Weighted Ancestral Area Analysis and a Solution of the Redundant Distribution Problem

12 Pages·2003·0.2 MB·English

Syst.Biol.47(3): 445± 456,1998
Weighted Ancestral Area Analysis and a Solution of the Redundant
Distribution Problem
BERNHARD HAUSDORF
ZoologischesInstitut und ZoologischesMuseum der UniversitaÈtHamburg, Martin-Luther-King-Platz3,
D-20146 Hamburg, Germany; E-mail:hausdorf@ zoologie.uni-hamburg.de
Abstract.Ð A new cladistic method for the estimationof ancestral areas is based on reversible
parsimony in combination with a weighting scheme that weights steps in positionally plesio-
morphicbranchesmorehighly thanstepsinpositionally apomorphic branches.By applying this
method to cladograms of human mitochondrial DNA, the method is superior to previously
proposed algorithms.The methodis also anappropriate toolforthe solutionofthe redundant
distribution problem in area cladograms. Under the assumption of allopatric speciation, redun-
dant distributions, i.e., sympatry of sister groups, show that dispersal has occurred; thus, the D
o
ancestral area of at least one sister group was smaller than the combined distribution of its w
n
descendants.Withtheweightedancestralareaanalysis,theancestralareascanbecon® nedandat lo
a
leastsomedispersaleventscanbedistinguishedfrompossiblevicarianceevents.Asappliedtoa d
e
calnaadloygsirsa(massoufmthpetiPoonly0)patenrdidcaoem,wpoeingehnttedanaanlycesisstruanldaereraasasnuamlypstiisoinsss1upaenrdio2rt(NoeBlrsooonkasnpdaPrsliamtnoicnky, d from
1981, Systematics and biogeography: Cladistics and vicariance. Columbia Univ. Press, New h
York.) inresolving redundancies. The results ofthe weightedancestralarea analysis may di(cid:128)er ttp
fromtheresultsofdispersal-vicarianceanalysis,becausetherulesofdispersal-vicarianceanalysis ://s
y
indirectly favor the questionable assumption that the ancestral species occupiedonly one unit sb
io
area.[Ancestralarea;biogeography;dispersal;humanmtDNA;Polypteridae;redundant distribu- .o
x
tion;sympatry.] fo
rd
jo
u
Inthispaper,Ifocusontwo issuesofhistor- today, no ancestral area analysis is necessary. rna
ls
icalbiogeographythathavenotbeenlinkedto However, if the distribution of the ancestral .o
rg
eachotherthusfar:ancestralareaanalysisand speciesisassumedto besmallerthanthe com- b/
theredundant distributionprobleminareacla- binedareasofitsdescendants,amethodforthe y g
dograms. estimationoftheancestralareawouldbedesir- ue
s
Bremer (1992) was the ® rst to develop a able. Bremer (1992:440) justi® ed the assump- t o
n
procedureforestimatingancestralareasofindi- tion that the area of the ancestral species was N
o
vidualgroupsfromthetopologicalinformation smallerthanthe combinedareasofits descen- ve
m
in their area cladograms, using Camin± Sokal dantswiththehypothesis``thatthesizeofspe- b
e
(irreversible) parsimony. Ronquist (1994, ciesdistributionareaswasaboutthesameinthe r 8
1995) has shown that the results of Bremer’s pastastheyaretoday.’’Thishypothesisissimi- , 2
0
methodarenot alwaysinaccordance withthe lartothebasicassumptionofdispersalbiogeo- 16
assumption that positionally plesiomorphic graphy,namely,thateachgrouporiginatedina
areas in an area cladogram are more likely more orless small ancestralarea,the center of
partsoftheancestralareathanarepositionally origin,andthatthedistributionareashavesub-
apomorphic areas. Therefore, he proposed an sequently expandedbydispersal.Thisassump-
alternativemethodfortheestimationofances- tion was rejected by the school of vicariance
tralareasbyusing reversible parsimony.How- biogeography (e.g.,Croizatetal.,1974;Nelson
ever, Bremer (1995) demonstrated that Ron- and Platnick, 1981; Humphries and Parenti,
quist’s method also has some problems. The 1986).
