Rate Heterogeneity, Ancestral Character State Reconstruction, and the Evolution of Limb ...

18 Pages·2010·1.54 MB·English

Syst.Biol.59(6):723–740,2010
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DOI:10.1093/sysbio/syq055
AdvanceAccesspublicationonOctober1,2010
RateHeterogeneity,AncestralCharacterStateReconstruction,andtheEvolutionofLimb
MorphologyinLerista(Scincidae,Squamata)
(cid:3)
ADAMSKINNER
SchoolofEarthandEnvironmentalSciences,TheUniversityofAdelaide,SouthAustralia5005,Australia,andSouthAustralianMuseum,
NorthTerrace,Adelaide,SouthAustralia5000,Australia;
∗
Correspondencetobesentto:SchoolofEarthandEnvironmentalSciences,
TheUniversityofAdelaide,SouthAustralia5005,Australia;E-mail:[email protected].
Received5April2009;reviewsreturned31July2009;accepted21June2010 D
AssociateEditor:ToddOakley o
w
n
lo
Abstract.—Ratesofphenotypicevolutionderivefromnumerousinterrelatedprocessesactingatvaryingspatialandtempo- a
d
ralscalesandfrequentlydiffersubstantiallyamonglineages.Althoughcurrentmodelsemployedinreconstructingances- e
d
tbreatlwcheeanradctieffresrteanttesstpaetrems),ittihnedseepreantedsenatrerattyepsifcoarlldyisatsinsuctmtyepdetsoobfetriadnesnittiiocnal(ffoorrwaallrdbraanndchreevseirnseatprahnysliotigoennsya.nIndtthraisnspitaipoenrs, from
Ipresentageneralmodelofcharacterevolutionenablingrateheterogeneityamongbranches.Thismodelisemployedin h
assessingtheextenttowhichtheassumptionofuniformtransitionratesaffectsreconstructionsofancestrallimbmorphol- ttp
opgatyteinrntsh.ePsecrimnciitdtinligzarradtecvlaadrieaLtieornistaamaonndg,abcrcaonrcdhinesglsyi,gtnhieficpaontetlnytiiamlpforrovraetsemvaordiaeblifilittfyotrobmotihsltehaedminafneruesnacnesdotfheevpoelsu.tAioncoarny- s://a
c
strainedmodelinwhichtherateofdigitacquisitionisassumedtobeeffectivelyzeroisstronglysupportedineachcase; a
d
whencomparedwithamodelassumingunconstrainedtransitionrates,thismodelprovidesasubstantiallybetterfitfor e
m
themanusandanearlyidenticalfitforthepes.Ancestralstatesreconstructedassumingtheconstrainedmodelimplypat- ic
ternsoflimbevolutiondifferingsignificantlyfromthoseimpliedbyreconstructionsforuniform-ratemodels,particularly .o
u
forthepes;whereasancestralstatesfortheuniform-ratemodelsconsistentlyentailthereacquisitionofpedaldigits,those p
forthemodelincorporatingamong-lineagerateheterogeneityimplyrepeated,unreverseddigitloss.Theseresultsindicate .co
thattheassumptionofidenticaltransitionratesforallbranchesinaphylogenymaybeinappropriateinmodelingtheevo- m
lutionofphenotypictraitsandemphasizetheneedforcarefulevaluationofphylogenetictestsofDollo’slaw.[Character /sy
s
evolution;Dollo’slaw;likelihood;limbreduction;lizard;model;skink.] b
io
/a
Phylogenetic inference of ancestral character states drift and selection establish these phenotypes within rtic
affords an efficient, generally applicable means of ex- demes, and dispersal and associated introgression dis- le
-a
amining patterns and rates of character state transi- tribute phenotypes across (all) demes. Pronounced en- b
s
tion and, consequently, has been employed extensively vironmental heterogeneity within the distributions of tra
c
in studies of phenotypic evolution (e.g., Kohlsdorf many species, promoting geographical differentiation, t/5
and Wagner 2006; Leschen and Buckley 2007; Wiens would tend to impede the third of these phases (e.g., 9/6
et al. 2007; Brandley et al. 2008). Approaches to re- Lieberman and Dudgeon 1996; Gould 2002; Eldredge /7
2
constructing ancestral traits have become increasingly et al. 2005), and the stabilization of novel phenotypes 3/1
sophisticatedduringthepast2decades, andtheuseof inmanylineagesmayinsteadbeascribedtospeciation 71
1
maximum likelihood (Schluter et al. 1997; Pagel 1999) (Futuyma 1987). Thus, the probability of a transition 5
8
andBayesianMarkovchainMonteCarlo(Huelsenbeck occurring on a branch in a phylogeny may be affected 7
b
et al. 2003; Pagel et al. 2004) methods, incorporating by the frequency of unobserved speciation (or, con- y g
explicit stochastic models of character evolution, is versely, extinction) events along its length, as well as ue
s
nowusual.Althoughthesemethodsenableassessments those factors influencing the rate at which novel phe- t o
of uncertainty associated with reconstructed ancestral notypes are established within and conveyed among n 0
states, their ability to mislead inferences of evolution- demes (including deme size, mutation rate, selection 9 A
ary patterns has been noted by several authors (e.g., pressures, developmental constraints, and rate of dis- p
Wiens et al. 2007; Ekman et al. 2008). Proposed ex- persal). Considering the manifold causes determining ril 2
0
planations for demonstrably inaccurate estimation of rates of phenotypic evolution, it is unsurprising that 1
9
ancestralstatesfrequentlyimplicateviolationoftheas- paleontological studies have revealed substantial rate
sumption of uniform rates of character state transition heterogeneityamonglineages(see, e.g., Belletal.1985;
acrossaphylogeny;recentmodelspermitdifferingrates Cheetham1986;Sheldon1987;Geary1995).
