not, terminate the search.
119

120. PartitionFinder Morphology
Are partitioned models often the best-fit model
for empirical datasets?
120

121. PartitionFinder Morphology
Are partitioned models often the best-fit model
for empirical datasets?
When they are, does this make a difference to
the tree estimated?
121

122. Modeling
● We used PartitionFinder Morphology to
partition 209 datasets
○ 3 criteria: AIC, BIC and AICc
2k- 2lnL -2 (lnL + 2k * n-k-1)
-2lnL + k * lnn
n
122

123. Modeling
● We used PartitionFinder Morphology to
partition 209 datasets
○ 3 criteria: AIC, BIC and AICc
Least conservative
Most conservative
123

124. Estimation
● Estimate trees under likelihood and
Bayesian implementations of the Mk model
using the partitioned data and unpartitioned
data
124

125. PartitionFinder Morphology
Are partitioned models often the best-fit model
for empirical datasets?
125

126. 126

127. 127

128. 128

129. PartitionFinder Morphology
Are partitioned models often the best-fit model
for empirical datasets?
Yes.
129

130. PartitionFinder Morphology
When a partitioned model is the best fit, does
this make a difference to the tree estimated?
130

131. LikelihoodBayesian
Scaled Robinson-Foulds Distance
131

132. When a partitioned model is the best fit, does
this make a difference to the tree estimated?
Yes, in empirical datasets we often estimate
different trees.
132

133. Specific Example
133

134. 134
Unpartitioned Data Partitioned Data

135. 135

136. When a partitioned model is the best fit, does
this make a difference to the tree estimated?
Yes, and the likelihood surface is more peaked.
136

137. Conclusions
137

138. Conclusions
● Chapter One: Likelihood-based methods are
effective for estimating phylogeny for
morphological data, even in the presence of
biased missing data
138

139. Conclusions
● Chapter Two: Use of a prior on equilibrium
state frequencies can improve the
performance of Bayesian estimation using
morphological data
139

140. Conclusions
● Chapter Three: PartitionFinder Morphology
is a promising lead for evaluation of
partitioning schemes
140

141. Thank you!
Committee
David Hillis
Martha Smith
David Cannatella
Randy Linder
Bob Jansen
Labmates
Ben, Emily Jane, Thomas, Patricia,
Becca, Mariana, Shannon, Patrick, Chris,
J9, Matt, Sandi, Carlos, Taylor, Katie,
Devon, Anne, Jim, Jeremy, Tracy
Other
UT vert paleo, especially Julia, Robert,
Zach
And the people who make
this worth doing:
You know who you are.
And Jason and unnamed baby girl Wright Stinnett.
Collaborators:
Graeme Lloyd, Paul Fransden, David Bapst, Nick
Matzke, Matt Brandley, Rob Lanfear
141