results of Ronquist’s method are very indeci- However, in the same classical paper in
sive, and the di(cid:128)erence between the relative which Croizat et al. (1974:265) rejected ``the
probability values for alternative assignments Darwinian concept of center of origin and its
decreaseswith increasing tree size. corrollary,dispersalofspecies,asaconceptual
Ifone assumes that the ancestorofa group modelofgeneralapplicabilityinhistoricalbio-
occupied all areas settled by its descendants geography,’’they ``admit the reality ofdisper-
445
446 SYSTEMATIC BIOLOGY VOL. 47
salandspecify howexamplesofdispersalmay reverse Camin± Sokal parsimony. Comparing
berecognizedwithreferencebothtosympatry the number of necessary gains and losses
andto generalizedtracks.’’However,thesecri- under the two optimizations, respectively,
teriaarevalidonly ifoneassumesthatallopat- Bremer (1992) estimated which areas were
ric speciation is the predominant mode of most likely partsofthe ancestralarea.
speciation (Croizat et al., 1974). If sympatric In a critique of Bremer’s (1992) method,
speciation occurs,sympatry is not necessarily Ronquist (1994:269)stated,
evidence for dispersal. Nonetheless, allopatric
speciation is a basic assumption of vicariance Because Bremer’s method employs Camin-Sokal
biogeography andwill also be assumed in the (irreversible)parsimony inreconstructingancestral
following discussion. areas,itproducesmeaningfulresultsonlyifthepro-
Thus, from the beginning of the analytical cessisirreversible.Inotherwordswewouldhaveto
phase of biogeography, criteria have been assumethatdispersal(orrather,areashifts)always
available to indicate whether dispersal must occurredaway fromtheancestralarea. D
have beeninvolvedinthe origin ofadistribu- ow
n
tionpattern.Althoughthedistributionpatterns Ronquist (1994) proposed a method that lo
a
of most of the larger groups of organisms uses reversible parsimony for estimating the d
e
d
involve sympatry, PlatnickandNelson(1978) ancestral areas, to avoid the problems asso- fro
neglected the sympatry criterion fordispersal ciatedwithirreversible dispersal.Heestimated m
in their analytical method. Instead, they the probability that an area was the ancestral http
(Nelson and Platnick, 1981) introduced two areaby the numberofnecessary stepsSinthe ://s
assumptions to deal with sympatric occur- areacladogramunderthe assumptionthat the ys
b
rences(redundantdistributions),bothofwhich areawastheancestralarea.Themostprobable io
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ignorethe sympatry criterion.Sofar,thesym- ancestral area is the area that, given the tree, x
fo
patrycriterionhasnotbeenimplementedinany requires the minimum number of steps to rd
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analyticalmethod. explain the distribution of areas among term- u
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Inthefollowing,anewalgorithmforances- inaltaxa. a
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tralarea analysis is developedthat avoids the Unfortunately, the results produced by the .o
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drawbacksofbothBremer’s method andRon- methodproposedbyRonquist(1994)areoften b/
quist’s method.AsI will show,this methodis evenlessconsistentwiththeaboveassumption y g
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also anappropriatetoolforthe solutionofthe (i.e.,thattheprobabilityofanarea’sbeing part e
s
redundant distribution problem. With this oftheancestralareaincreaseswithitspresence t o
n
method, the ancestral areas of the individual in positionally plesiomorphic branches andits N
o
clades can be con® ned and at least some dis- general frequency in the area cladogram)than ve
m
persalevents canbe distinguishedfrompossi- those of Bremer’s method. The number of b
e
ble vicarianceevents. necessary steps S in an area cladogram under r 8
theassumptionthatagivenareawastheances- , 2
0
1
tralareadi(cid:128)ersforthe variousareasby two at 6
WEIGHTED ANCESTRAL AREA ANALYSIS
most (if two branches issue fromthe ancestral
Bremer(1992)coinedthetermancestralarea node; Ronquist, 1995). In the worst case, the
for the distribution area of the ancestor of a assumptionthatagiven areawasthe ancestral
monophyletic group. He described a cladistic area,althoughitisrepresentedinonlyoneora
procedurefortheestimationoftheprobability few positionally apomorphic branches, results
that parts of the recent distribution area of a in two additional steps, i.e., two loss steps in
group were part of the ancestral area. This the two primary sister groupsofthe analyzed
methodwasbasedonthe assumptionthat the taxon. It is a paradoxical scenario to assume
