stem-hy: species tree estimation using maximum likelihood ... · what is stem-hy? using stem-hy for...

What is STEM-hy?Using STEM-hy for Species Tree Estimation

Using STEM-hy for Hybridization AnalysisPractice Datasets

STEM-hy: Species Tree Estimation usingMaximum likelihood (with hybridization)

Laura Salter KubatkoDepartments of Statistics and

Evolution, Ecology, and Organismal BiologyThe Ohio State University

[email protected]

Tutorial info at: www.stat.osu.edu/∼lkubatko/uga2012.html

UGA Bioinformatics Symposium 2012



What is STEM-hy?Assumptions and Methods

Using STEM-hy for Species Tree EstimationData PreparationExample 1: Small Example with Intraspecific SamplingExample 2: Small Example with Missing DataExample 3: Bootstrap Analysis

Using STEM-hy for Hybridization AnalysisBackground: STEM’s Hybrid Species ModelsExample 4: Hybridization in Heliconius

Practice Datasets




Assumptions and Methods

What is STEM-hy?

I STEM-hy is a program to perform maximum likelihoodanalysis for estimation of the species tree from multilocusdata under the coalescent process. It includes the capability ofevaluating hybrid taxa.

I Basic functions:I Return the ML species tree.I Search the space of all species trees and return the k trees

with the highest likelihoods found.I Compute the likelihood of a user-specified tree with branch

lengths.I Find optimal branch lengths on a user-specified tree.I Carry out a bootstrap analysis to obtain bootstrap support

values for nodes in the species tree.I Evaluate hypotheses of hybridization in a model selection

framework.





Assumptions

I No recombination within loci

I Free recombination between loci

I No gene flow following speciation

I Only source of variability in single-gene histories is due to thecoalescence process

I There is a single θ for the entire tree, for each locus

I Evolutionary rates may vary across loci





Methods: ML Estimate of the Species Tree

I Liu et al. (2009) showed that the ML estimate of the species treecan be computed by sequentially clustering minimum observeddivergence times between pairs of species across genes.

I They have shown that when gene trees are known without error, theML species tree is a consistent estimator.

I A similar result was obtained by Roch & Mossel (2010) – they calltheir estimator the GLASS tree (an acronym for Global LAteStSplit, based on the algorithm they developed to compute it).

I STEM computes the ML estimate of the species tree this way.





Methods: Estimation of ML Times for an Arbitrary Species Tree

I The results of Liu et al. (2009) can be extended to derive theML estimates of the speciation times for an arbitrary speciestree.

I Thus, the likelihood of any species tree can be readilycomputed by using this result to obtain ML branch lengths.

I This is important in that it allows us to compare alternativephylogenetic hypotheses.





Methods: Searching Species Tree Space for Trees of High Likelihood

I A simulated annealing algorithm is used to search the space ofall species trees for trees that have high likelihoods.

I The k best trees found during the search are saved andprinted to a file (k is set by the user).

I Exploration of the likelihood surface is particularly importantfor many of these problems.

I The details of the simulated annealing algorithm are similar tothose given in Salter & Pearl (2001).





Features of STEM-hy

I No limits (that I know of) on the number of taxa or thenumber of loci.

I Can handle intraspecific sampling.

I Allows information concerning mutation rate for each locus tobe used in the analysis.

I Can handle different taxon samples across genes.

I Version 1.0 is written in Java (using Clojure).




Data PreparationExample 1: Small Example with Intraspecific SamplingExample 2: Small Example with Missing DataExample 3: Bootstrap Analysis

Data Preparation - Gene Trees

I STEM-hy takes as its input one gene tree for each locus.

I Thus, a first step in an analysis using STEM-hy is to estimategene trees with branch lengths for each locus.

I Any method can be used to do this, but note a couplerequirements:

I Branch lengths are assumed to be in units of expected numberof substitutions per site per unit time.

I Branch lengths must be estimated subject to a molecularclock. This is not checked by the program.

