Evaluating the performance of phylogeneticinference methods on heterogeneous data

Mark HolderDepartment of Ecology and Evolutionary BiologyUniversity of KansasLawrence, Kansas, USA

Thanks:

• Dr. Ziheng Yang, Dr. Nick Goldman and the Royal Society

• Dr. Derrick Zwickl

• Dr. Gavin Naylor, Dr. Junhyong Kim, Dr. David Hillis, Dr. Paul Lewis,Dr. Dave Swofford, Tracy Heath, Dr. A. Town Peterson

• National Science Foundation

Weaknesses of early models of sequence evolution

They assumed that

• the process of evolution is identical across all sites,

• the process of evolution is fixed over time,

• sites evolve independently of one another.

Assuming homogeneity across sites

G A T A C C G A T

G A T A C C G A T

reality:

Simplest iid model’s view:

Among-site rate heterogeneity

G A T A C C G A T

G A T A C C G A T

G A T A C C G A T

reality:

no rate heterogeneity

with rate heterogeneity:

Among-site heterogeneity in substitution patterns

G A T A C C G A T

G A T A C C G A T

Reality:

Partitioned or mixure model:

Stationarity assumption

Reality (perhaps): Stationary model:

Changes in evolutionary process over time

• Covarion models

• State frequency changes

• models that allow for changes to ω on a specific branch

• relaxed and local clock methods

. . .

Independence assumption

Real PatternAssuming

Independence

Asn AAY His CAY

Lys AAR Gln CAR6

6¸

¸

AAY

AAR

CAY

CAR

CAY

CAR

AAY

AAR

Interactions among sites and neighborhood effects

• Codon models

• Doublet models for RNA

• Context-dependent models

. . .

Amazing progress in the development of models for phylogenetic inference,but . . .

• Are current models sufficient?

• How should we decide between alternative models?

• Are current models sufficient?

Not for difficult “deep phylogeny” questions. For example, it is fairlycommon to see strong support for a grouping, but sensitivity to taxonsampling.

• How should we decide between alternative models?

Delsuc et al. (2006):

©!2006!Nature Publishing Group!

!

alternative in which cephalochordates emerge before echinoderms.These two topologies appeared significantly worse that theML tree ofFig. 1, even for the conservative Shimodaira–Hasegawa test13.Our results therefore indicate a strong phylogenetic affinity

between tunicates and vertebrates to the exclusion of cephalo-chordates. However, obtaining high statistical support for a giventopology does not necessarily indicate that the phylogenetic inferenceis correct. Indeed, the phylogenetic analysis of large-scale data setsrequires particular attention to potential systematic biases associated,for instance, with differences in evolutionary rates among species,compositional biases and heterotachy8. In particular, a long-branchattraction (LBA) artefact14 may potentially occur since tunicatesinclude fast (Ciona ssp.) and very fast (O. dioica) evolving species(Fig. 1). A high evolutionary rate of tunicate genes was alreadynoticed in rRNA genes5 and in complete mitochondrial genomes15.Our results confirm these observations for a large number of nucleargenes. As fast evolutionary rates are also often associated withcompositional bias or with heterotachy, it is a necessary first stepto exclude the possibility that the observed grouping of tunicateswith vertebrates results from a tree reconstruction artefact.The most obvious potential artefact, an LBA, predicts that the fast-

evolving tunicates would be attracted towards the outgroup, and notby the slowly evolving vertebrates. This would produce a topologycompatible with the classical hypothesis of chordate evolution wherethe slow-evolving cephalochordates and vertebrates group together.This prediction is perfectly congruent with the lower support forOlfactores observed with MP (90%), a method known to be moresensitive to LBA than probabilistic methods14. Indeed, whenO. dioica