oftransitionamongcharacterstates, buttheseratesare Schluter et al. (1997) have defended the use of a
typically assumed to be identical for all branches (see constant-rate Markov process to characterize transi-
MooersandSchluter1999;Pagel1999). tions among discrete character states, arguing that this
Rates of phenotypic evolution derive from numer- relativelysimplestochasticmodelshouldbeviewedas
ousinterrelatedprocessesactingatvaryingspatialand aneffectivemeansofdescribingtheunpredictabilityof
temporal scales. As Eldredge et al. (2005) have dis- evolutionandnotasanaccuraterepresentationofevo-
cussed,characterstatetransitionsperceivedatthelevel lutionary mode. Nonetheless, they noted that existing
ofspeciesmaybeconsideredtooccurin3phases:novel models may fail to incorporate significant aspects of
phenotypes originate via mutation and recombination, phenotypic evolution, identifying “The assumption of
723
724 SYSTEMATICBIOLOGY VOL.59
constantrates”as“perhapsthemostglaringweakness” the pattern and mode of limb evolution. The primary
(Schluter et al. 1997, p. 1700). The adequacy of models aim motivating this study was to assess the possibility
that assume rate constancy across a phylogeny may be that model misspecification associated with heteroge-
evaluated empirically using model selection criteria. neous rates of character state transition contributed
Although not conceptually difficult (model evaluation significantly to this failure. Aside from evaluating the
isanintegralpartofcontemporaryphylogenetics),such potentialinfluenceofamong-lineagerateheterogeneity
assessmentswouldnecessitatemorerealisticmodelsal- on the analyses of Skinner et al. (2008), I consider the
lowingratesofcharacterstatetransitiontovaryamong broader implications of rate variation for phylogenetic
branches. In this study, I develop a general model of tests of Dollo’s law, emphasizing the need for careful
phenotypic evolution permitting rate heterogeneity appraisalofevidenceforreversibleevolution.
amonglineages,extendingtheuniform-ratemodeldis-
cussedbySchluteretal.(1997,seealsoPagel1994,1999). D
o
Thismodelisemployedinassessingtheextenttowhich w
theassumptionofuniformtransitionratesaffectsrecon- MATERIALSANDMETHODS nloa
DataandPhylogeneticAnalysis d
structions of ancestral limb morphology in the scincid e
d
lizard clade Lerista and, accordingly, the potential for A phylogeny incorporating the 72 species of Lerista fro
rate variability to mislead inferences of evolutionary consideredbySkinneretal.(2008),5subspeciesnotin- m
patternandmode. cludedintheanalysisofSkinneretal.(2008)(L.microtis http
Lerista is regarded generally as an exemplary model intermedia, L. microtis schwaneri, L. macropisthopus galea, s
forstudyingtetrapodlimbreduction, comprisingmore L. macropisthopus macropisthopus, and L. macropisthopus ://a
c
a
than 75 species exhibiting at least 20 distinct pha- remota), and 6 outgroup taxa (Anomalopus leuckartii, d
e
langeal configurations, from the plesiomorphic con- Calyptotis lepidorostrum, Coggeria naufragus, Ctenotus ro- m
ic
dition for squamates (phalangeal formulae of 2.3.4.5.3 bustus, Eulamprus kosciuskoi, and Glaphyromorphus fus- .o
u
and 2.3.4.5.4 for the manus and pes, respectively) to cicaudis) was inferred from nucleotide sequences for p
.c
entirely limbless (Greer 1987, 1990). In a recent paper, a nuclear intron and 6 mitochondrial genes (see Sup- o
m
Skinner et al. (2008) presented the first explicitly phy- plementary Material, available at http://www.sysbio /s
y
logenetic investigation of limb reduction and loss in .oxfordjournals.org; Tables 1 and 2). All sequences s
b