probabilityofanarea’sbeing partoftheances- that an area was the ancestral area of a taxon
tralareaincreaseswithitspresenceinposition- but was not the ancestralarea of either of the
ally plesiomorphic branches and its general twoprimarysistergroups.Afurtherproblemis
frequency in the area cladogram. Each area is thatthenumberofstepsSisdependent onthe
treatedasasinglecharacter,whichisoptimized sizeofacladogram(Bremer,1995).Toobtaina
onto thecladogrambyusing eitherforwardor measure ofthe relative probability forvarious
1998 HAUSDORFÐ WEIGHTED ANCESTRALAREA ANALYSIS 447
ancestralareahypotheses (RPvalue),Ronquist tion is 1/x, in which x is the number of inter-
(1994)invertedthenumberofstepsSandmul- nodes as counted from the common ancestor.
tipliedthemwiththesmallest Svalue.Because Thisfunctionwillbe appliedinthe following.
the number of steps S between the best Ifstepsinpositionallyapomorphicandposi-
hypothesis and the worst hypothesis is two tionally plesiomorphic branches are weighted
at most, the RP values will be much more di(cid:128)erently, then an optimization algorithm
similar for large cladograms with many steps must be chosen. Consider ® rst the calculation
than for small cladograms with few steps ofthegainsteps.Ifitismorelikely thatanarea
(Bremer, 1995). These problems are obvious was colonized once by an ancestor, andsome
in the examplesof the human mtDNA phylo- descendant lineages are no longer present in
genies (see below). that area because ofextinctionorthe subdivi-
In the method I propose (weighted ancestral sion of the ancestralarea by allopatric specia-
area analysis), a parsimony technique permit- tion (vicariance), the accelerated transfor-
ting reversible change between the states(i.e., mation optimization (Swo(cid:128)ord, 1993) has to D
theareas)isused,asrecommendedbyRonquist beused.If,onthe otherhand,it is more likely ow
n
(1994,1995).However,incontrasttoRonquist that anarea was colonized severaltimes inde- lo
a
(1994), the most probable reconstruction for pendently, then the delayed transformation d
e
d
the ancestor is not always the state that, optimizationis appropriate.Nowconsiderthe fro
given the tree, requires the minimum number calculationofthe loss steps.Ifit is more likely m
of steps to explain the distribution of states that a group is no longer present (because of http
among terminal taxa. Loss and gain steps extinctionorvicariance)inanareathatwaspart ://s
have opposite in¯uences on the calculation of oftheancestralarea,butsomesubgroupsofthe ys
b
the probability that an area was part of the group recolonized that area, then the acceler- io
.o
ancestralarea.A stepinwhichareaXisappar- ated transformation optimization has to be x
fo
entlyreplacedbyadi(cid:128)erentareadiminishesthe used. If, on the other hand, it is more likely rd
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probabilitythatareaXwaspartoftheancestral thatanareawaslostbyextinctionorvicariance u
rn
area. However, if area X is apparently recolo- several times independently, the delayed a
ls
nized by a subgroup of that branch, this step transformation optimization is appropriate. In .o
rg
increases the probability that this area was thefollowing,Ihaveusedtheacceleratedtrans- b/
actually part of the ancestral area. Therefore, formationoptimizationforallcalculations. All y g
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gain steps and loss steps concerning area X calculations were also done for the delayed e
s
are counted separately under the assumption transformation optimization(datanot shown), t o
n
that area X respectively was or was not the but in most examples examined so far, the N
o
ancestral area, similar to the case in Bremer’s choice of the optimization has had no e(cid:128)ect ve
m
(1992) method. An index to the probability onthe results, usually altering the valuesonly b
e
that area X was part of the ancestral area is slightly.Theonly exampleinwhichthechoice r 8
given by the quotient ofthe two values. of the optimization a(cid:128)ected the order of the , 2
0
1
An additional modi® cation is necessary to probability indices is the calculation of the 6
consider the assumption that ``[a]reas that are index of area A for clade 27 of the Polypter-
positionally plesiomorphic in the area clado- idae (see below), which is greater than the
gram are more likely parts of the ancestral indices of area B, C, and D in the calculation
area than are positionally apomorphic areas’’ with the accelerated transformation optimiza-
(Bremer,1992:440).Totakethisintoconsidera- tion, but lower than the indices of these
tion, the proposed methodincludes a weight- areas with the delayed transformationoptimi-
ing procedure that weights steps in the posi- zation.