was used as the single representative of tunicates, MP unambiguouslysupported (BP ! 100) an aberrant position for this group whichemerged before cnidarians, disrupting the monophyly of bilaterians(Supplementary Fig. S1). By contrast, the less sensitive ML methodrecovered Olfactores, albeit with decreased bootstrap support(BP ! 84) (Supplementary Fig. S2). Therefore, despite its extremeevolutionary rate, O. dioica retained enough phylogenetic signal forits position to be recovered with ML. This demonstrates that LBAis not responsible for the inferred grouping of tunicates and verte-brates, and represents a strong argument in favour of the authenticityof Olfactores. In addition, neither compositional bias nor hetero-tachy significantly influenced phylogenomic inference with our dataset (see Supplementary Information). In fact, the compositionaleffect would act against Olfactores, because vertebrates and theamphioxus share similar amino acid compositions (SupplementaryFig. S3). In conclusion, the strongly supported monophyly ofOlfactores cannot be explained by any kind of identifiable systematicbias (LBA, compositional bias, and heterotachy) and thereforeconstitutes the best current hypothesis for chordate phylogeny.The monophyly of deuterostomes remained moderately sup-

ported in our phylogenomic analyses (Fig. 1). Also, the monophylyof chordates is not found in the ML tree, but is the only alternativenot significantly rejected by likelihood-based statistical tests(Table 1). A unique origin of chordates and their distinctive featuressuch as notochord and hollow nerve cord cannot be excluded. Ourresults nevertheless favoured the intriguing possibility of a sister-group relationship between cephalochordates and echinoderms thatseems robust to analyses aimed at avoiding compositional bias and

Figure 1 | Phylogenetic analyses of genomic data strongly support thegrouping of tunicates and vertebrates into Olfactores. ML tree obtainedfrom the analysis of 33,800 aligned amino acid positions under a WAGsubstitution matrix plus a four-category gamma rate correction (a ! 0.5)using two independent reconstruction algorithms (see SupplementaryInformation). Weighted maximum parsimony and bayesian inference using

the same WAG " F " G4 model and WAG " F " G4 plus covarion modelalso retrieved the same topology (see Supplementary Information).Bootstrap proportions obtained after 100ML (red) and 1,000 MP replicates(blue), as well as bayesian posterior probabilities (black) are shown forselected branches. A star indicates that all three values are maximal (100%,100% and 1.0). Scale bar indicates number of changes per site.

LETTERS NATURE|Vol 439|23 February 2006

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Thanks to Gavin Naylor for the slide

Later that year, Bourlat et al. (2006) added taxa including Xenoturbella:

the sampling of the echinoderm clade with data from the sun starSolaster stimpsoni (5,614 ESTs). We searched these ESTs for ortho-logues of the 146 genes used by Philippe et al.17. We then supplemen-ted these with 35 genes having a representative orthologue in ourXenoturbella ESTs, as this taxon had the fewestmatches to the data setfrom ref. 17.We culled 11 alignments where orthology was uncertain,leaving 170 concatenated, aligned orthologous genes (35,588 reliablyaligned amino acids). Saccoglossus had data from 153 of 170 genesand 29,777 amino acids, Xenoturbella had 63 genes and 8,370 aminoacids and Solaster had 67 genes and 11,033 amino acids.

We compared results from our extended data set of 170 genes tothose of the 146-gene data set of Delsuc et al.2 by performing phylo-genetic analyses without the new hemichordate,Xenoturbella and sunstar sequences. Phylogenetic analyses using maximum-likelihoodand bayesian approaches recapitulated previous results (Fig. 1a).All nodes received maximum support from bayesian analysis (baye-sian posterior probability (BPP) 5 100%). Maximum-likelihoodnon-parametric bootstrap support (MLBP) was lower for somenodes (see Supplementary Information). The overall topology of thistree conforms to the ‘new animal phylogeny’18 with monophyleticprotostomes, deuterostomes, lophotrochozoans (represented hereby molluscs and an annelid), and ecdysozoans (represented hereby arthropods and a nematode; see Supplementary Information).Within the deuterostomes, we find support for monophyletic groupsof vertebrates, cyclostomes (hagfish and lamprey) and Olfactores(vertebrates plus urochordates). Importantly, we recovered the rela-tionship linking cephalochordates not to other chordates but toechinoderms: BPP 5 100%, Treefinder19 LRSH support (TF) 575% and MLBP 5 81%. This relationship was unexpected and wewanted to test the possibility that it was caused by systematic error.Two powerful ways of addressing systematic errors are to includeadditional taxa, thereby enabling better detection of misleading mul-tiple substitutions, and to remove problematic taxa (for example,long branches); we have used both approaches20.