this clade. Ancestral digit numbers reconstructed as- except those for the 5 additional subspecies are from io
/a
suming a uniform-rate model (incorporating separate Skinneretal.(2008), Reeder(2003), andSkinner(2007). rtic
parameters for forward and reverse transitions) and a Sequences for the additional subspecies were obtained le
-a
comprehensive phylogeny inferred from nucleotide se- as described by Skinner (2007). Primer sequences and b
s
quence data for a nuclear intron and 6 mitochondrial polymerase chain reaction (PCR) conditions are pre- tra
genes implied 19 instances of unreversed digit loss for sented in Table 1. Although previous analyses (Reeder ct/5
the manus. This result was not substantially affected 2003; Skinner 2007) indicate that Lerista is part of the 9
/6
by uncertainty in rates of character state transition or Australian Sphenomorphus group, basal relationships /7
2
the phylogeny. Ancestral states for the pes were less withinthismoreinclusivecladearesubstantiallyunre- 3
/1
stable, depending to a considerable extent on the rate solved. Accordingly, a diverse selection of Australian 7
1
parametervaluesassumed.Althoughnumbersofpedal Sphenomorphus group scincids was employed as an 15
8
digits reconstructed assuming maximum likelihood outgroup. 7
b
ratesentailednumerousinstancesofdigitreacquisition, Alignment of ND4 sequences did not require the y
g
rates only insignificantly less likely than the maximum insertion of internal gaps and was straightforward. u
e
likelihood estimates yielded ancestral states implying Structural RNA and adenosine triphosphate (ATP) st o
repeateddigitlosswithnoreversals. synthetase subunit (cid:12) intron sequences were aligned n
0
As Skinner et al. (2008) discussed, an argument can with MAFFT v6.717b (see Katoh et al. 2009) using 9
A
be made for preferring reconstructions for the pes the L-INS-i method with default options. Exclusion p
entailing repeated, unreversed limb reduction; when of ambiguously-aligned sites identified using Gblocks ril 2
0
considered together with the (very robust) ancestral v0.91b (Castresana 2000) does not significantly affect 1
9
states for the manus, these reconstructions nearly in- the inferred phylogeny or comparisons of models of
variably imply ancestral digit configurations displayed phenotypic evolution (see Supplementary Material).
byextantspeciesofLerista.Ancestralstatesentailingre- PhylogeneticrelationshipswereinferredusingRAxML
elaborationofthepes,bycontrast,implydigitconfigu- 7.0.0 (Stamatakis 2006). All analyses employed either
rationsformanyinternalnodesdifferingfundamentally the -m GTRGAMMA or the -m GTRGAMMAI option
from observed phenotypes (specifically, configurations (see below) and were repeated 10 times, each repe-
of either 5 or 4 manual digits and 2 pedal digits are tition beginning with a randomly selected maximum
implied for most basal nodes, although extant species parsimony tree. An appropriate partitioning strategy
of Lerista never exhibit fewer digits for the pes than was selected on the basis of the Akaike information
the manus). Thus, there is evidence that the analyses criterion (modified for small sample size, AIC ), as de-
c
of Skinner et al. (2008) failed to accurately estimate scribedbyMcGuireetal.(2007).Atotalof8partitioning
ancestral states for the pes (i.e., when maximum likeli- strategies were compared, having from 1 to 7 parti-
hood rates were assumed), confounding inferences of tions (Table 3). RAxML implements only 2 nucleotide
2010 SKINNER—RATEHETEROGENEITYANDLIMBEVOLUTIONINLERISTA 725
C) TABLE2. Partitionsassumedinthisstudy
◦
g(
