Reconstruction of species trees from gene trees using...

Reconstruction of species trees from gene trees using ASTRAL

Siavash Mirarab University of California, San Diego (ECE)

ttp://

in collaboration with Warnow lab (UIUC)

Phylogenomics

More data (#genes)

Inference error

“gene” here refers to a portion of the genome (not a functional gene)

gene 999gene 2ACTGCACACCG ACTGC-CCCCG AATGC-CCCCG -CTGCACACGG

CTGAGCATCG CTGAGC-TCG ATGAGC-TC- CTGA-CAC-G

AGCAGCATCGTG AGCAGC-TCGTG AGCAGC-TC-TG C-TA-CACGGTG

CAGGCACGCACGAA AGC-CACGC-CATA ATGGCACGC-C-TA AGCTAC-CACGGAT

gene 1000gene 1

Orangutan

Gorilla

Chimpanzee

Gene tree discordance

Orang.Gorilla ChimpHuman Orang.Gorilla Chimp Human

gene1000gene 1

OrangutanGorilla ChimpHuman

The species tree

A gene treeOrang.Gorilla ChimpHuman Orang.Gorilla Chimp Human

gene1000gene 1

OrangutanGorilla ChimpHuman

The species tree

A gene treeOrang.Gorilla ChimpHuman Orang.Gorilla Chimp Human

Causes of gene tree discordance include:• Incomplete Lineage Sorting (ILS) • Duplication and loss • Horizontal Gene Transfer (HGT)

gene1000gene 1

Incomplete Lineage Sorting (ILS)

• A random process related to the coalescence of alleles across various populations

Tracing alleles through generations

• Omnipresent: possible for every tree

• Likely for short branches or large population sizes

MSC and Identifiability• A statistical model called multi-species coalescent

(MSC) can generate ILS.

• Any species tree defines a unique distribution on the set of all possible gene trees

• In principle, the species tree can be identified despite high discordance from the gene tree distribution

gene 2

ACTGCACACCG ACTGC-CCCCG AATGC-CCCCG -CTGCACACGG

gene 1000

gene 1

Summary method

Orangutan

Gorilla

Chimpanzee

Approach 2: Summary methods

Approach 1: ConcatenationOrangutan

Gorilla

Chimpanzee

Phylogeny inferenceACTGCACACCG

ACTGC-CCCCG AATGC-CCCCG -CTGCACACGG

CAGAGCACGCACGAA AGCA-CACGC-CATA ATGAGCACGC-C-TA AGC-TAC-CACGGAT

supermatrixgene 2 gene 1000gene 1

Gene tree estimation

Orang.

GorillaChimp

Humangene

Orang.

Gorilla Chimp

Humangene

Orang.

Gorilla

Humangene

Multi-gene tree estimation pipelines

There are also other very good approaches: co-estimation (e.g., *BEAST),

site-based (e.g., SVDQuartets, SNAPP)

gene 2

gene 1000

gene 1

Summary method

Orangutan

Gorilla

Chimpanzee

Gorilla

Chimpanzee

Orang.

GorillaChimp

Humangene

Orang.

Gorilla Chimp

Humangene

Orang.

Gorilla

Humangene

Statistically inconsistent [Roch and Steel, 2014]

Can be statistically consistent given true gene treesData

Error-free gene trees

gene 2

gene 1000

gene 1

Summary method

Orangutan

Gorilla

Chimpanzee

Gorilla

Chimpanzee

Orang.

GorillaChimp

Humangene

Orang.

Gorilla Chimp

Humangene

Orang.