By adding sequences from three taxa that are likely to be related tothe echinoids (asteroid, hemichordate and Xenoturbella) we couldtest the possibility that the cephalochordate/echinoderm relationshipmight result from a systematic error such as long-branch attraction21.The effect of including these three taxa in our analysis is clear; sup-port for a cephalochordate plus echinoderm clade disappears andsupport for the canonical monophyletic chordates increases(Fig. 1b). The monophyletic chordate clade in our new analysis hasBPP 5 100% and TF5 53%, but no MLBP support. This change intopology on the addition of taxa that divide the echinoid branch isconsistent with the idea that the attraction between the cephalochor-date and the echinoid results from a systematic error; the addition ofnon-problematic taxa tends to improve the reliability of a phylo-geny21. We compared the support for the optimal topology to thatfor the alternative topology, which groups the cephalochordates withAmbulacraria and Xenoturbella using the Shimodaira–Hasegawa(SH) tests and Bayes factors. The SH test did not reject the alternativetopology as significantly worse than the optimal topology (SHP5 0.476), but the alternative topology was rejected as significantlyworse using the Bayes factors test (2loge (B10)5 24), although thistest might not be conservative. The inclusion of data from the othermajor taxon of cephalochordates—the Epigonichthyidae—willdivide the cephalochordate branch and, we predict, will furtherincrease support for the monophyletic chordates.

A parallel possibility is that rapidly evolving urochordates, alongwith their sister group the vertebrates, have been attracted towardsthe base of the tree by long-branch effects22. Two lines of evidencesupport this possibility. First, in the analyses described above, weused diploblast metazoans (ctenophore and cnidarian) as close out-groups; the inclusion of more distant outgroups (yeast and choano-flagellates), as in ref. 2, results in a more basal position for Olfactoreswith the corollary that cephalochordates group with echinoderms.This result is observed even when the asteroid, hemichordate

Solaster stimpsonii

Echinoidea

Saccoglossus kowalevski

Xenoturbella bocki

Ciona intestinalis

Halocynthia roretzi

Molgula tectiformis

Eptatretus burgeri

Petromyzon marinus

Homo sapiens

Branchiostoma sp.

Protopterus dolloi Lepidosiren paradoxaRaja porosa

Danio rerioChelonia mydas

Homo sapiens Boa constrictor

Myxine glutinosa Eptatretus burgeri

Lampetra fluviatilisPetromyzon marinus

Branchiostoma belcheriEpigonichthys lucayanus

Xenoturbella bockiAstropecten polyacanthusAsterina pectiniferaLuidia quinaliaAsterias amurensisPisaster ochraceusStrongylocentrotus purpuratusParacentrotus lividusArbacia lixula

Cucumaria miniataFlorometra serratissima

Balanoglossus carnosusSaccoglossus kowalevskii

Ciona intestinalis Ciona savignyi

Doliolum nationalis Halocynthia roretzi

Ecdysozoa + Lophotrochozoa

Vertebrata

Cephalochordata

Xenoturbellida

Echinodermata

Hemichordata

Urochordata

Vertebrata

Cephalochordata

Xenoturbellida

Echinodermata

Hemichordata

Urochordata

100/83/82

100/68/70

100/94/91

100/99/68

100/75/86

100/53/-

Ciona intestinalis

Halocynthia roretzi

Molgula tectiformis

Eptatretus burgeri

Petromyzon marinus

Homo sapiens

Branchiostoma sp.