I Gene trees must be fully resolved; however, polytomies can beincluded by setting branch lengths to 0 for an arbitraryresolution of the polytomy.





Data Preparation - Population Genetics Parameters

I A value of the parameter θ = 4Nµ must be provided. Notethat this is the “per-site θ”, not a “per-locus” value as usedby other population genetics programs.

I This will be used to convert gene tree branch lengths tocoalescent units (number of 2N generations) by dividing allgene tree branch lengths by θ.

I Estimates of θ could be obtained by standard methods.Typical values of θ will be between 0.001 and 0.1.





Data Preparation - Population Genetics and Mutation Parameters

I Each locus can also be given a rate multiplier.

I These can adjust forI Variation in mutation rate across loci.I Ploidy (e.g., haploid loci – mtDNA – should be given a rate of

0.5).

I At the least, one should estimate rate variation from the databy something like the following:

I Compute average pairwise sequence divergence of eachsequence to the outgroup.

I Divide all of these values by their overall mean, and assign thatnumber as the rate multiplier for each gene.

I Adjust specific genes for ploidy, if necessary.





Example 1: Small Example with Intraspecific Sampling

I Start with a small example where we can work things out byhand

I Four species, eight lineages, and two loci (N = 2)

I Suppose that the gene trees for the two loci are

1

2

3

4

5

6

7

8

3.46

2.46

1.23

1.20

2.40

1.00

1.20

1

2

3

4

5

6

7

8

3.50

2.86

2.54

1.23

1.20

1.00

1.10





STEM Example 1: Small Example with Intraspecific Sampling

I Now we can run STEM and look at output

I First, let’s compute the relevant distances by hand:

{D1ab}:

2 3 4 5 6 7 81 1.23 2.46 2.46 3.46 3.46 3.46 3.462 - 2.46 2.46 3.46 3.46 3.46 3.463 - - 1.2 3.46 3.46 3.46 3.464 - - - 3.46 3.46 3.46 3.465 - - - - 1.0 2.4 2.46 - - - - - 2.4 2.47 - - - - - - 1.2

{D2ab}:

2 3 4 5 6 7 81 1.23 2.56 2.56 2.86 2.86 3.5 3.52 - 2.56 2.56 2.86 2.86 3.5 3.53 - - 1.2 2.86 2.86 3.5 3.54 - - - 2.86 2.86 3.5 3.55 - - - - 1.0 3.5 3.56 - - - - - 3.5 3.57 - - - - - - 1.1








2 3 4 5 6 7 81 1.23 2.46 2.46 3.46 3.46 3.46 3.462 - 2.46 2.46 3.46 3.46 3.46 3.463 - - 1.2 3.46 3.46 3.46 3.464 - - - 3.46 3.46 3.46 3.465 - - - - 1.0 2.4 2.46 - - - - - 2.4 2.47 - - - - - - 1.2

→S1 S2 S3 S4

S1 - 1.2 3.46 3.46S2 - 1.0 2.4S3 - 1.2S4 -

2 3 4 5 6 7 81 1.23 2.56 2.56 2.86 2.86 3.5 3.52 - 2.56 2.56 2.86 2.86 3.5 3.53 - - 1.2 2.86 2.86 3.5 3.54 - - - 2.86 2.86 3.5 3.55 - - - - 1.0 3.5 3.56 - - - - - 3.5 3.57 - - - - - - 1.1