Gorilla

Humangene

Statistically inconsistent [Roch and Steel, 2014]

Can be statistically consistent given true gene trees

STAR, STELLS, GLASS, BUCKy (population tree), MP-EST, NJst (ASTRID), … ASTRAL, ASTRAL-II, ASTRAL-III

Error-free gene trees

ASTRAL used by the biologists• Plants: Wickett, et al., 2014, PNAS • Birds: Prum, et al., 2015, Nature • Xenoturbella, Cannon et al., 2016, Nature • Xenoturbella, Rouse et al., 2016, Nature • Flatworms: Laumer, et al., 2015, eLife • Shrews: Giarla, et al., 2015, Syst. Bio. • Frogs: Yuan et al., 2016, Syst. Bio. • Tomatoes: Pease, et al., 2016, PLoS Bio. • Angiosperms: Huang et al., 2016, MBE • Worms: Andrade, et al., 2015, MBE

This talk: ASTRAL• Outlines of the method

• Accuracy in simulation studies

• With strong model violations

• The impact of

• Fragmentary sequence data

• Sampling multiple individuals

Unrooted quartets under MSC model

For a quartet (4 species), the unrooted species tree topology has at least 1/3 probability in gene trees (Allman, et al. 2010)

Orang.

Gorilla Chimp

HumanOrang.

GorillaChimp

Orang.

Gorilla

θ2=15% θ3=15%θ1=70%Gorilla

Orang.

Gorilla Chimp

HumanOrang.

GorillaChimp

Orang.

Gorilla

θ2=15% θ3=15%θ1=70%Gorilla

Orang.

The most frequent gene tree = The most likely species tree

Orang.

Gorilla Chimp

HumanOrang.

GorillaChimp

Orang.

Gorilla

θ2=15% θ3=15%θ1=70%Gorilla

Orang.

The most frequent gene tree = The most likely species tree

shorter branches ⇒ more discordance ⇒ a harder species tree reconstruction problem

Orang.Gorilla ChimpHuman Rhesus

More than 4 speciesFor >4 species, the species tree topology can be different from the most like gene tree (called anomaly zone) (Degnan, 2013)

1. Break gene trees into (n 4 ) quartets of species

2. Find the dominant tree for all quartets of taxa 3. Combine quartet trees

Some tools (e.g.. BUCKy-p [Larget, et al., 2010])

1. Break gene trees into (n 4 ) quartets of species

2. Find the dominant tree for all quartets of taxa 3. Combine quartet trees

Some tools (e.g.. BUCKy-p [Larget, et al., 2010])

Alternative: weight all 3(n

4 ) quartet topologies by their frequency

and find the optimal tree

Maximum Quartet Support Species Tree

• Optimization problem:

Find the species tree with the maximum number of induced quartet trees shared with the collection of input gene trees

the set of quartet trees induced by T

a gene treeScore(T ) =

|Q(T ) \Q(ti)|

Maximum Quartet Support Species Tree

• Optimization problem:

• Theorem: Statistically consistent under the multi-species coalescent model when solved exactly

Find the species tree with the maximum number of induced quartet trees shared with the collection of input gene trees

the set of quartet trees induced by T

a gene treeScore(T ) =

|Q(T ) \Q(ti)|

ASTRAL-I and ASTRAL-II [Mirarab, et al., Bioinformatics, 2014] [Mirarab and Warnow, Bioinformatics, 2015]

• Solve the problem exactly using dynamic programming

• Constrains the search space to make large datasets feasible

• The constrained version remains statistically consistent

• Running time: polynomially increases with the number of genes and the number of species

ASTRAL-I and ASTRAL-II [Mirarab, et al., Bioinformatics, 2014] [Mirarab and Warnow, Bioinformatics, 2015]

• Solve the problem exactly using dynamic programming

• Constrains the search space to make large datasets feasible

• The constrained version remains statistically consistent

• Running time: polynomially increases with the number of genes and the number of species

• ASTRAL-II:

• Increased the search space

• Improved the running time

• Can handle polytomies (lack of resolution) in input gene trees

Simulation study

Truegenetrees Sequencedata

Es�matedspeciestree

Finch Falcon Owl Eagle Pigeon

Es�matedgenetreesFinch Owl Falcon Eagle Pigeon

True(model)speciestree

Simulation study

• Evaluate using the FN rate: the percentage of branches in the true tree that are missing from the estimated tree