Echinoidea

Vertebrata

Cephalochordata

Urochordata

Echinodermata

100/100/95

100/99/100

c

a

b

Figure 1 | Phylogenetic analyses of 170 nuclear proteins and 13mitochondrial proteins support a monophyletic chordate clade and anindependent deuterostome phylum of Xenoturbellida. a, Bayesian analysisof nuclear data before the addition of the new asteroid, hemichordate andxenoturbellid data. The cephalochordate groups with the echinoderm,implying that the chordates are paraphyletic. b, Bayesian analysis of nucleardata after the addition of asteroid, hemichordate and xenoturbellid data. Thenew sequences join the branch to the echinoderm, and the cephalochordatesnow join the chordate branch. This indicates that the previous result is dueto systematic error. Xenoturbella is the sister group of the Ambulacraria(echinoderms plus hemichordates). c, Bayesian analysis of mitochondrialdata with the amino acids M, I, N and K recoded as missing data places thecephalochordates with vertebrates; Xenoturbella is the sister group ofAmbulacraria. Support for critical nodes is shown in the order BPP (%), TF(%) and MLBP (%). Long branches leading to the urochordates have beenshortened as indicated by a break (/) in the branch (see SupplementaryInformation for unaltered tree and scale).

LETTERS NATURE |Vol 444 |2 November 2006

86Nature Publishing Group ©2006

Thanks to Gavin Naylor for the slide

• Are current models sufficient?

Not for difficult “deep phylogeny” questions.

• How should we decide between alternative models?

“Black-box” model choice methods (LRT, AIC, BIC, Bayes Factors,. . .) are very helpful at assessing the fit.

However, they may not do a good job of identifying the model thatis the best estimator of the parameters that we care about (e.g. thetree).

This particularly a concern when none of the models considered isclose to being “true.”

constantfast slow

ACGT

M1: one rate class – RejectedM2: constant-ACGT -sites + 1 variable rate classM3: 3 rate classes

Either M2 or M3 may be chose by an automated model selection procedure,but M3 is more likely to return the correct tree.

From a paper a Systematic Biology by Marshall et al. (2006) comparingmodels (all of which had Γ-distributed rates).

Model Tree length ln Lpartitioned by codon, one mean rate 2.00 −9942.24

unpartitioned 1.13 −10414.96

From a paper a Systematic Biology by Marshall et al. (2006) comparingmodels (all of which had Γ-distributed rates).

Model Tree length ln Lpartitioned by codon, one mean rate 2.00 −9942.24

unpartitioned 1.13 −10414.96partitioned by codon, SSB 1.13 −9866.67partitioned by codon, SSR 1.15 −9842.41

See also Buckley et al. (2001) for discussion of performance of subset-specific rate models without Γ-distributed rate heterogeneity.

How should we decide between alternative models?

• Standard model selection tools are certainly helpful,

• Performance-based model selection (e.g. Minin et al., 2003),

• Performance of a model on previous real data analyses,

• Performance of inference methods on data derived from computersimulations.

Using computer simulations to evaluate models and methods:

• flexible, fast, and transparent

but. . .

• simulations often generate data that is too “clean” (but see work ofJunhyong Kim and his collaborators).

• simulated data may bear little resemblance to the real world.

Evaluating performance using computer simulation

1. Choose a simulation model

2. Choose a tree shape

3. Simulate many data sets

4. Infer trees using a variety of methods

5. Compare inferred tree to true (model) tree.

In the following slides we’ll deal with a very complex, parameter-richsimulation model – Halpern and Bruno (1998) model of site-specific residuefrequencies.