→S1 S2 S3 S4

S1 - 1.2 2.86 3.5S2 - 1.0 3.5S3 - 1.1S4 -








S1 S2 S3 S4S1 - 1.2 3.46 3.46S2 - 1.0 2.4S3 - 1.2S4 -

S1 S2 S3 S4S1 - 1.2 2.86 3.5S2 - 1.0 3.5S3 - 1.1S4 -

→S1 S2 S3 S4

S1 - 1.2 2.86 3.46S2 - 1.0 2.4S3 - 1.1S4 -







S1 S2 S3 S4S1 - 1.2 3.46 3.46S2 - 1.0 2.4S3 - 1.2S4 -

S1 S2 S3 S4S1 - 1.2 2.86 3.5S2 - 1.0 3.5S3 - 1.1S4 -

→

S1 S2 S3 S4S1 - 1.2 2.86 3.46S2 - 1.0 2.4S3 - 1.1S4 -

1

4

2

3

1.2

1.1

1.0






Step 1: Prepare the gene trees

Option 1: Place all gene trees in a single file called genetrees.tre:Newick format requiredOne gene tree per lineRate multipliers must be given in brackets in front of each gene tree

[1.0](((Name1:0.00123,Name2:0.00123):0.00123,(Name3:0.00121,Name4:0.00121):0.00125):0.0010,((Name5:0.0010,Name6:0.0010):0.0014,(MyName7:0.0012,Name8:0.0012):0.0012):0.00106);[1.0]((((Name1:0.00123,Name2:0.00123):0.00133,(Name3:0.0012,Name4:0.0012):0.00134):0.0003,(Name5:0.0010,Name6:0.0010):0.00186):0.00064,(MyName7:0.0011,Name8:0.0011):0.0024);






Step 1: Prepare the gene trees

Option 2: Place sets of gene trees in separate filesFile names will be supplied to STEM-hy in the settings fileRate multipliers will also be supplied in the settings fileAll genes in a single file are assumed to have the same rate

genetrees1.tre:

(((Name1:0.00123,Name2:0.00123):0.00123,(Name3:0.00121,Name4:0.00121):0.00125):0.0010,((Name5:0.0010,Name6:0.0010):0.0014,(MyName7:0.0012,Name8:0.0012):0.0012):0.00106);

genetrees2.tre:

((((Name1:0.00123,Name2:0.00123):0.00133,(Name3:0.0012,Name4:0.0012):0.00134):0.0003,(Name5:0.0010,Name6:0.0010):0.00186):0.00064,(MyName7:0.0011,Name8:0.0011):0.0024);






Step 2: Prepare the settings file - input option 1

yaml format: headings with indented parameters defined below

properties:run: 1 #0=user-tree, 1=MLE, 2=search, 3=hybridization, 4=bootstraptheta: 0.001num saved trees: 15beta: 0.0005seed: 3435893

species:Species1: Name1, Name2, Name3Species2: Name4, Name5Species3: Name6, MyName7Species4: Name8






Step 2: Prepare the settings file - input option 2


properties:run: 1 #0=user-tree, 1=MLE, 2=search, 3=hybridization, 4=bootstraptheta: 0.001num saved trees: 15beta: 0.0005seed: 3435893


files:genetrees1.tre: 1.0 # notice the space after each ’:’genetrees2.tre: 1.0






Step 2: Prepare the settings file


properties:run: 1 #0=user-tree, 1=MLE, 2=search, 3=.....theta: 0.001num saved trees: 15beta: 0.0005seed: 3435893


files:genetrees1.tre: 1.0 # notice the space after each ’:’genetrees2.tre: 1.0

Some parameters will

only be used for

certain “run” settings.

They are ignored

otherwise, and can be

omitted from the

settings file.





Example 1: Small Example with Intraspecific Sampling - Results

I Analysis 1: Find the ML species tree (run with run: 1)

I Run at the command line with: java -jar stem-hy.jar

***************************************** Welcome to STEM 2.0 *****************************************

The settings file was successfully parsed...

Using theta = 0.0010

The settings file contained 4 species and 8 lineages.