Truegenetrees Sequencedata

Es�matedspeciestree

Finch Falcon Owl Eagle Pigeon

Es�matedgenetreesFinch Owl Falcon Eagle Pigeon

True(model)speciestree

Number of species impacts estimation error in the species tree

1000 genes, “medium” levels of ILS, simulated species trees [S. Mirarab, T. Warnow, 2015]

ASTRAL: accurate and scalable

10 50 100 200 500 1000number of species

rror (

ASTRAL−IIMP−EST

1000 genes, “medium” levels of ILS, simulated species trees[S. Mirarab, T. Warnow, 2015]

ASTRAL: accurate and scalable

rror (

ASTRAL−IIMP−EST

rror (

ASTRAL−IIMP−EST

1000 genes, “medium” levels of ILS, simulated species trees[S. Mirarab, T. Warnow, 2015]

Comparison to concatenation: depends on the ILS level

200 species, recent ILS

1000 genes 200 genes 50 genes

10M 2M 500K 10M 2M 500K 10M 2M 500Ktree length (controls the amount of ILS)

rror (

FN) ASTRAL−II

NJstCA−ML

more ILS more ILS more ILSL M H L M H L M H

Comparison to concatenation: depends on the ILS level

200 species, recent ILS

rror (

FN) ASTRAL−II

NJstCA−ML

more ILS more ILS more ILSL M H L M H L M H

Horizontal Gene Transfer (HGT)[R. Davidson et al., BMC Genomics. 16 (2015)]

~70%~55% ~35% ~30% discordance

Model violation: the simulated discordance is due to both ILS and randomly distributed HGT

50 species, 10 genes

Horizontal Gene Transfer (HGT)[R. Davidson et al., BMC Genomics. 16 (2015)]

~70%~55%

~35% ~30% discordance

Randomly distributed HGT is tolerated with enough genes

50 species, varying # genes

# genes

UCSD Work 1. Statistical support 2. ASTRAL-III

• Better running time • GPU and CPU Parallelism • Multi-Individual datasets

3. Impact of fragmentary data

Branch support• Traditional approach:

Multi-locus bootstrapping (MLBS)

• Slow: requires bootstrapping all genes(e.g., 100×m ML trees)

• Inaccurate and hard to interpret [Mirarab et al., Sys bio, 2014; Bayzid et al., PLoS One, 2015]

• We can do better!

[Mirarab et al., Sys bio, 2014]

Local posterior probability• Recall quartet frequencies follow a multinomial distribution

• P ( topology seen in m1 / m gene trees is the species tree ) = P ( θ1 > 1/3 )

Orang.

Gorilla Chimp

HumanOrang.

GorillaChimp

Orang.

Gorilla

m 2 = 63 m3 = 57m 1 = 80

θ2 θ3θ1

Local posterior probability• Recall quartet frequencies follow a multinomial distribution

• P ( topology seen in m1 / m gene trees is the species tree ) = P ( θ1 > 1/3 )

• Can be analytically solved

• We implemented this idea in astral and called the measure “the local posterior probability” (localPP)

Orang.

Gorilla Chimp

HumanOrang.

GorillaChimp

Orang.