nnealinerature 48 50 55 55–58 48 Partition Alignedsites Variablesites Dipsatitntecrtnssite
Ap 12SrRNA 910 440 509
m
16SrRNA 563 221 272
e
t tRNA-His,tRNA-Ser,
tRNA-Leu 141 82 111
ND4,1stcodonposition 228 110 131
ND4,2ndcodonposition 229 33 60
nc ND4,3rdcodonposition 229 226 229
conM) AT(cid:12)Pisnytrnotnhetasesubunit 592 266 386
gCl2(m 2 2 4 2 4 Notes:Alternativepartitioningstrategieswithfewerthan7partitions Dow
M (seeTable3)resultfrommerging2ormoreofthesepartitions.rRNA, n
lo
ribosomalRNA;tRNA,transferRNA. a
d
e
d
02) substitution models (general time-reversible [GTR]+(cid:0) from
ditionsusedinthisstudy Primers tPhe5’-AAAGCACRGCACTGAAGATGC-3’(Wiensetal.1999)12e5’-GTRCGCTTACCWTGTTACGACT-3’(Wiensetal.1999) 16aR25’-CCCGMCTGTTTACCAAAAACA-3’(Reeder2003)Reeder1995)16d5’-CTCCGGTCTGAACTCAGATCACGTAG-3’( LeuND45’-TGACTACCAAAAGCTCATGTAGAAGC-3’(Forstneretal.1995)Skinneretal.2005)M2465’-TTTTACTTGGATTTGCACCA-3’( ´ND45’-CACCTATGACTACCAAAAGCTCATGTAGAAGC-3’(Arevaloetal.1994)Skinner2007)M5415’-CCAGGGAAAGGAGTTAGC-3’((cid:12)ATPSf15’-CGTGAGGGHAAYGATTTHTACCATGAGATGAT-3’(Jarmanetal.20Skinner2007)G6135’-TCTGTCCATAAACTAGCG-3’( A,transferRNA. bepafifmptcaPpsocqbofbAIpmaiortuohlnbffeeyueahh7eoosMucraesmMA)absrsrddrneyaomLtpsthtmetrsmnSlaaeoalamtiebaionahotGostmrfiddc1lscnrniiciiendlyautegtastieedb0notTd.tstutolnlgaiuaerle6pinaaiitsnRtddopntdonlaneoarm2ottpatiido+fsanaaiwanhetogy0nrbafoyreisttllt5I)ntgewunreesasiPnnht+p.piMeriotatpmgnmashesG(cid:0)eieisinommnatccorutteotrne)rrooibeTueordnenu,tsbomaseodatsdheeflRoaem.snyadsefchaetevrteeaau,tee+dnpoinrseynTea7oelvftbrSgmudsIalaptoettathvllaot+eetyepl(alruiidnrnhwawyiaTtictfr,dto(cid:0)tmaslahtettaioaataaaiEnee2atfrdfainrosltogbrisobootidpasylsvRosidsnuiuneylaortlrngtt;huosaeneerenuglibaniilsieltaytoWmxcatssutanehsssrhe4lfahosnanlyesttnirr(o)oniesecaetiimfssousi,.snpfdotiyfhdgso.nsiodonumemnTattt(aiperp,vdmiire.rigspnttarhro,gn.huaeaieirprdelaemeaoTvtseneinynmererdyc.ehcmtdrpirnite,stdsglocotcfieimeimoeuoAiprataio(eiinnenAtehmicnmdastglsnnstaiaoBuogsdstiueaoetaneeeredixnotedesAevranmncsntlrcrsibstdnisiesl,auiemeg)rnyTStevt.nreslss.eangsiachaEgoaatoeagulpATnilmtadmrwbenntnsinliimaedrhpais(unnslmocddadisleocetniuraang1ehnrtynirCesdeooluuses6tl5ageeeu2igdiMhvenh,s)gtabgdsksb,aelpeaisfogc:unnemepydummhogrst3rioorlcberseaoprees1ySistlesaenmoodschmehlssrp)euosenstatteuddesuoaceieieeastuottottsebtsmieenrrosmgeeechhctduatersealelliidddddhhyeeeesssss------l,. https://academic.oup.com/sysbio/article-abstract/59/6/723/1711587 by guest on 09 April 2019
con NA- n RN uniform-rate model employed by Skinner et al. (2008),
ersandPCR RNA-Ser,tR (cid:12)bunitintro omalRNA;t iicbnnulegrwbatohettiitcwnhhdeeeefaopncreqawnuldlaisseridtntaitotaernnasd;tae2nsr)deaavnlouedrsnssdiefoiorfterrdmcating-tsrriaitatstin,eosrnmietssioop(dnceoecsltrairivreneeslwppyooh)nsoiscdcih---
T1.PrimABLE Gene(s) 12SrRNA 16SrRNA ND4,tRNA-His,t ATPsynthetasesu Note:rRNA,ribos fatewinootnardawwrpld.athars2riaacsd0nnh0dsta8hitn)thrr;ideooe3vnur)resegaravhtsoeeeufraonstmlrfeilafodotnirrnriseagmtiniettti-shrorviaaantecintsoqnenuoi(mnasnisgseooitidcidnscoetiuanlgtrthiweiteassiattsarh(essesecseopouceronamdnrdBeaesrrtdtmeaerdnaotridoadnfloteeeberldyes)-
726 SYSTEMATICBIOLOGY VOL.59
(cid:12)unitintron (cid:12)intron NA,transfer cPstoarmraTttiApetigaBoryLniEsion4ng.sPaMrtiotidoenlingstrategylnaLndnuclePoatirdaemseutebrsstitutionAmICodcel