The species-to-lineage mappings are:

Species4: Name8Species3: MyName7, Name6Species2: Name4, Name5Species1: Name1, Name2, Name3






I Analysis 1: Find the ML species tree (run with run: 1)

I Run at the command line with: java -jar stem.jar

I Results are written to the file mle.tre

****************Results*****************

D AB Matrix:

[ 0.00000 1.20000 2.86000 3.46000][ 0.00000 0.00000 1.00000 2.40000][ 0.00000 0.00000 0.00000 1.10000][ 0.00000 0.00000 0.00000 0.00000]

Likelihood Species Tree (Newick format):

(Species1:1.20000,(Species4:1.10000,(Species2:1.00000,Species3:1.00000):0.10000):0.10000);

Log likelihood for tree: -52.43701947216076

****************** Done ****************






I Analysis 2: Find likelihood of all 15 trees (run with run: 2)

I Output files:

***************************************** Welcome to STEM 2.0 *****************************************

The settings file was successfully parsed......

Beginning search now (this could take a while)...

Search completed.

Here are the results (also written to file ’search.tre’):

[-52.43702] (Species1:1.20000,(Species4:1.10000,(Species2:1.00000,Species3:1.00000):0.10000):0.10000);[-53.63718] (Species1:1.20000,(Species3:1.00000,(Species2:1.00000,Species4:1.00000):0.00000):0.20000);[-56.63684] ((Species4:1.10000,Species1:1.10000):0.00000,(Species2:1.00000,Species3:1.00000):0.10000);[-56.63720] (Species4:1.10000,(Species1:1.10000,(Species2:1.00000,Species3:1.00000):0.10000):0.00000);[-60.23760] (Species4:1.10000,(Species2:1.00000,(Species1:1.00000,Species3:1.00000):0.00000):0.10000);[-62.63758] ((Species1:1.00000,Species3:1.00000):0.00000,(Species2:1.00000,Species4:1.00000):0.00000);[-62.63778] (Species3:1.00000,(Species1:1.00000,(Species2:1.00000,Species4:1.00000):0.00000):0.00000);[-62.63790] (Species2:1.00000,((Species1:1.00000,Species4:1.00000):0.00000,Species3:1.00000):0.00000);[-62.63806] (Species2:1.00000,((Species1:1.00000,Species3:1.00000):0.00000,Species4:1.00000):0.00000);

****************** Done ****************






I Analysis 3: Find the likelihood of a particular species tree

I Place the tree(s) of interest in the file user tree in the samedirectory as STEM-hy

((Species1:0.000222,Species3:0.000222):0.016444,(Species2:0.000222,Species4:0.000222):0.016444);

I Branch lengths must be included. STEM-hy gives thelikelihood of the tree with the user-specified branch lengths,as well as the ML branch lengths along the user tree.






***************************************** Welcome to STEM 2.0 *****************************************

The settings file was successfully parsed...

.

.

.

Read 1 species tree[s] from ’user.tre’

****************Results*****************

User tree:((Species1:0.000222,Species3:0.000222):0.016444,(Species2:0.000222,Species4:0.000222):0.016444)Log likelihood for tree: -153.62929947216077

**************Optimized Trees************

Optimized user tree:((Species1:0.99995,Species3:0.99995):0.00005,(Species2:0.99995,Species4:0.99995):0.00005);Log likelihood: -62.63865947216076

****************** Done ****************





Example 2: Missing Data Example

I genetrees.tre:

[1.0](((Name1:0.00123,Name2:0.00123):0.00123,(Name3:0.00121,Name4:0.00121):0.00125):0.0010,((Name5:0.0010,Name6:0.0010):0.0014,(MyName7:0.0012,Name8:0.0012):0.0012):0.00106);[1.0]((((Name1:0.00123,Name2:0.00123):0.00133,(Name3:0.0012,Name4:0.0012):0.00134):0.00032,(Name5:0.0010,Name6:0.0010):0.00186);[1.0](((Name1:0.00123,Name2:0.00123):0.00123,(Name3:0.00121,Name4:0.00121):0.00125):0.0010,((Name5:0.0010,Name6:0.0010):0.0014,(MyName7:0.0012,Name8:0.0012):0.0012):0.00106);[1.0]((((Name1:0.00123,Name2:0.00123):0.00133,(Name3:0.0012,Name4:0.0012):0.00134):0.0003,(Name5:0.0010,Name6:0.0010):0.00186):0.00064,(MyName7:0.0011,Name8:0.0011):0.0024);[1.0](((Name1:0.00123,Name2:0.00123):0.00123,(Name3:0.00121,Name4:0.00121):0.00125):0.0010,((Name5:0.0010,Name6:0.0010):0.0014,(MyName7:0.0012,Name8:0.0012):0.0012):0.00106);[1.0]((((Name1:0.00123,Name2:0.00123):0.00133,(Name3:0.0012,Name4:0.0012):0.00134):0.0003,(Name5:0.0010,Name6:0.0010):0.00186):0.00064,(MyName7:0.0011,Name8:0.0011):0.0024);[1.0](((Name1:0.00123,Name2:0.00123):0.00123,(Name3:0.00121,Name4:0.00121):0.00125):0.0010,((Name5:0.0010,Name6:0.0010):0.0014,(MyName7:0.0012,Name8:0.0012):0.0012):0.00106);[1.0]((((Name1:0.00123,Name2:0.00123):0.00133,(Name3:0.0012,Name4:0.0012):0.00134):0.0003,(Name5:0.0010,Name6:0.0010):0.00186):0.00064,(MyName7:0.0011,Name8:0.0011):0.0024);






I Look at gene trees:

Name1

Name2

Name3

Name4

Name5

Name6

MyName7

Name8

4 loci

Name1

Name2

Name3

Name4

Name5

Name6

1 locus

Name1

Name2

Name3

Name4

Name5

Name6

MyName7

Name8

3 loci






Note: The settings file remains unchanged.Below is the output.

****************Results*****************

D AB Matrix:

[ 0.00000 1.20000 2.86000 3.46000][ 0.00000 0.00000 1.00000 2.40000][ 0.00000 0.00000 0.00000 1.10000][ 0.00000 0.00000 0.00000 0.00000]

Maximum Likelihood Species Tree (Newick format):

(Species1:1.20000,(Species4:1.10000,(Species2:1.00000,Species3:1.00000):0.10000):0.10000);

log likelihood for tree: -967.874444171144

****************** Done ****************





Example Data: Heliconius Butterflies

H. melpomene H. heurippa H. cydno

2

1

3

H. hecale

ABCD

BCD

CDBD





Example 3: Bootstrap Analysis

I The current version of STEM-hy can be used to estimate bootstrapproportions on the ML tree, as well as to construct a bootstrapconsensus tree.

I Sequence data must be provided in PHYLIP format (separatefiles need to be used for each gene).

I Each gene is bootstrapped a user-specified number of times, B,to produce B bootstrap samples (alignments) for each gene.

I Gene trees are estimated for each bootstrap sample using theprogram SSA. This program uses a simulated annealingmethod to estimate gene trees under the assumption of amolecular clock.

I B species trees are reconstructed using STEM-hy and printedto both the screen and to the file bootstrap.results.






For this example, we’ll consider four taxa and six genes inHeliconius butterflies.

The settings file is shown below, with changes in blue

properties:run: 4 #0=user-tree, 1=MLE, 2=search, 3=hybridization, 4=bootstrapbootstrap samples: 100phylip files: co 4tax.phy,dll 4tax.phy,inv 4tax.phy,sd 4tax.phy,tpi 4tax.phy,white 4tax.phytheta: 0.01num saved trees: 15beta: 0.0005seed: 3435893

species:H. melpomene: M95H. hecale: HhH. cordula: M187H. heurippa: Strib40






Below is the output. All bootstrap trees are written to a file calledbootstrap.results and can be read into another program andsummarized.

...The species-to-lineage mappings are:

H. heurippa: Strib40H. cordula: M187H. hecale: HhH. melpomene: M95

Bootstrapping trees (this might take a while)...