tionally plesiomorphic branches more highly Tosumup,onecancalculateanindexforthe
than in the positionally apomorphic branches. probability that anindividual areawaspart of
Althoughvariousweighting schemes arepos- the ancestralareathroughthe following steps.
sible, it seems preferable to apply a concave
weighting function, which weights plesio- 1. Optimize area X (character X) on the tree,
morphic branches distinctly more highly than under the assumption that area X was not
apomorphic branches. A simple concave func- part of the ancestral area.
448 SYSTEMATIC BIOLOGY VOL. 47
2. Weight thestepsinthebranchesabovethe to the results of Bremer’s method, it is more
xinternodewith1/xandcountthenumber probable that area A was the ancestral area
of weighted gain steps (GSW). thanthat area B was.According to Ronquist’s
3. Optimize area X on the tree under the method,bothareaswere just as likely to have
assumption that area X was part of the beenpartoftheancestralarea.However,areaA
ancestral area. wouldhaveto becolonizedtwiceifit wasnot
4. Weight the steps as described and count the ancestralarea,whereas area B wouldhave
the number of weighted loss steps (LSW). to be colonizedonly once.Becauseofthe sec-
5. Repeat steps 1± 4 for every area. ond(positionally apomorphic)cladeoccurring
6. Calculatetheprobabilityindex,PI5 GSW/ inA,thenareaA wasmorelikely the ancestral
LSW, for every area. area.Theresultsofthethreealgorithmsforthe
cladogram depicted here in Figure 1b
Bremer (1992) has proposed to rescale the
(Ronquist, 1994; his Fig. 3) are shown in
G/LquotientsbydivisionwiththelargestG/L
quotient found for the cladogram (to a maxi- Table 1. Again, according to the weighted D
ancestralareaanalysis,incontrasttotheresults ow
mum value of 1). However, the size of the n
rescaledquotients(AA)dependsonthehighest ofBremer’s methodbutinaccordancewiththe loa
results of Ronquist’s method, area A is more d
G/L value of any area, whereas the actual ed
probability that anarea was part ofthe ances- likely part ofthe ancestralareathanisareaB. fro
m
tral area is not dependent on the probability h
that another area was part of the ancestral ttp
area.Moreover,theAAvaluecannotbecalcu- REAL EXAMPLE: GEOGRAPHIC ORIGIN OF ://sy
s
lated if the G/L value is in® nite, because all HUMAN MTDNA bio
membersofacladearerepresentedinthatarea. .o
Ialsohaveusedweightedancestralareaana- x
The delimitation of the areas can a(cid:128)ect the fo
lysis to reexamine the dataonthe geographic rd
results ofthe ancestralareaanalysis.Eacharea origin of human mitochondrial DNA jou
withadi(cid:128)erent combinationoftaxashouldbe (mtDNA).Bremer (1992)andRonquist (1994) rna
analyzed separately. Lumping together areas ls
have analyzed the phylogenetic trees of .o
wesittihmadti(cid:128)eetrheentdceogmrebeinoatfiosnysmopfattaryxaawndillhoevnecre- Vigilant et al. (1991) and Maddison et al. brg/
overestimatetheminimumnumberofdispersal (r1es9u9l2ts) owfitthhethmeierthmodetshoodfsB.reInmeTrab(1le9922),thoef y gue
events.Somecombiningofsmallareasmightbe st o
acceptable,butthee(cid:128)ectsofdi(cid:128)erentareadeli- n
N
mitationsshouldbecontrolled. o
v
It is possible to de® ne a thresholdPIvalue, em
b
below which an area is considered unlikely to e
have been part of the ancestral area. If it is r 8, 2
reasonable to suppose that a distribution area 01
6
is not larger thannareas,one canalso restrict
the numberofareasthat may havebeenoccu-
piedbyanyancestralspeciestothenareaswith
the highest PIvalues.