hisstudy Partitions (cid:12)tRNAs,andND4;ATPsynthetasesubunitintron(cid:12)andtRNAs;ND4;ATPsynthetasesubunitintron(cid:12)andtRNAs;ND4,1stand2ndcodonpositions;ND4,3rdcodonposition;ATPsynthetasesubunitintronandtRNAs;ND4,1stcodonposition;ND4,2ndcodonposition;ND4,3rdcodonposition;ATPsynthetasesub(cid:12)tRNAs;ND4;ATPsynthetasesubunitintron(cid:12)tRNAs;ND4,1stand2ndcodonpositions;ND4,3rdcodonposition;ATPsynthetasesubunitintrontRNAs;ND4,1stcodonposition;ND4,2ndcodonposition;ND4,3rdcodonposition;ATPsynthetasesubunit partitions;strategieswiththesamenumberofpartitionsaredifferentiatedbyletters.rRNA,ribosomalRNA;tR pttPPPPPPPPNMsteaatcomdtat(o2orioihitafl12345567ntn0frrinmnoeacABfiatgeadl0ddtGvehgnvdtetrie2esecetoerustesaiigos)rtt:izrdidgnia,riexhyriteerAvateysiitcidstaevhPtrtooehqIoae(eete7Ceesgnlat.euasetxv)ceyrchtceaesscaetpr—iishlrspnqdinqa.ezmoroaatitAduyt(ruedtreenn2steGGGGGGGGGGGGGGGGeinaktaxetri0soedrhcsTTTTTTTTTTTTTTTTmtaoanyn0mco)anneeiiRRRRRRRRRRRRRRRR7.n;etkstcfndotb)thGi++++++++++++++++oieeodA.hi4otdtsdie(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)IIIIIIIIeaTdAhfini++++++++)eIini(noetRCteapag(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)esgipifacln+cooltooenxsiroo)hItsreevntanmm.a+mvfmahyflceg(cid:0)asAbbeoAs––––––––––––––––leaoetolrpeiossur4443433333333333eltsafnsdhdluyindrr0009099999999999ueftgsobalee,,,,,,,,,,,,,,,,bewaeseele4218085343974342mnBtezewdsciclvl8958301850958416svontertrwelct3204609326948063iiiernubcaeiiatrrayesn................eunav2685353994325782iholnu,sdnto;rg2305351445513115otnppeee,ifdte0709491217515080rwaorpalasorai7aodylensociinwnmtenlhtorasspnelmdiydddlpuzirai,osncectsiroeeupmemnnhteGatht5drrloicieattaotaeo)eetvaivcrtatdoolaidle11122233333444adaeliavelaninpndre2481480505622967f(fiylstlrsdeyrd.cedufe.om1laohai(tedi(vydeinAfhs9s2li.rraifioeos)fisdg8eo10ro.fcdtdcu,sed5f0a0srhfcpesupseem;oea(cid:0)c8ossieartlloftcmsl)8887877777877777Shr6rterpoelre0009099888099888rftdyeomihinamnir–rde,,,,,,,,,,,,,,,,abdtd9537160896050796liwbwaitreoltn7929048268575612soiw1eeoiedmptsr8957837463990686ttngsgn0artdaeaa................itiieea4372940457330692i(cid:0)rlmtirntbodttetfiy6106044539500802tilddhnoeegys4-f--l9283601125942733-t,, Downloaded from https://academic.oup.com/sysbio/article-abstract/59/6/723/1711587 by g
nt A,A,A,A,A;A;A; of Ifocussedonmodelswithorderedcharacterstatetransi- ue
edi RNRNRNRNRNRNRN ber tionswhenassessingtheeffectofenablingratevariation st o
rategiesevaluat Alldata12SrRNA,16Sr12SrRNA,16Sr12SrRNA,16Sr12SrRNA,16Sr12SrRNA;16Sr12SrRNA;16Sr12SrRNA;16Sr ndicatethenum ataitimboiePonosvonwtoeegvenbelrtyierinaaesaluclaydcgmoiehsmmste.rtmiienbroguodtgciaeohtnnaeerdooaifcuntsreatrrhtaesetsteafsoftoeuorrfttrahpallhnaebsnnirdtaoionfityncfphthpeicrsmoeibovnadobtlehuilles-- n 09 April 2019
st si phylogeny. As in recent models of molecular evolution
oning script iemtapll.e2m00e6n)t,inIgasasurmeleadxeadlomgnoolercmualalrdicsltorcibku(tDiornuomfmraotnesd,
rtiti sub although other distributions (e.g., the gamma distri-
pa gy bution) could also be employed. Applying a discrete
ve ate approximation approach analogous to that described
ernati ngstr bgyenYeiatny,gId(1i9v9id4e)dfothrismdoidsterliibnugtioamnionntgo-asisteerireasteofheeqteuraol--
Alt oni probability segments, or rate categories, and for each
3. ng rtiti branch in the phylogeny, summed transition probabili-
TABLE Partitionistrategy P1P2P3P4PA5PB5P6P7 Notes:PaRNA. tmciheaastrroaivxcetesrrpreastctaeiftyceasintbeggyotQhriee(ssm.eDeeaebnneoltotriwann)gs,iatthnioeinnosvrtaeatrneatslalnatmeraoonunssigtriaoatnlel
2010 SKINNER—RATEHETEROGENEITYANDLIMBEVOLUTIONINLERISTA 727
TABLE5. Modelsofphenotypicevolutionevaluatedinthisstudy
Model Characterstate Rates Parameters Constraints
transitions
Model1 Unordered Uniform (cid:11);(cid:12) Allparametersunconstrained
Model2 Ordered Uniform (cid:11);(cid:12) Allparametersunconstrained
Model3 Ordered Uniform (cid:11);(cid:12) (cid:11)setto(cid:24)0