****************Results*****************

The maximum likelihood species tree estimate is:

(H. hecale:6.82133,(H. melpomene:0.74608,(H. heurippa:0.07658,H. cordula:0.07658):0.66950):6.07525);

The 100 bootstrapped species trees:

(H. heurippa:0.29907,(H. hecale:0.17664,(H. melpomene:0.12424,H. cydno:0.12424):0.05240):0.12243);(H. hecale:1.52825,(H. melpomene:0.35022,(H. heurippa:0.31089,H. cydno:0.31089):0.03933):1.17803);





Some Notes on Program Versions

I There are some important differences between STEMv1.1aand STEMv2.0/STEM-hyv.10

I Multifurcations are handled differently.

STEM v1.1a and lower: Zero-length branches are set to0.00001.

STEMv2.0 / STEM-hyv1.0: Zero-length branches are treatedas missing data.

I Other big differences are improvements to input format andincreased functionality in later versions.




Background: STEM’s Hybrid Species ModelsExample 4: Hybridization in Heliconius

STEM’s Hybrid Species Model

A B C

ττ

γγ

1−γγ

A B C

P(C(AB)) = 1−(2/3)exp(−ττ)P(A(BC))=(1/3)exp(−ττ)P(B(AC))=(1/3)exp(−ττ)

MutationProcess

ττ

A B C

P(C(AB))=(1/3)exp(−ττ)P(A(BC))=1−(2/3)exp(−ττ)P(B(AC))=(1/3)exp(−ττ)

MutationProcess

ττ






Species tree subject to hybridization

A B C

ττ

γγ

1−γγ

A B C


MutationProcess

ττ

A B C


MutationProcess

ττ






Hybridization parameter to model the extent of the contributionfrom each parent

A B C

ττ

γγ

1−γγ

A B C


MutationProcess

ττ

A B C


MutationProcess

ττ






Possible parental species trees

A B C

ττ

γγ

1−γγ

A B C


MutationProcess

ττ

A B C


MutationProcess

ττ






Probabilities associated with each gene tree topology for eachparental tree under the coalescent model

A B C

ττ

γγ

1−γγ

A B C


MutationProcess

ττ

A B C


MutationProcess

ττ






Sequence evolution proceeds along gene trees

A B C

ττ

γγ

1−γγ

A B C


MutationProcess

ττ

A B C


MutationProcess

ττ





Inference of Trees Subject to Hybridization

Assumptions:

I Hybridization results in a mosaic genome, so that a sampledgene has a probability distribution that its history originatedfrom one of several parental species trees

I Genes in the sample are independent given the species tree

I Hybridization events happen only between sister taxa

I No factors other than coalescence and hybridization lead toincongruence between gene trees and the species tree





Likelihood Calculation for the Three-taxon Case

I Let f (gi |S) be the probability density of gene tree gi givenspecies tree S under the coalescent model (Rannala and Yang,2003)

I The likelihood function for the three-taxon case is

N∏i=1

{γf (gi |S1) + (1− γ)f (gi |S2)}

whereS1 and S2 are two possible parental species treesγ ∈ [0, 1]





Likelihood Calculation for the Three-taxon Case

N∏i=1

{γf (gi |S1) + (1− γ)f (gi |S2)}

A B C

ττ

γγ

1−γγ

A B Cf(g | S1) Mutation

Process

ττ

A B Cf(g | S2) Mutation

Process

ττ





Beyond Three Taxa . . .

I Propose a method which incorporates any number ofhybridization events, provided they occur between sister taxa

I Each putative hybridization event is assigned a parameter,γ1, γ2, . . .