FIGURE1. Hypotheticalareacladogramsfordemon-
strating the di(cid:128)erentresults of various methodsfor re-
HYPOTHETICAL EXAMPLES constructing ancestralareas.(a)Example fromRonquist
This algorithm has been applied to the (1994;hisFig.2):WhereasBremer’smethodindicatesthat
BismorelikelythanAtobetheancestralarea,Ronquist’s
examples of Ronquist (1994) in which Bre-
methodestimatesthatbothareasareequallylikelytobe
mer’s method is not consistent with his the ancestralarea,andweightedancestral area analysis
assumptions. The results of the three algo- indicatesthatA ismorelikely thanBto betheancestral
rithms for the cladogram depicted here in area(seeTable1).(b)ExamplefromRonquist(1994;his
Fig.3):WhereasBremer’smethodindicatesthatBismore
Figure 1a (Ronquist, 1994; his Fig. 2) are
likelythanAtobetheancestralarea,Ronquist’smethod
shown in Table 1. According to the results of
andweightedancestralareaanalysisproducetheopposite
weightedancestralareaanalysis,butincontrast result(seeTable1).
1998 HAUSDORFÐ WEIGHTED ANCESTRALAREA ANALYSIS 449
TABLE 1. Estimation of the ancestral area for the cladograms depicted in Figure 1 by the methods of Bremer
(1992)andRonquist (1994)andweightedancestralareaanalysis (WAAA). G 5 numberof necessary gains under
forward Camin± Sokal parsimony; L5 number of necessary losses under reverse Camin± Sokal parsimony;
S5 numberof necessary steps if the area was the ancestralarea; RP5 S values rescaledto amaximumvalue of
1 by inverting them and multiplying by the smallest S value; GSW 5 number of weighted gain steps;
LSW 5 numberof weightedloss steps; PI5 GSW/LSW.