Gorilla

m 2 = 63 m3 = 57m 1 = 80

θ2 θ3θ1

Quartet support v.s. localPP

!3Background: How many targets are enough? The number of loci required for confidently resolving a phylogenetic relationship depends on its “hardness”. Discordant gene trees due to incomplete lineage sorting (ILS) can make branches of a species tree very difficult to resolve. ILS is a function of the branch length and population size. This means that shorter branches or larger population sizes increase ILS, and can make species tree reconstruction more difficult. The co-PI has recently developed a new approach for estimating the support of a branch in a coalescent-based framework based on the proportion of gene trees that support quartet topologies in gene trees[31]. This new approach is analogous to finding the probability that a three-sided die is loaded towards each facet by observing outcomes of many tosses. We can also ask the reverse question: if we have an estimate of the degree of bias of a die, how many tosses are needed to confidently find its loaded side. Similarly, this approach[31] sheds light on the relationship between the number of genes required to achieve a level of support for a branch of a certain length in coalescent units (Fig. 3). While the co-PI’s method of calculating support, which is implemented in ASTRAL [32, 33], gives the basic mathematical framework, more method development is needed (see below).

Research Approach Specimens Suitable specimens of more than 80 species of Sabellidae and >120 Terebelliformia species have been collected from localities around the world in the last 15 years by the PI. Further collecting will be undertaken for some key taxa for a few more transcriptomes and for targeted DNA capture. We also have agreements from other experts in Sabellidae and Terebelliformia to provide other needed ethanol-preserved specimens for targeted capture. We will obtain ~ 50% of the known sabellid diversity and ~25% of terebelliforms for targeted capture sequencing (~500 species total). Our plan is to sample all genera, particularly focusing on their type species. This should allow for the generation of robust phylogenies, from which we will revise the taxonomy. Specimens will be vouchered at the SIO Benthic Invertebrate Collection and biodiversity information curated on the Encyclopedia of Life. Sequencing (transcriptomes and targeted capture of DNA) A targeted capture approach will be used with an appropriate number of loci (see below) to generate robust phylogenies of Sabellidae and Terebelliformia. Two different sets of targets will be designed from transcriptomes, across Sabellidae and Terebelliformia repectively. We have already generated new transcriptomes for nine sabellids, a serpulid and a fabriciid (bold terminals in Fig. 4), and nine Terebelliformia (bold terminals in Fig. 5) and combined this data with the few publicly available transcriptomes. Based on direct sequencing data already obtained for several genes for Sabellidae and Terebelliformia [Rouse in prep.; Stiller et al. in prep.], our sampling arguably spans the extant diversity of each clade. Several more transcriptomes will be needed to ensure the targeted capture methods will be robust. Methods for generating these transcriptomes will follow those previously used by us[6, 34]. How many targets are needed? A targeted capture pipeline typically starts from a large number of loci sequenced from a small number of species using genome-wide approaches (e.g., transcriptomics)[7, 8, 35]. This initial dataset is then used to select a smaller subset of loci for the targeted capture phase, which involves a larger set of species. To reduce the cost and effort, one would want to minimize the number of loci in the second phase, as long as sufficient loci are selected to confidently resolve relationships of interest. To date the number of loci has been determined in an ad hoc manner, either by the ultra conserved elements discovered[7, 8] or limitations of the targeted capture technology[13]. Initial analyses of our two datasets demonstrates how the number of

Fig. 3. Impact of number of genes (colors) and amount of ILS (x-axis) on support (posterior probability) for a branch (y-axis). Under the coalescent model, for four species separated with an unrooted branch of length d, the probability of a gene tree being identical to the species tree is 1-2/3e-d (we use this as a measure of ILS). We measure support using local pp [31] for various numbers of gene trees (assuming no gene tree estimation error). More ILS (ie., low 1-2/3e-d) requires more genes to get high support.

quartet frequency

Increased number of genes (m ) ⇒ increased support

Decreased discordance ⇒ increased support

localPP is more accurate than bootstrapping

250 500

1000 1500

0.00 0.25 0.50 0.75 1.000.00 0.25 0.50 0.75 1.00

False Positive Rate

Recall

MLBS Local PP

250 500

1000 1500

0.00 0.25 0.50 0.75 1.000.00 0.25 0.50 0.75 1.00

False Positive Rate

Recall

MLBS Local PP

250 500

1000 1500

0.00 0.25 0.50 0.75 1.000.00 0.25 0.50 0.75 1.00

False Positive Rate

Recall

MLBS Local PP

250 500

1000 1500

0.00 0.25 0.50 0.75 1.000.00 0.25 0.50 0.75 1.00

False Positive Rate

Recall

MLBS Local PP

Avian simulated dataset (48 taxa, 1000 genes)

