Defense Talk Slides

Estimating phylogenetic trees from discrete morphological data

Thesis DefenseApril M. WrightApril 14, 2015

Supervising Professor: David M. Hillis1

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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

Why Morphology?

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

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

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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)

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Image: W

ikimedia C

omm

ons

Image: W

ikimedia C

omm

ons

● Smaller● Selection bias

● Sequence data sets large● Take the whole sequence

Image: W

ikimedia C

omm

ons

● Smaller● Selection bias● Morphology has to be

interpreted

● Sequence data sets large● Take the whole sequence● Characters have more

clearly-defined properties

● 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

Image: W

ikimedia C

omm

ons

● Smaller● Morphology has to be

interpreted ● ...not so much

● DNA data sets large● Clearly-defined properties● Explicit, well-developed

models for sequence evolution

Likelihood models

● Given a model and data, how likely is a tree?

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Likelihood models

● Given a model and data, how likely is a tree?

Devoniantimes.org 13

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

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Likelihood models

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

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Likelihood models

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

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Likelihood models


■ Change can occur at any instant along a branch■ Change is symmetrical between states

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Likelihood models



● This model is statistically consistent

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Likelihood models



● This model is statistically consistent○ Caveat: As long as the assumptions hold○ Also, we don't have infinite data 19

Does a parametric approach (Mk) outperform non-parametric approach

(parsimony) when model assumptions are violated?

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An example

Image: Nobu Tamura

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● Full data set


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

● Random missing data

○ Most studies have looked at random missing data


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

An example

Image: Nobu Tamura

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An example

Image: Nobu Tamura

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An example

Image: Nobu Tamura

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● 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


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

Missing data

● In these conditions, some model assumptions have been violated

● Given these model violations, is it preferable to use parsimony?

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A simulation framework

Pyron 201129


● Simulate characters along the tree from the previous slide

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● Simulate characters

○ 350 & 1000 character data sets

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● Simulate characters

○ 350 & 1000 character data sets

● Estimate topology using the Mk model and parsimony

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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

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Fast Medium Slow


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

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Reminder

Image: Nobu Tamura

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Rate heterogeneity

● Diversity of rate classes can be helpful for resolving different regions of phylogenetic trees

○ Likelihood models account for superimposed changes

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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

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ResultsAll nodes wrong

All nodes right

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Comparison of methods

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Per

cent

age

Topo

logi

cal E

rror

Average Evolutionary Rate 40

Per

cent

age

Topo

logi

cal E

rror

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Summary - Chapter One

Does a parametric approach (Mk) outperform non-parametric approach

(parsimony) when model assumptions are violated?

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Does a parametric approach (Mk) outperform non-parametric approach (parsimony) when

model assumptions are violated?Yes

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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

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

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Model Assumptions

● Change is symmetrical between states

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Model Assumptions

● Change is symmetrical between states○ We know this is not always true

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Wright, Lyons, Brandley and Hillis, in review 49

Model Assumptions

● Change is symmetrical between states○ We know this is not always true

What if we could relax this assumption?

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Relaxing this assumption

● In Bayesian estimation, we can put priors on the parameters in our analyses

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● In Bayesian estimation, we can put priors on the parameters in our analyses

● Transition probabilities are the product of exchangeabilities and frequencies

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Probability of G to T change

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Probability of G to T change (exchangeability)

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Probability of G to T change (exchangeability)Equilibrium frequency of T

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.75 * 0 = 0

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.75 * .25 = 0.1875

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.75 * .25 = 0.1875

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0 1

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0 1 0 1

Empirical Datasets

● 206 datasets○ 5 to 279 taxa○ 11 to 364 characters○ Biased towards vertebrates

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Empirical Datasets

● 206 datasets○ 5 to 279 taxa○ 11 to 364 characters○ Biased towards vertebrates

● Modeled character change asymmetry according to the 6 distributions

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Empirical Datasets

Which priors best match empirical data?Does using the best-fit prior matter to

phylogenetic inference?

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Simulations

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

distributions

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Simulations


distributions○ One generating model, 3 misspecified models

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Zheng 2009

Simulations


distributions○ One generating model, 3 misspecified models

● Also simulated missing data

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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

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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?

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Empirical - Results

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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

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Empirical Datasets

Does using the best-fit prior matter to phylogenetic inference?

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Empirical Datasets

Does using the best-fit prior matter to phylogenetic inference?

Variable.

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Simulated Datasets

Can we detect the generating value of α among misspecified values of α?

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Simulated Data

Can we detect the generating value of α among misspecified values of α?

Yes.

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Simulated Data

Does using the best-fit α result in a more correct tree?

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Sca

led

Rob

inso

n-Fo

ulds

Dis

tanc

e to

Tru

e Tr

ee

Zheng Trees8-Taxon

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Simulations

Does using the best-fit alpha result in a more correct tree?

No missing data: Yes.

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Analytical Model97

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

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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

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

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Partitioning

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

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Partitioning

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

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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

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Partitioning

● Less well-explored in morphology

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Partitioning

● Less well-explored in morphology○ Clarke and Middleton (2008) is one of the few

explorations of partitioning in a likelihood context for morphology

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Partitioning



○ Used anatomical subregion partitioning

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Partitioning



○ Used anatomical subregion partitioning○ Found improved model fit and different topology with

partitioned data

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Partitioning



○ Used anatomical subregion partitioning○ Found improved model fit and different topology with

partitioned data

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PartitionFinder Morphology

● Adaptation of technology for partitioning of genome-scale information

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

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● Estimate a phylogenetic tree from the unpartitioned data matrix

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● Fit parameters of the evolutionary model to the whole dataset as a single set of sites

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● 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)

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● Generate rates of evolution for each site in the dataset

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● Use k-means clustering to split the subset in two based on these rates

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● Use k-means clustering to split the subset in two based on these rates

● Fit parameters of the model for these new subsets

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

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● 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.

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Are partitioned models often the best-fit model for empirical datasets?

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When they are, does this make a difference to the tree estimated?

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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

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Modeling

● We used PartitionFinder Morphology to partition 209 datasets○ 3 criteria: AIC, BIC and AICc

Least conservative

Most conservative

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Estimation

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

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Yes.

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

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LikelihoodB

ayesian

Scaled Robinson-Foulds Distance

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Yes, in empirical datasets we often estimate different trees.

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Specific Example

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Unpartitioned Data Partitioned Data


Yes, and the likelihood surface is more peaked.

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Conclusions

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Conclusions

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

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Conclusions

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

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Conclusions

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

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Thank you!CommitteeDavid HillisMartha SmithDavid CannatellaRandy LinderBob Jansen

LabmatesBen, Emily Jane, Thomas, Patricia, Becca, Mariana, Shannon, Patrick, Chris, J9, Matt, Sandi, Carlos, Taylor, Katie, Devon, Anne, Jim, Jeremy, Tracy

OtherUT 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

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