Bremer Ronquist WAAA
Area G L G/L S RP GSW LSW PI
CladogramFigure 1a
A 2 4 0.50 2 1.00 1.20 1.00 1.20
B 4 2 2.00 2 1.00 1.00 1.20 0.83
CladogramFigure 1b
A 3 4 0.75 2 1.00 1.67 0.50 3.34
B 4 3 1.33 3 0.67 0.50 1.67 0.30 D
o
w
n
lo
Ronquist(1994),andoftheweightedancestral not consistent with the assumption that the a
d
e
areaanalysisare compiled. probabilityofanarea’sbeing partoftheances- d
Concerning thetreeofVigilantetal.(1991), tralareaincreaseswithitspresenceinposition- fro
m
all three methods agree that Africa is most ally plesiomorphic branches and its general h
likely part of the ancestral area. However, in frequency inthe areacladogram. ttp
contrast to the results of Bremer’s method Forthe tree of Maddison et al.(1992; their ://sy
s
andthe weightedancestralareaanalysis,Ron- Fig. 4), the results of the three methods di(cid:128)er bio
quist (1994)concludedthat theotherareasare considerably. Bremer’s method suggests that .o
x
almost equally likely parts of the ancestral Europe andAfrica are most likely parts of the fo
rd
area.The14deepestbranchesinthecladogram ancestralarea,andRonquist’smethodsuggests jo
u
of Vigilant et al. (1991) lead exclusively to thatAsiaandNewGuineaaremostlikely parts rn
a
African mtDNA types. mtDNA types from ofthe ancestralareaÐ althoughthe RPvalues ls.o
otherareasarerepresentedonlyinpositionally ofallareasare very similar. The weighted an- rg
apomorphic branches. For example, only one cestralareaanalysissuggeststhatNewGuinea by/
g
positionally apomorphic branch leads to an is most likely part of the ancestral area, fol- u
e
Australian mtDNA type. Ronquist’s (1994) lowed by Asia. The outcome of the weighted st o
conclusion that Australia is almost equally as ancestral area analysis re¯ects the data that n N
likely asAfricatobepartoftheancestralareais one of the primary branches in the cladogram ov
e
m
b
e
TABLE2. EstimationoftheancestralareaforhumansbasedonmtDNA cladogramsofVigilantetal.(1991)and r 8
Maddisonet al.(1992: theirFig.4)by themethodsofBremer(1992)andRonquist (1994)andweightedancestral , 2
area analysis (WAAA). Abbreviationsas in Table 1. 01
6
Bremer Ronquist WAAA
Area G L G/L S RP GSW LSW PI
Vigilant et al.(1991)
Africa 31 24 1.29 25 1.00 2.33 0.38 6.13
Europe 14 36 0.39 27 0.93 0.55 2.00 0.28
Asia 18 52 0.35 27 0.93 0.64 2.21 0.29
New Guinea 12 39 0.31 27 0.93 0.34 2.00 0.17
Australia 1 17 0.06 27 0.93 0.08 2.00 0.04
Maddisonetal.(1992;theirFig.4)
Africa 18 26 0.69 29 0.97 0.98 2.42 0.40
Europe 12 17 0.71 29 0.97 0.74 2.26 0.33
Asia 20 32 0.63 28 1.00 1.87 1.71 1.09
New Guinea 9 23 0.39 28 1.00 1.48 1.15 1.29
Australia 1 12 0.08 29 0.97 0.09 2.00 0.05
450 SYSTEMATIC BIOLOGY VOL. 47
of Maddison et al.(1992) consists exclusively they are today.’’ This hypothesis was also ac-
of mtDNA types from New Guinea and that ceptedbyRonquist(1994).Onecouldobjectto
thetwo deepest branchesofthe otherprimary this hypothesis on the basis that in former
branch lead to Asian mtDNA types; the two times,atleastonland,fewerspecieswerepres-
following branches also lead mainly to Asian ent and, hence, the biotic environment was
mtDNA types.Onthe other hand, the results more equal over the globe and interspeci® c
of Ronquist’s method are again not in accor- competition was less sti(cid:128). Consequently, spe-
dancewiththe abovestatedassumption.Con- ciesmighthaveoccupieddistinctly largergeo-
sider, for example, Australia: It is represented graphicranges thanthey do today.