I The likelihood is computed by looking at all combinations ofpossible parental species trees, weighted appropriately by theγj parameters





A Big(-ger) Example

Recall our motivatingexample:

A B C D E F A B C D E F

A B C D E F A B C D E F

Consider the hybrid species tree:

A C E FDB





The Likelihood Function

A C E FDB

→A B C D E F

γγ1γγ2

S1

A B C D E F(1−γγ1)γγ2

S3

A B C D E Fγγ11−γγ2)

S2

A B C D E F(1−γγ1)(1−γγ2)

S4

∏Ni=1 {γ1γ2f (gi |S1) + γ1(1− γ2)f (gi |S2)

+(1− γ1)γ2f (gi |S3) + (1− γ1)(1− γ2)f (gi |S4)}





Comments on Computation

I Parameters in the likelihood function: γ1, γ2, branch lengths

I For a given hybrid species tree and sample of gene trees withdivergence times, maximum likelihood branch lengths can beanalytically determined

I Fitting the likelihood model for a hypothesized hybrid speciestree only requires optimization of γ parameters

I Implemented in a modified version of the program STEM,called STEM-hy (“stemmy”)





Selecting the Best Hybrid Species Tree

I For the example hybrid species tree, pick the best hybridmodel from among possible models using the AIC:

Model Tree γ1 γ2 Number of Parameters

1 A B C D E F 0 0 5

2 A B C D E F 0 1 5

3 A B C D E F 1 0 5

4 A B C D E F 1 1 5





Selecting the Best Hybrid Species Tree

Model Tree γ1 γ2 Number of Parameters

5 A B C E FD 0 (0,1) 6

6 A B C E FD 1 (0,1) 6

7 A C D E FB (0,1) 0 6

8 A C D E FB (0,1) 1 6

9 A C E FDB (0,1) (0,1) 7





STEM-hy: Assumptions

I In practice, the γi are not given (neither are times ofspeciation or hybridization events). The algorithm finds MLEsfor these parameters.

I STEM-hy inherits all of STEM-hy’s other assumptions (e.g.,no gene flow after speciation if no hybridization, gene treevariability is not taken into consideration, etc.).





STEM-hy: Assumptions

I One important point: STEM-hy looks for evidence ofhybridization in the presence of incomplete lineage sorting.

I By using the model in STEM-hy to compute likelihoods, thecoalescent process is incorporated.

I The AIC is used to compare models:

I AIC = −2lnL(M|D) + 2k

where M is the model and D is the data. LnL(M|D) is thelikelihood from STEM-hy for the hybridization model underconsideration.





Example 4: Hybridization in Heliconius

I Input data format is the same as for previous analyses:

I Gene trees are placed in the file called genetrees.tre (option1) or the files containing the gene trees are listed in thesettings file (option 2).

I The settings file (in yaml format) is used to give usersettings (e.g., θ).

I The run option is set to 3.






I The user must additionally provide information abouthybridization:

I The only option at present is to use a user-specified tree – thepresent version of the program assumes that the overall speciesphylogeny is known.

I The user-specified tree is one of the possible parental trees – itdoesn’t matter which one.

I The putative hybrid species are identified in thesettings.yaml file.






H. melpomene H. heurippa H. cydno

2

1

3

H. hecale

ABCD

BCD

CDBD





STEM-hy Example: Heliconius Butterflies

I Example genetrees.tre file:

[0.37137]((Hheurippa:0.005989,(Hcydno:0.001322,Hmelpomene:0.001322):0.004667):0.022778,Hhecale:0.028767);[1.17059]((Hmelpomene:0.049843,(Hcydno:0.000001,Hheurippa:0.000001):0.049843):0.001,Hhecale:0.049943);[0.11434](((Hcydno:0.021024,Hheurippa:0.021024):0.020051,Hmelpomene:0.041076):0.002610,Hhecale:0.043685);[1.35454](((Hheurippa:0.010740,Hcydno:0.010740):0.003498,Hmelpomene:0.014238):0.037654,Hhecale:0.051892);[0.39096](((Hheurippa:0.008764,Hmelpomene:0.008764):0.001686,Hcydno:0.010450):0.003969,Hhecale:0.014419);[1.22683](((Hheurippa:0.002431,Hcydno:0.002431):0.062919,Hmelpomene:0.065350):0.0000001,Hhecale:0.065351);