the ROC curves show (fig. 5), for the same number offalse positives branches, local posterior probabilities result inbetter recall than MLBS. This pattern is more pronouncedfor shorter alignments, which have increased gene treeerror. For example, for the 250 bp model condition, if wechoose a support threshold that results in 0.01 FPR, with localposterior values, we still recover 84% of correct branches,whereas with MLBS, the same FPR results in retaining70% of correct branches. Thus, for a desired level of precision,better recall can be obtained using local posteriorprobabilities.

Branch LengthBranch length accuracy on the avian dataset was a function ofgene tree estimation error whether ASTRAL or MP-EST wasused (table 4). With true gene trees, branch length log error

FIG. 4. Branch length accuracy on the A-200 dataset with Medium ILS. See supplementary figures S7 and S8, Supplementary Material online forlow and high ILS. The estimated branch length is plotted against the true branch length in log scale (base 10). Blue line: a fitted generalizedadditive model with smoothing (Wood 2011).

Table 3. Branch Length Accuracy on the A-200 Dataset.

Dataset n Log Err RMSE

True gt Est. gt True gt Est. gt

Low ILS 1,000 0.10 0.42 5.57 6.75Low ILS 200 0.16 0.44 6.22 6.99Low ILS 50 0.25 0.48 6.84 7.29Med ILS 1,000 0.03 0.20 0.22 0.86Med ILS 200 0.07 0.22 0.44 0.91Med ILS 50 0.13 0.26 0.74 1.05High ILS 1,000 0.06 0.15 0.03 0.13High ILS 200 0.11 0.18 0.07 0.15High ILS 50 0.18 0.24 0.14 0.19

NOTE.—Logarithmic error (Log Err) and RMSE are shown for true species treesscored with true gene trees or estimated gene trees (Est. gt).

250 500

1000 1500

0.00 0.25 0.50 0.75 1.000.00 0.25 0.50 0.75 1.00False Positive Rate

MLBS Local PP

FIG. 5. ROC curve for the avian dataset based on MLBS and local PPPPsupport values. Boxes show different numbers of sites per gene (con-trolling gene tree estimation error).

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[Sayyari and Mirarab, MBE, 2016]

100Xfaster

ASTRAL can also estimate internal branch lengths

True gene trees

1500 1000

500 250

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−7.5 −5.0 −2.5 0.0 2.5 −7.5 −5.0 −2.5 0.0 2.5true branch length (log scale)

−7.5

−5.0

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−7.5 −5.0 −2.5 0.0 2.5true branch length (log scale)

With true gene trees, ASTRAL correctly estimates BL

ASTRAL can also estimate internal branch lengths

True gene trees

1500 1000

500 250

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−7.5 −5.0 −2.5 0.0 2.5true branch length (log scale)

was only 0.06, corresponding to branches that are about 14%shorter or longer than the true branch. As gene tree estima-tion error increases with reduced number of sites (see table 1for gene tree error statistics), the branch length error also

increases. Thus, while 1,500 bp genes give 0.17 log error,250 bp genes result in 0.59 error, which corresponds tobranches that are on average 3.9 times too short or long.Moreover, unlike true gene trees, the error in branch lengthsestimated based on estimated gene trees is biased towardunderestimation (fig. 6), a pattern that increases in intensitywith shorter alignments.

ASTRAL and MP-EST have similar branch length accuracymeasured by log error for highly accurate gene trees, butASTRAL has an advantage with increased gene tree error(supplementary fig. S10, Supplementary Material online andtable 4). Error measured by root mean squared error (RMSE)(which emphasizes the accuracy of long branches) is compa-rable for the two methods, but MP-EST has a slight advantagegiven accurate gene trees.