Model4 Ordered Lognormallydistributed (cid:11);(cid:12);(cid:27) Allparametersunconstrained
Model5 Ordered Lognormallydistributed (cid:11);(cid:12);(cid:27) (cid:11)setto(cid:24)0
Note:(cid:11)—forwardtransitionrate(i.e.,therateofdigitacquisition);(cid:12)—reversetransitionrate(i.e.,therateofdigitloss);(cid:27)—standarddeviation
ofthelognormaldistributionofrates(wherethemeanofthisdistributionissetto1;seetext).
D
o
w
probabilitiesP(t)forabranchoflengthtaregivenby Goldberg and Igic 2008). Accordingly, this state was n
lo
assigned a prior probability of 1 for the third and fifth a
d
∑k models, in which the rate of digit acquisition is set to e
P(t)= 1k i=1 e(cid:0)riQt; eIfafescstuivmeelydzeeqruoa(lseperiaobropvero).bFaobrilitthieesrefomraainllinsgtamteosd(eslese, d from h
Pagel 1999). Model likelihoods were calculated using ttp
wrihisetrheekmisedthiaenarsastuemfoerdrnautemcbateergoofryrait,esccaalteedgosruicehs tahnadt Rva(lRueDsefvoerloapllmpeanrtamCoerteerTse(aim.e.,20th08o)s,easvsaulumeisngmoapxitmimiza-l s://ac
themeanofthediscretedistributionofratesisequalto ing the likelihood); code for the models incorporating ad
e
that of the continuous distribution, set to 1 (see Yang rate variation among branches is presented in the Sup- m
1994). The instantaneous rate matrix Q determines the plementary Material. As the models examined do not ic.o
relativeratesforeachkindofcharacterstatetransitionin composeanestedseries,modelcomparisonsweremade up
themodel,whichremainconstantacrossthephylogeny on the basis of the Akaike information criterion, modi- .co
m
(whereastheabsolutetransitionrates,obtainedfromthe fiedforsmallsamplesize(seeBurnhamandAnderson /s
y
matrices riQ, are permitted to differ among branches, 2002): sb
tthheeifroruartitohsaanrdenfioftth).mFoordtehles)m, odelsconsideredhere(i.e., AICc=(cid:0)2(lnL)+2p+ n2p(cid:0)(pp+(cid:0)11); io/artic
  le
(cid:0)(cid:11) (cid:11) 0 0 0 0 whereListhemaximizedlikelihood,pisthenumberof -a
b
 (cid:12) (cid:0)((cid:11)+(cid:12)) (cid:11) 0 0 0  estimable parameters, and n is the sample size, treated stra
  hereasthenumberofterminalnodesinthephylogeny c
Q= 0 (cid:12) (cid:0)((cid:11)+(cid:12)) (cid:11) 0 0 ; (seeO’Mearaetal.2006). t/59
 0 0 (cid:12) (cid:0)((cid:11)+(cid:12)) (cid:11) 0  As the number of rate categories k assumed in the /6/7
 0 0 0 (cid:12) (cid:0)((cid:11)+(cid:12)) (cid:11)  models permitting rate heterogeneity among branches 23
0 0 0 0 (cid:12) (cid:0)(cid:12) isincreased,thediscretedistributionofratesapproaches /171
the continuous lognormal distribution; however, in- 1
5
whererow(andcolumn)jcorrespondstoj(cid:0)1digitsand creasingly accurate representation of this continuous 87
distribution is offset by increasing computation time, b
(cid:11) and (cid:12) are rates of digit acquisition and loss, respec- y
placing a practical upper limit on the number of cate- g
tively.Theunconstrainedmodel(i.e.,thefourthmodel) u
e
has 3 estimable parameters, the transition rates (cid:11) and ganodrieesstsipmeactiefidedp.aAranmeextaemr vinaalutieosnaosfthmeondueml lbikeerliohforoadtes st o
(cid:12),andthestandarddeviationofthelognormaldistribu- n
categoriesisincreasedindicatesthatbotharerelatively 0
tionofrates((cid:27),wherethemeanofthisdistributionisset 9
stable when 28 or more categories are assumed (see A
to1;seeabove). p
AsPagel(1994)describedfortheuniform-ratemodel, Fig.1);thus,Iemployed30ratecategoriesforallanaly- ril 2
ses. 0
thelikelihoodoftheobservedcharacterstatesattheter- 1
Ancestral numbers of digits for the manus and pes 9
minalnodesofaphylogenycan becalculatedfromthe
wereinferredindependentlyforeachofthefivemodels.