only by one positionally apomorphic branch Preliminarily, we may accept the null hy-
and therefore the probability that this area pothesis of vicariance biogeography, namely,
was part of the ancestral area should be dis- that the area occupied by the ancestor of a
tinctly lower than that of the other areas. group is equivalent to the combined distribu-
Ronquist (pers. comm.) stressed that in this tion of its descendants. However, if this hy- D
example it is impossible for any area to have pothesis results in an overlap of the ancestral ow
n
anRPvaluelessthan0.97andthattheRPvalue areas of sister groups, the sympatry indicates lo
a
is not a probability, but only an index to the thatdispersalhashappenedandthattheareaof d
e
d
probability.However,thisexampleshowsthat atleastoneoftheancestralspeciesofthesister fro
RP is an inferior index in comparison to PI, groupswassmallerthanthecombineddistribu- m
becauseit doesnot indicatethedi(cid:128)erences be- tionofitsdescendants. http
tweenthe probabilitiesofthe hypotheses that Inthiscase,weightedancestralareaanalysis ://s
Asia and that New Guinea were parts of the is an appropriate tool for examining which ys
b
ancestral area (the same is true for Africa, areas were occupied by the ancestral species io
.o
Europe, and Australia). The result of Bremer’s ofeachsistergroupandwhichareaswerecolo- x
fo
method appears to be inconsistent with his nizedsecondarily by the two groups.The fol- rd
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assumption. Although one of the primary lowing procedure can be used to investigate u
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branches leads exclusively to mtDNA types vicariance-dispersalscenarios: a
ls
from New Guinea, the G/L value for New .o
rg
GuineaisdistinctlysmallerthantheG/Lvalues 1. Calculate for each of the primary sister b/
forAfrica,Europe,andAsia.TheG/Lvaluefor groups the PI for every area. y g
u
Asiaislowerthanthe G/LvalueforEuropeor 2. Compare the PI values for each individual e
s
Africa, although the four deepest branches of area. Each individual area was more likely t o
n
theotherprimary branchleadmainly to Asian part of the ancestral area of that sister N
o
mtDNA types. group for which it has the higher PI ve
m
value. Regions that were not part of the b
e
ancestral area of a clade must have been r 8
WHY AND HOW TO APPLY WEIGHTED colonized secondarily by some members , 2
0
ANCESTRAL AREA ANALYSIS of that clade. If the PI values for an area 16
The examples above show that weighted are similar in the two sister groups, the
ancestral area analysis avoids the drawbacks determination is ambiguous as to which
of Bremer’s method as well as those of ancestral area that area was a part of. This
Ronquist’s method. Consequently, this algo- may be due to an allopatric speciation
rithmisasuitableanalyticaltoolfortheestima- within that area. In that case, parts of that
tion of ancestral areas. However, why should areamight have been partsofthe ancestral
we assume that the ancestral area was smaller area of both sister groups. Or, it may also
than the present area? As Bremer (1992:440) be due to sympatric speciation.
stated,``We may ofcourse accept the null hy- 3. Repeat steps1 and2 forallsistergroupsin
pothesis of vicariance biogeography, i.e., the thecladogram.By thisproceduretheances-
ancestral area was equivalent to the present tral areas of the individual clades can be
area.’’ Bremer (1992:440)proposedanalterna- con® nedandatleast some dispersalevents
tivehypothesis,``thatthesizeofspeciesdistri- can be distinguished from possible vicar-
butionareaswasabout the sameinthe past as iance events.
1998 HAUSDORFÐ WEIGHTED ANCESTRALAREA ANALYSIS 451
AproblemwiththisapproachisthatthePIis cladesarelistedinTable3.Theancestralareas
in® nite forall areas of terminal branches. This ofthecladesarecon® nedbyusingthesevalues
mayresultinanoverestimationoftheancestral asdescribedandare shown in Figure 2.Iftwo
areaofwidespreadterminaltaxaandanunder- sistergroupshavethesamePIvalueforanarea,
estimation of the ancestral area of their sister this area is listed for both groups in paren-
groups. One way possibly to solve this pro- theses. This canmean that either the area was
blemis to constrain the ancestraldistributions occupiedbyonly oneofthetwoancestralspe-
to containmaximally xareas. ciesorthatpartsofthat areawere partsofthe
The idea of the described procedure has ancestralareaofbothsistergroups.Sympatric
already beenused in a study ofthe Dyakiidae speciation within that area is also a possible
(Gastropoda) (Hausdorf, 1996). However, in interpretation. Areas with a PIvalue less than
that study the algorithm of Bremer (1992) 0.2 areincludedin square brackets.