Biological DatasetsFor each biological dataset, we show MLBS support and thelocal posterior probabilities, computed based on RAxML genetrees available from respective publications. We also collapsegene tree branches with <33% bootstrap support and usethese collapsed gene trees to draw local posterior probabili-ties. For ease of discussion, we show local posterior probabil-ities as percentages and refer to them simply as posterior orcollapsed posterior (for values based on collapsed gene trees).We discuss the confidence in important branches in eachtree.

1KP. Three of the key relationships studied by Wickett et al.(2014) are the sister branch to land plants, the base of theangiosperms, and the relationship among Bryophytes (horn-worts, liverworts, and mosses). In the ASTRAL tree, manybranches have full support regardless of the measure of thesupport used, but the remaining branches reveal interestingpatterns (fig. 7). The sister relationship betweenZygnematales and land plants receives a moderate 80% BS,but has 100% posterior. Wickett et al. (2014) also recoveredthis relationship by concatenation of various data partitions.There are 12 other branches that have collapsed posteriorsthat are at least 10% higher than BS (fig. 7); no branch hassubstantially higher BS than collapsed posterior. Collapsedposterior for monophyly of Bryophytes and for Amborellaas sister to other angiosperms are 100% (compared with97% and 93% BS, respectively).

When we collapse low-support branches in gene trees,posterior goes up for several branches: nine branches haveimprovements of 10% or more, and only two branches havecomparable reductions. An interesting case is Coleochaetalesas sister to Zygnematalesþ land plants, which has only 62%BS and 61% posterior, but has 100% collapsed posterior.Finally, note that several branches have low posterior, evenafter collapsing.

Our estimated branch lengths are short for several nodes.For example, the branch that unites (ChloranthalesþMagnoliids) and Eudicots has a length of 0.14 in coalescentunits. Other branches that have been historically hard to re-cover also tend to have short branches; however, these arenot necessarily extremely short branches that would

FIG. 6. ASTRAL branch length accuracy on the avian dataset. Logtransformed estimated branch lengths are shown versus true branchlengths, and a generalized additive model is fitted to the data. Onebranch with length 10"6 is trimmed out here, but full results, includ-ing MP-EST, is shown in supplementary figure S9, SupplementaryMaterial online.

Table 4. Branch Length Accuracy for the Avian Dataset.

No. of sites Log Err RMSE

ASTRAL MPEST ASTRAL MPEST

True gt. 0.06 (0.10) 0.07 (0.11) 0.44 (0.44) 0.30 (0.30)1,500 0.17 (0.20) 0.14 (0.18) 0.83 (0.83) 0.70 (0.70)1,000 0.22 (0.27) 0.22 (0.25) 1.08 (1.07) 1.01 (1.00)500 0.37 (0.42) 0.42 (0.46) 1.65 (1.64) 1.65 (1.64)250 0.59 (0.63) 0.81 (0.84) 2.25 (2.24) 2.28 (2.26)

NOTE.—Logarithmic error and root mean squared error are shown for true speciestrees scored with true gene trees or estimated gene trees with various numbers ofsites using ASTRAL and MP-EST. An extremely short branch with length 10"6 wasremoved from the calculations, but error including that branch is shownparenthetically.

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low gene tree error

High gene tree error

Moderate g.t. error

Medium g.t. error

With true gene trees, ASTRAL correctly estimates BLWith error-prone estimated gene trees, ASTRAL underestimates BL

Running time complexity & ASTRAL-III

(unpublished work)

Maryam Rabiee Hashemi Chao ZhangJohn Yin

ASTRAL-III new features• Improved running time with a single CPU

• We have ~3-5X running time improvement, and guaranteed polynomial running time

• ~8 hours for 1000 genes, 1000 species

• Handling datasets with multiple individuals

• GPU and CPU parallelism

Parallelism

Can infer trees with 10,000 species & 400 genes in a day27

GPU (1000 species)

GPU (500 species)

1 2 4 8 12 16 20 24# cores

d−up

1000 species

500 species

# CPU cores (comet)

Multiple individuals• What if we sample multiple

individuals from each species?