transition probabilities for each branch using
Alternativestatesforinternalnodeswereevaluatedac-
Felsenstein’s (1981) pruning algorithm. For the models
cordingtotheratiooftheircontributionstothe“global”
incorporating rate heterogeneity among branches, the
likelihood for a model (see Schluter et al. 1997; Pagel
procedurediffersonlyinthatthetransitionprobabilities
areweightedsumsofvaluesderivedfrommultiplerate 1999); wherethisratioexceedede2 (i.e., 7.389), thelike-
matrices (i.e., the k matrices rQ), as opposed to values lihoods for two states were considered to differ signif-
i
derivedfromasingleratematrix.Inbothcases,asetof icantly (see Schluter et al. 1997). For each model, the
prior probabilities must be specified for the alternative set of states incorporating the maximum likelihood es-
states at the root node of the phylogeny (Pagel 1999; timateandallstatesonlyinsignificantlylesslikelythan
GoldbergandIgic2008).Theassumptionthatdigitloss thisestimatewasdeterminedforeachnode;ancestorre-
is irreversible implies that the most recent shared an- constructions for a pair of models were considered in-
cestorofthespeciesconsideredhereispentadactyl(see consistentwherethissetofstatesdisplayednooverlap.
728 SYSTEMATICBIOLOGY VOL.59
L.praepedita,L.stylis,andL.wilkinsi)orabsent(L.ameles
andL.apoda)aredistributedamongmultipledistantly-
related clades. The 4 subspecies of L. macropisthopus
(L.m.fusciceps,L.m.galea,L.m.macropisthopus,andL.m.
remota)composeapolyphyleticgroup,whereasL.areni-
cola is nested within a clade including the 3 subspecies
of L. microtis (L. m. intermedia, L. m. microtis, and L. m.
schwaneri),renderingthelatterspeciesparaphyletic.
Although the uniform-rate model assuming ordered
character state transitions and unconstrained rates of
digit acquisition and loss fits the data for the pes sig-
nificantly better than the uniform-rate model in which D
o
direct transitions are possible between all states, the w
n
latter model provides a substantially better fit for the loa
d
manus (Table 6). The uniform-rate model with ordered e
d
characterstatetransitionsandunconstrainedtransition fro
ratesprovidesabetterfittothedataforthemanusand m
pes than the constrained model in which the rate of http
digit acquisition is assumed to be effectively zero (i.e., s
the third model; Table 6). Permitting transition rates to ://a
c
a
vary among branches significantly improves model fit d
e
forboththemanusandthepes,withthemodelsincor- m
ic
porating heterogeneous transition rates yielding AICc .o
u
differences of 5.713–34.502 when compared with the p
.c
uniform-ratemodels(Table6).Therateofmanualdigit o
m
acquisition inferred for the model with unconstrained /s
y
transition rates (i.e., the fourth model) is close to zero, s
b
effectively prohibiting reversals of digit loss (Table 6). io
/a
Althoughrenderedequivalenttotheconstrainedmodel rtic
inthisrespect,theunconstrainedmodelassumesequal le
-a
priorprobabilitiesforalternativestatesattherootnode b
s
of the phylogeny (see Materials and Methods section). tra
As a result, the constrained model (in which the spec- ct/5
ified prior probabilities are consistent with irreversible 9
/6
digit loss) has a higher likelihood and provides a sig- /7
2
nificantly better fit to the data for the manus (Table 6). 3
/1
FIGURE 1. Relationships between the number of rate categories Themodelsallowingrateheterogeneityacrossthephy- 71
specified(k)and(a)modellikelihood(lnL)and(b)theinferredrateof logeny provide very similar fits to the data for the pes, 15
digitloss((cid:11))andstandarddeviationoftheratedistribution((cid:27)).These 8
withAIC scoresfortheunconstrainedandconstrained 7
plotsareforthemanusandweregeneratedassumingtheconstrained c b
modelsdifferingbyonly0.050(Table6). y
model,inwhichtherateofdigitacquisitionissettoeffectivelyzero g
(i.e.,thefifthmodel).Similarplotsareobtainedfortheunconstrained Ancestralcharacterstatesreconstructedforthemanus ue
modelandthepes. and pes assuming the uniform-rate model in which di- st o
rect transitions are permitted between all states are n