Halpern and Bruno (1998) model of coding sequenceevolution

• All nucleotides share a set of parameters for a mutational model,

• Each amino acid residue has a set of equilibrium frequencies

Halpern and Bruno (1998) model properties

1. Extreme heterogeneity of process

2. Sites (within the same codon) are not independent

3. Among-site rate heterogeneity, but not following a simple distribution(such as the Γ-distribution).

I wrote software to:

1. find MLEs of parameters of the Halpern and Bruno (1998) model, and

2. simulate under the Halpern-Bruno model (on a user-defined tree).

Estimated parameters on a dataset of 1610 mammalian cytochrome-bsequences (376 amino acid residues, ≈ 7, 150 substitution parameters)

http://nladr-cvs.sdsc.edu/svn/CIPRES/cipresdev/trunk/python-example/org.cipres.bull

username: guest

password: guest

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MAJORPROPITHECUS TATTERSALLIDAUBENTONIA MADAGASCARIENSISTARSIUS BANCANUSOTOLEMUR CRASSICAUDATUSNYCTICEBUS COUCANGLORIS TARDIGRADUSOVIS ARIES1OVIS ARIES2OVIS ARIES5OVIS ARIES4OVIS VIGNEIOVIS AMMONOVIS DALLI1OVIS DALLI2OVIS CANADENSISBUDORCAS TAXICOLOR1BUDORCAS TAXICOLOR2OVIS ARIES3OVIBOS MOSCHATUS1OVIBOS MOSCHATUS2OVIBOS MOSCHATUS3OVIBOS MOSCHATUS4OVIBOS MOSCHATUS5CAPRICORNIS CRISPUS2CAPRICORNIS CRISPUS1NEMORHAEDUS CAUDATUSOREAMNOS AMERICANUS1OREAMNOS AMERICANUS2AMMOTRAGUS LERVIARUPICAPRA PYRENAICARUPICAPRA RUPICAPRAHEMITRAGUS JEMLAHICUS1HEMITRAGUS JEMLAHICUS2CAPRA SIBIRICACAPRA NUBIANACAPRA AEGAGRUS1CAPRA CYLINDRICORNISCAPRA CAUCASICACAPRA FALCONERI1CAPRA FALCONERI2CAPRA AEGAGRUS2CAPRA HIRCUS1CAPRA HIRCUS6CAPRA HIRCUS2CAPRA HIRCUS3CAPRA HIRCUS5CAPRA HIRCUS4CAPRA AEGAGRUS3CAPRA HIRCUS7CAPRA HIRCUS8CAPRA IBEXPSEUDOIS NAYAURPANTHOLOPS HODGSONIDAMALISCUS PYGARGUSDAMALISCUS LUNATUSBEATRAGUS HUNTERIALCELAPHUS BUSELAPHUS1ALCELAPHUS BUSELAPHUS2ALCELAPHUS LICHTENSTEINISIGMOCEROS 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TAJACU1PECARI