• In recently diverged species individuals may have different trees for each gene

• Sampling multiple individuals may provide useful information

• The ASTRAL approach can be extended to these types of data

Multiple individuals helpful?

Variable effort500 genes; 200 species

Fixed effortgenes x inds = 1000; 200 species

Fixed effort500 genes; species x inds = 200

ce) 1 ind.

2 ind.

5 ind.

Yes, it marginally helps accuracy

Simulations with very shallow trees (500K generations in total)

ce) 1 ind.

2 ind.

5 ind.

But not if sequencing effort is kept fixed

ce) 1 ind.

2 ind.

5 ind.

But not if sequencing effort is kept fixed

Impact of fragmentary data

Erfan Sayyari James B. Whitfield

Two types of missing data• Missing genes: a taxon

misses the gene fully (taxon occupancy)

• Fragmentary data: the species is partially sequenced for some genes

Figure from Hosner et al, 2016

Does missing data matter?• Missing genes:

• Evidence suggests summary methods are often robust

Does missing data matter?• Missing genes:

• Evidence suggests summary methods are often robust

• Fragmentary data:

• Less extensively studied

• Hosner et al. indicated:

• Fragments matter

• They suggest removing genes with many fragments

Our study• Empirical data:

• An insect dataset of 144 species and 1478 genes

• 600 million years of evolution

• Transcriptomics, so plenty of missing data of both types

• Simulated data:

• 100 taxon, medium ILS, 1000 genes

• Added fragmentation with patterns similar to the insect data

Fragmentary data hurt gene trees and species trees

no−filtering 10 20 25 33 50 66 75 80 orig−seqFiltering method

with fragments

without fragments

Species tree error: 2.8% errorG

Fragmentary data hurt gene trees and species trees

Fragmentary data dramatically increase

gene tree and the species tree error

with fragments

without fragments

Species tree error: 2.8% errorG

Species tree error: 7.0% error

How do we solve this?• Hosner et al. suggested removing entire genes.

• This is too conservative in our opinion.

How do we solve this?• Hosner et al. suggested removing entire genes.

• This is too conservative in our opinion.

• We simply remove the fragmentary sequence from the gene and keep the rest of the gene

• What is fragmentary?

• Anything that has at most X% of sites

• We study different X values

Filtering helps to some level (simulations)

●●

●● ● ●

Gene tree error Species tree error

How about real data?

no-filtering

oup A B C

C E F G H I J K L M N P

Strongly Supported Weakly Supported Weakly Reject Strongly Reject

66% filtering

Gene trees seem to improve (less gene tree discordance)

no-filtering

oup A B C

C E F G H I J K L M N P

Strongly Supported Weakly Supported Weakly Reject Strongly Reject

66% filtering

The species tree also improves

IngroupABC

D/B/CEFGHIJKLMNP

no filter

25 33 50

66 75 80

Supported0% 50% 100%

Weakly Rejected(<95%)

StronglyRejected(>=95%)

• ASTRAL trees differed with concatenation initially

• After filtering, ASTRAL and concatenation were very similar

• Differences on controversial nodes

ASTRAL …• Reconstructs species trees from gene trees with both

• high accuracy

• scalability to large datasets • robust to some levels of model violations

• Like any other summary method, remains sensitive to gene tree estimation error

• try best to obtain highly accurate gene trees

• removing fragmentary data seems to help

Future of ASTRAL• Can it be changed to use characters directly?

possible but slow for binary characters …

• More broadly, can alternative scalable methods be developed for better gene tree estimation?