STEM-hy Example: Heliconius Butterflies

I Example settings file:

properties:run: 3theta: 0.001beta: 0.0005burnin: 100seed: 3435893bound totali ter : 20num savedt rees : 10hybrid species: H. heurippahybrid tree: user-heliconius.tre

species:H. melpomene: M95H. hecale: HhH. cordula: M187H. heurippa: Strib40






I Example user-heliconius.tre:

(((H. heurippa:0.000085,H. cydno:0.000085):0.347479,H. melpomene:0.355979):3.332091,H. hecale:3.68807);






****************Results*****************....

Parental trees:

gamma(H. heurippa) = 1((H. cydno:0.00009,(H. heurippa:0.00009,H. melpomene:0.00009):0.00000):3.68801,H. hecale:3.68810);Lik: -357.4325907499209AIC: 720.8651814998418k: 3

gamma(H. heurippa) = 0(((H. heurippa:0.00009,H. cydno:0.00009):0.35589,H. melpomene:0.35598):3.33212,H. hecale:3.68810);Lik: -349.9185707499209AIC: 705.8371414998418k: 3

Hybrid trees:

(((H. heurippa:0.00009,H. cydno:0.00009):0.35589,H. melpomene:0.35598):3.33212,H. hecale:3.68810);Lik: -349.5409832924012gamma(H. heurippa): 0.6600000000000004AIC: 707.0819665848024k: 4

****************** Done ****************





What hybrid species can be considered?

I Care must be taken in selecting hybrid species:

I Both members of a sister group cannot be selected as hybridtaxa in a single analysis. However, two analyses can be run(one with each of the sister group identified as the hybrid) andresults will be comparable across runs.

I The outgroup cannot be selected as a hybrid.

I Both of these restrictions result from the fact that for nowhybridization is only considered between sister taxa.

I More general hybridization relationships can be considered “byhand” using the user-specified tree feature of STEM-hy.





STEM-hy: Strengths and Weaknesses

I STEM-hy makes some fairly strong assumptions:

I Error in estimating gene trees and branch lengths is notincorporated!!!! But the possibility of carrying out bootstrapanalysis helps.

I Information in the sequence data is not used directly; it is onlyused as summarized by estimated gene divergence times.

I There is a single value of θ for the entire tree.

I There are trade-offs involved, and STEM-hy does some things well:

I It is quick (even the tree search does not take long).I It can handle missing data easily and intuitively.I Simulations demonstrate reasonable performance (unlikely to

be misleading; may be uninformative).




Challenge Datasets

I I’ve created four datasets under varying conditions:

M1 No hybridization, long intervals between speciation events.

M2 No hybridization, short intervals between speciation events.

M3 Low-levels of hybridization - B is a hybrid of A and C (speciestree as in M1 and M2).

M4 Extensive hybridization - B is a hybrid of A and C (species treeas in M1 and M2).

I All data sets have 6 species, 2 individuals/species, and 10 loci.

I GOAL: match the data set to the condition listed aboveSolutions are at www.stat.osu.edu/∼lkubatko/uga2012.html




STEM-hy Information, References, etc.

Recommended citations - species tree estimation:

I Kubatko, L.S., B. C.Carstens, and L. L. Knowles. 2009. STEM: Species Tree Estimation using Maximumlikelihood under coalescence. Bioinformatics 25(7): 971-973.

I Liu, L., L. Yu, and D.K. Pearl. 2009. Maximum tree: a consistent estimator of the species tree. Journal ofMathematical Biology 60(1):95-106.

I Mossel, E. and S. Roch. 2010. Incomplete lineage sorting: Consistent phylogeny estimation from multipleloci. IEEE/ACM Transactions on Computational Biology and Bioinformatics 7(1): 166-171.

Recommended citations - hybridization:

I Kubatko, LS. 2009. Identifying Hybridization Events in the Presence of Coalescence via Model Selection,Systematic Biology 58(5): 478-488.

Thank you!

STEM-hy is available at http://www.stat.osu.edu/∼lkubatko/software/STEM/

Questions concerning the programs can be sent to [email protected].


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