TAJACU2TAYASSU PECARICATAGONUS WAGNERISTENELLA LONGIROSTRIS1STENELLA LONGIROSTRIS5STENELLA LONGIROSTRIS6STENELLA LONGIROSTRIS7STENELLA LONGIROSTRIS3STENELLA LONGIROSTRIS2STENELLA LONGIROSTRIS4STENELLA ATTENUATA1STENELLA ATTENUATA4STENELLA ATTENUATA2STENELLA ATTENUATA3STENELLA FRONTALIS1STENELLA FRONTALIS2STENELLA CLYMENESTENELLA COERULEOALBA1STENELLA COERULEOALBA2DELPHINUS TROPICALISDELPHINUS CAPENSIS1DELPHINUS CAPENSIS2DELPHINUS DELPHIS2DELPHINUS DELPHIS1TURSIOPS ADUNCUS1TURSIOPS ADUNCUS2TURSIOPS TRUNCATUS1TURSIOPS TRUNCATUS4TURSIOPS TRUNCATUS2TURSIOPS TRUNCATUS3SOUSA CHINENSIS1SOUSA CHINENSIS2LAGENODELPHIS HOSEI1LAGENODELPHIS HOSEI2LAGENORHYNCHUS ACUTUSGRAMPUS GRISEUS1GRAMPUS GRISEUS2PSEUDORCA CRASSIDENSGLOBICEPHALA MELAS1GLOBICEPHALA MELAS2GLOBICEPHALA MACRORHYNCHUS1GLOBICEPHALA MACRORHYNCHUS2PEPONOCEPHALA ELECTRAFERESA ATTENUATAORCINUS ORCA1ORCINUS ORCA3ORCINUS ORCA2ORCAELLA BREVIROSTRIS1ORCAELLA BREVIROSTRIS3ORCAELLA BREVIROSTRIS2LAGENORHYNCHUS 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LIBERIENSISVICUGNA VICUGNALAMA PACOSLAMA GLAMALAMA GUANICOE1LAMA GUANICOE2CAMELUS BACTRIANUSCAMELUS DROMEDARIUS1CAMELUS DROMEDARIUS2CERATOTHERIUM SIMUMDICEROS BICORNISRHINOCEROS UNICORNISTAPIRUS TERRESTRISTAPIRUS INDICUSEQUUS ASINUSEQUUS GREVYIEQUUS CABALLUS1EQUUS CABALLUS3EQUUS CABALLUS2HERPESTES AUROPUNCTATUSFELIS CATUS1FELIS CATUS4FELIS CATUS3FELIS CATUS2PANTHERA TIGRIS1PANTHERA TIGRIS3PANTHERA TIGRIS8PANTHERA TIGRIS9PANTHERA TIGRIS4PANTHERA TIGRIS5PANTHERA TIGRIS6PANTHERA TIGRIS7PANTHERA TIGRIS2PANTHERA LEO1PANTHERA LEO2CANIS FAMILIARIS1CANIS FAMILIARIS2VULPES VULPESHALICHOERUS GRYPUSPHOCA HISPIDAPHOCA VITULINA1PHOCA VITULINA2PHOCA LARGHACYSTOPHORA CRISTATAPHOCA GROENLANDICAPHOCA FASCIATAERIGNATHUS BARBATUSMONACHUS SCHAUINSLANDILEPTONYCHOTES WEDDELLIHYDRURGA LEPTONYXMIROUNGA LEONINAZALOPHUS CALIFORNIANUSEUMETOPIAS JUBATUSARCTOCEPHALUS FORSTERIARCTOCEPHALUS GAZELLAODOBENUS ROSMARUSAILURUS FULGENSSELENARCTOS THIBETANUSURSUS