Future of ASTRAL• Can it be changed to use characters directly?

possible but slow for binary characters …

• More broadly, can alternative scalable methods be developed for better gene tree estimation?

• ASTRAL scales to 10K leaves. We have 90K bacterial genomes.

• Can we scale further?

S.M. Bayzid Théo Zimmermann

Erfan Sayyari Shubhanshu Shekhar

Maryam Rabiee Hashemi

Chao ZhangTandy Warnow

John Yin

James B. Whitfield

Theoretical sample complexity results

How many genes are enough to reconstruct the tree?

●●

●●●●●● ●

●●

ε0.050.10.20.33

BalancedCaterpillarTheoretical

Gene trees seem to improve (bootstrap)

●●

● ● ●

● ●

●●

●● ●

no−filtering20 25 33 50 66 75 80Fragment filtering threshold

Bootstrap support ● ● ● ●=0 <=33 >=75 =100

● ●●

●● ● ●

no-filtering 20 25 33 50 66 75 90Filtering method

0.6 0.7 0.8 0.9

occupancy

Impact of gene tree error (using true gene trees)

10M 2M 500K

1e−061e−07

50 200 1000 50 200 1000 50 200 1000genes

rror (

ASTRAL−II ASTRAL−II (true gt) CA−ML

Figure S6: Comparison of ASTRAL-II run on estimated and true gene trees with 200 taxa and

varying tree shapes and number of genes.

Medium ILSLow ILS High ILS

10M 2M 500K

0.41e−06

1e−07

50 200 1000 50 200 1000 50 200 1000genes

rror (

Impact of gene tree error (using true gene trees)

• When we divide our 50 replicates into low, medium, or high gene tree estimation error, ASTRAL tends to be better with low error

10M 2M 500K

1e−061e−07

50 200 1000 50 200 1000 50 200 1000genes

rror (

10M 2M 500K

0.41e−06

1e−07

50 200 1000 50 200 1000 50 200 1000genes

rror (

ASTRAL-I versus ASTRAL-II

10M 2M 500K

1e−061e−07

50 200 1000 50 200 1000 50 200 1000genes

rror (

ASTRAL−I ASTRAL−II ASTRAL−II + true st

10M 2M 500K

1e−061e−07

50 200 1000 50 200 1000 50 200 1000genes

Figure S2: Comparison of various variants of ASTRAL with 200 taxa and varying tree shapes

and number of genes. Species tree accuracy (top) and running times (bottom) are shown. ASTRAL-II +true st shows the case where the true species tree is added to the search space; this is included to approximatean ideal (e.g. exact) solution to the quartet problem.

10M 2M 500K

1e−061e−07

50 200 1000 50 200 1000 50 200 1000genes

rror (

10M 2M 500K

1e−061e−07

50 200 1000 50 200 1000 50 200 1000genes

5200 species, deep ILS

ASTRAL-I versus ASTRAL-II

10M 2M 500K

1e−061e−07

50 200 1000 50 200 1000 50 200 1000genes

rror (

10M 2M 500K

1e−061e−07

50 200 1000 50 200 1000 50 200 1000genes

10M 2M 500K

1e−061e−07

50 200 1000 50 200 1000 50 200 1000genes

rror (

10M 2M 500K

1e−061e−07

50 200 1000 50 200 1000 50 200 1000genes

5200 species, deep ILS

Dynamic programming

A-A’A’A-A’A’A-A’A’

• Recursively break subsets of species into smaller subsets

Dynamic programming

A-A’

• : Compare u against input gene trees and compute quartets from gene trees satisfied by u

Dynamic programming

A-A’

• : Compare u against input gene trees and compute quartets from gene trees satisfied by u

Exponential

Constrained version

• Restrict “branches” in the species tree to a given constraint set X.

Deep ILS

rror (

ASTRAL−IINJstCA−ML

200 species, simulated species trees, deep ILS [Mirarab and Warnow, ISMB, 2015]

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