0
similar to the maximum likelihood states reported by 9
A
Skinner et al. (2008). There is no evidence for the reac- p
RESULTS quisition of manual digits, with maximum likelihood ril 2
0
Themaximumlikelihoodphylogenyinferredassum- ancestral states implying 23 instances of digit loss and 1
9
ing 7 partitions and the GTR+I+(cid:0) substitution model noinstancesinwhichdigitsaregained(seeSupplemen-
(see Figs. 2–8) is very similar to the phylogeny pre- tary Material). Ancestral states for the pes, by contrast,
sented by Skinner et al. (2008). A substantial propor- entail numerous instances of digit reacquisition; maxi-
tion of clades are strongly supported, with bootstrap mumlikelihoodestimatesofancestralnumbersofpedal
values for 41 of 82 internal nodes exceeding 90 (see digits imply 15 cases of digit loss, with 12 reversals
Supplementary Material). As with the phylogeny of to an increased number of digits (see Supplementary
Skinner et al. (2008), the species and subspecies pos- Material). The estimated rate of manual digit acquisi-
sessing pentadactyl limbs (L. arenicola, L. bougainvillii, tion for the uniform-rate model with ordered character
L.microtisintermedia, L.m.microtis, L.m.schwaneri, and statetransitionsissubstantiallyhigherthanthatforthe
L. viduata) compose 2 relatively remote clades, neither uniform-rate model permitting direct transitions be-
of which is positioned basally within Lerista. Similarly, tween all states (Table 6), altering the implied pattern
those species in which the limbs are greatly reduced of limb evolution considerably; maximum likelihood
(L. carpentariae, L. cinerea, L. humphriesi, L. karlschmidti, ancestral states entail 26 reductions in the number of
2010 SKINNER—RATEHETEROGENEITYANDLIMBEVOLUTIONINLERISTA 729
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FIGURE2. Ancestralcharacterstatesforthemanusreconstructedassumingtheuniform-ratemodelwithorderedcharacterstatetransitions.
Maximumlikelihoodstatesarepresentedadjacenttointernalnodes;whereapplicable,statesonlyinsignificantlylesslikelythanthemaximum
likelihoodstatearepresentedinparentheses.Modaldigitconfigurationsfollowspecieslabels.Branchesareshadedaccordingtothenumberof
digits.AcolorversionofthisfigureispresentedintheSupplementaryMaterial.
730 SYSTEMATICBIOLOGY VOL.59
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FIGURE 3. Ancestral character states for the manus reconstructed assuming the two models permitting rate heterogeneity among
branches (i.e., the fourth and fifth models). Maximum likelihood states are presented adjacent to internal nodes; where applicable, states
only insignificantly less likely than the maximum likelihood state are presented in parentheses. Modal digit configurations follow species
labels.Branchesareshadedaccordingtothenumberofdigits.AcolorversionofthisfigureispresentedintheSupplementaryMaterial.
2010 SKINNER—RATEHETEROGENEITYANDLIMBEVOLUTIONINLERISTA 731
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FIGURE4. Ancestralcharacterstatesforthepesreconstructedassumingtheuniform-ratemodelwithorderedcharacterstatetransitions.
Maximumlikelihoodstatesarepresentedadjacenttointernalnodes;whereapplicable,statesonlyinsignificantlylesslikelythanthemaximum
likelihoodstatearepresentedinparentheses.Modaldigitconfigurationsfollowspecieslabels.Branchesareshadedaccordingtothenumberof
digits.AcolorversionofthisfigureispresentedintheSupplementaryMaterial.
732 SYSTEMATICBIOLOGY VOL.59
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FIGURE5. Ancestralcharacterstatesforthepesreconstructedassumingtheconstrainedmodelpermittingrateheterogeneityamonglineages
(i.e.,thefifthmodel,inwhichtherateofdigitacquisitionissettoeffectivelyzero).Maximumlikelihoodstatesarepresentedadjacenttointernal
nodes; whereapplicable,statesonlyinsignificantlylesslikelythanthemaximumlikelihoodstatearepresentedinparentheses.Modaldigit
configurationsfollowspecieslabels.Branchesareshadedaccordingtothenumberofdigits.Acolorversionofthisfigureispresentedinthe
SupplementaryMaterial.