THIBETANUSURSUS AMERICANUS1URSUS AMERICANUS2HELARCTOS 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MELAMPUS5MARTES MELAMPUS11MARTES MELAMPUS8MARTES MELAMPUS13MARTES MELAMPUS15MARTES MELAMPUS12MARTES MELAMPUS9MARTES MELAMPUS14MARTES MELAMPUS10MARTES MELAMPUS16MARTES MELAMPUS6MARTES PENNANTIGULO GULOMUSTELA VISONMUSTELA PUTORIUSMUSTELA ERMINEAPTERONURA BRASILIENSISLUTRA MACULICOLLISLUTRA LUTRA1LUTRA LUTRA2AMBLONYX CINEREUSAONYX CAPENSISENHYDRA LUTRIS1ENHYDRA LUTRIS2LONTRA LONGICAUDISLONTRA FELINALONTRA CANADENSISTAXIDEA TAXUSMELES MELESPROCYON LOTORBASSARICYON GABBIISPILOGALE PUTORIUSMEPHITIS MEPHITISARTIBEUS JAMAICENSIS1ARTIBEUS JAMAICENSIS3ARTIBEUS OBSCURUS1ARTIBEUS OBSCURUS2ARTIBEUS PLANIROSTRISARTIBEUS LITURATUSARTIBEUS INTERMEDIUSARTIBEUS FIMBRIATUSARTIBEUS INOPINATUSARTIBEUS HIRSUTUSARTIBEUS FRATERCULUSARTIBEUS TOLTECUSARTIBEUS PHAEOTISARTIBEUS GLAUCUS1ARTIBEUS AZTECUSARTIBEUS GLAUCUS2ARTIBEUS GLAUCUS3ARTIBEUS CINEREUSARTIBEUS ANDERSENIARTIBEUS CONCOLOR1ARTIBEUS CONCOLOR2ARTIBEUS HARTIIERINACEUS EUROPAEUS1ERINACEUS EUROPAEUS2TALPA EUROPAEA1TALPA EUROPAEA2TALPA ALTAICAMOGERA WOGURA1MOGERA WOGURA2MOGERA WOGURA3MOGERA IMAIZUMIIMOGERA TOKUDAEMOGERA INSULARISEUROSCAPTOR MIZURAUROTRICHUS TALPOIDESCROCIDURA RUSSULASOREX TUNDRENSIS2SOREX ASPER1SOREX ASPER2SOREX CORONATUS1SOREX CORONATUS2SOREX GRANARIUS1SOREX GRANARIUS2SOREX ARANEUS1SOREX ARANEUS2SOREX ARANEUS3SOREX ARCTICUS1SOREX ARCTICUS2SOREX SAMNITICUS1SOREX SAMNITICUS2SOREX UNGUICULATUSSOREX ISODON1SOREX ISODON2SOREX SHINTO1SOREX SHINTO2SOREX CAECUTIENS1SOREX CAECUTIENS2SOREX MINUTUSSOREX MINUTISSIMUS1SOREX MINUTISSIMUS2SOREX RADDEI1SOREX RADDEI2SOREX EXCELSUS1SOREX EXCELSUS2SOREX ALPINUS1SOREX ALPINUS2SOREX CINEREUS2SOREX HAYDENI1SOREX HAYDENI2SOREX VAGRANSSOREX PACIFICUS1SOREX PACIFICUS2SOREX MONTICOLUS1SOREX MONTICOLUS2SOREX PALUSTRIS1SOREX PALUSTRIS2SOREX HOYISOREX FUMEUS1SOREX FUMEUS2SOREX TROWBRIDGII1SOREX TROWBRIDGII2NEOMYS ANOMALUSNEOMYS FODIENS

Space of 4-taxon simulation trees

0.05 1.0

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Figure 3.6

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Figure 3.7

Parsimony with step matrix Maximum likelihood (GTR + rate het.)

Contrasting parsimony and maximum likelihood

115

Figure 3.22

A contrast of DNA-based weighted parsimony and maximum likelihood using GTR

with preferred rate heterogeneity made by subtracting the number of successes by one

method from the number of successes by the other method across the paremeter space

shown in Figure 3.2. The maximum value is 100 (shown in deep blue), the minimum

value is –100 shown as deep red. White indicates equivalent performance.

Maximum likelihood and distance (GTR + rate het.)

100

Figure 3.7

106

Figure 3.13

Maximum likelihood Minimum evolution

228-taxon model tree

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• Parsimony tree for angiosperm tree

• Model tree for Hillis (1996, 1998)

(blue on the next slides)

• Inferred branch lengths and 10×(red on the next slides)

228-taxon tree: Parsimony (stepwise addition)

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Model trees for 50 leaves generated:

• by a pure birth process, followed by selection of 50% of the taxa.

• rate of evolution then allowed to evolve along the tree Kishino et al.(2001)

• mean branch length has an expected # changes per site ≈ 0.02

The following results are very preliminary.

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Performance on a simulation of 1 copy of cyt. b

Non-zero AAGarli/AA/WAG+I+Γ

PhyloBayes/AA/Poisson+CAT

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Garli/Nuc/GTR+I+ΓMrBayes/Nuc/GTR+I+Γ

MrBayes/Nuc/GTR+I+Γ by codon posPhyloBayes/Nuc/GTR - CAT

Garli/RY/GTR+I+Γ

Parsimony

Minimum evolution

Performance on a simulation of 10 copies of cyt. b

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PhyloBayes/AA/Poisson+CAT

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Garli/Nuc/GTR+I+ΓMrBayes/Nuc/GTR+I+Γ

MrBayes/Nuc/GTR+I+Γ by codon pos ∗PhyloBayes/Nuc/GTR - CAT ∗

Garli/RY/GTR+I+Γ

Parsimony

Minimum evolution

Conclusions from simulations under Halpern-Brunomodel fit to cytochrome b data

• in general, likelihood-based inference on the nucleotide level appearsrobust,

• mixture/partitioned approaches performing well,

• parsimony’s performance was quite variable (depending on model treeshape),

• distance methods are much more sensitive to model violation,

• analyses at the amino acid level were substantially less accurate

however. . .

Caveats about simulations under Halpern-Bruno modelfit to cytochrome b data

• On small trees, the simulator generates amino sequences with relativelylittle variation

– cyt b is constrained,– overfitting of amino acid parameters could be decreasing the variability

• Still too simple:

– homogeneity of mutational process (over space and time),– lack of codon bias

Could cause the nucleotide-level conclusions to be too optimistic.

These drawbacks can be addressed by fitting parameters from more genes,and using parameter estimates from other clades estimate the rate of changein parameter values over time.

Perspective and Discussion questions

Devising realistic, complex simulators still an open area of research. Suchtools could allow us to compare fundamentally different analysis styles (e.g.codon vs. nucleotide vs amino acid), and could provide sound guidanceabout the appropriateness of a model – evidence to be used in conjuctionwith standard model choice techniques.

• Is it feasible to develop compelling simulators? Can we really make themcomplex, and yet realistic without knowing the “true” model?

• Suppose that AIC (or your-favorite-model-selection) framework stronglyprefers model X over model Y. Would a simulation study saying thatmodel Y is more robust and reliable sway you?

References

Bourlat, S., Juliusdottir, T., Lowe, C., and Freeman, R. (2006).Deuterostome phylogeny reveals monophyletic chordates and the newphylum xenoturbellida. Nature.

Buckley, T. R., Simon, C., and Chambers, G. K. (2001). Exploring among-site rate variation models in a maximum likelihood framework usingempirical data: effects of model assumptions on estimates of topology,branch lengths, and bootstrap support. Systematic Biology, 50(1):67–86.

Delsuc, F., Brinkmann, H., Chourrout, D., and Philippe, H. (2006).Tunicates and not cephalochordates are the closest living relatives ofvertebrates. Nature.

Halpern, A. L. and Bruno, W. J. (1998). Evolutionary distances for protein-coding sequences: modeling site-specific residue frequencies. MolecularBiology and Evolution, 15(7):910–917.

Hillis, D. M. (1996). Inferring complex phylogenies. Nature, 383(6596):130–131.

Hillis, D. M. (1998). Taxonomic sampling, phylogenetic accuracy, andinvestigator bias. Systematic Biology, 47(1):3–8.

Kishino, H., Thorne, J. L., and Bruno, W. J. (2001). Performance of adivergence time estimation method under a probabilistic model of rateevolution. Molecular Biology and Evolution, 18:352–361.

Marshall, D., Simon, C., and Buckley, T. (2006). Accurate branch lengthestimation in partitioned bayesian analyses requires accommodation ofamong-partition rate variation and attention to branch length priors.Systematic Biology, 55(6):993–1003.

Minin, V., Abdo, Z., Joyce, P., and Sullivan, J. (2003). Performance-based selection of likelihood models for phylogeny estimation. SystematicBiology, 52(5):674–683.