wasappliedforthe ancestralareaanalysis. Consider, for example, the two primary
Asanexamplefortheproposedprocedure,I sister groups,clade 18 andclade 26.The geo- D
willanalyzethephylogenyofthePolypteridae, graphicalrangeofclade18includestheareasA, ow
n
based on the analysis by Platnick and Nelson B,C,D,andII;thegeographicalrangeofclade lo
a
(1984)(Fig.2).The PIvaluesofallareasforall 26 includes the areasA, B,C,D,I,andII.The d
e
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1
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FIGURE2. CladogramofthePolypteridae(speciesPC± PA)andtheirdistributionareas(A,Guinea;B,NigerRiver;C,
LakeTchad;D,Nile;I,coastalregionfromNigerdeltatoChiloango;II,CongoBasintoLakeTanganyka)(afterPlatnick
andNelson,1984;theirFig.3left).Abovethebranches,theancestralareasinferredbycomparisonofthePIvalues(see
Table3andtext)arenoted.
452 SYSTEMATIC BIOLOGY VOL. 47
TABLE3. PI values ofthe clades ofthe Polypteridae based on the cladogram in Figure 2.
Clade
Area 15 16 17 18 19 20 21 22 23 24 25 26 27
I 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.33 0.17 0.13 0.10 0.08
II 1.00 0.00 1.00 1.00 1.00 ¥ 3.00 1.00 3.00 3.00 4.00 0.71 0.78
A 0.00 1.00 0.33 0.17 1.00 ¥ 3.00 0.00 0.00 0.75 0.29 1.11 0.60
B 1.00 1.00 0.33 0.55 1.00 0.00 0.33 0.00 0.00 0.17 0.13 0.10 0.38
C 1.00 1.00 0.33 0.55 1.00 0.00 0.33 0.00 0.00 0.17 0.13 0.10 0.38
D 1.00 1.00 0.33 0.55 1.00 0.00 0.33 0.00 0.00 0.17 0.13 0.10 0.38
geographicalranges of the two primary sister ® shes by utilizing Brooks parsimony analysis
groupswidely overlap,andthenullhypothesis (Wiley,1988;Brooks,1990).Whereasthe ® rst
ofvicariancebiogeographymustberejected.It vicarianceevent inthehistory ofthepolypter- D
is more probablethat the areas II,B,C,andD idswasprobablybetweenareaII1 B1 C1 D ow
n
were part of the ancestral area of clade 18, andareaA(plusperhaps,althoughimprobably, lo
a
becausethe PIvaluesofthese areasarehigher area I) according to the weighted ancestral d
e
d
forclade18thanforclade26,whereasitismore area analysis (Fig. 2), the primary vicariance fro
probablethattheareasAandIwerepartofthe event was between area I and areas II1 m
ancestral area of clade 26. However, the PI A1 B1 C 1 D, according to the general http
value of area I for clade 26 is very small and, area cladogram (Fig. 3a) constructed with ://s
therefore, one might question whether this Brooks parsimony analysis.However, areaIis ys
b
area was actually part of the ancestral area of inhabited by one terminal species only and io
.o
clade 26 (although this possibility cannot be therefore it is very unlikely that there was a x
fo
excludedbytheavailabledata).IfaPIthreshold primary vicariance event between area I and rd
jo
valuewere® xed,e.g.,at0.2,areaIwouldnotbe areas II1 A1 B1 C 1 D. This result is an u
rn
consideredpartoftheancestralareaofclade26. artifact caused by the rooting with an hypo- a
ls
If sound paleogeographical data are available, thetical outgroupÐ in which no member of .o
rg
they might also be used to estimate the like- theexaminedgroupispresentandwhichthere- b/
lihood that an area was part of the ancestral fore clusters with area I in which only one y g
u
area a posteriori. Both area A, the probable species is present. e
s
ancestral area of clade 26, and area I are part Onthe basis ofthe same data,Platnickand t o
n
oftheAfricancraton;theywerethereforeinthe Nelson(1984)alsopreparedageneralareacla- N
o
samerelative position,atleastintheCenozoic dogram for the polypterid ® shes, using com- ve
m
andthe Mesozoic.Bothareasarewidely sepa- ponent analysis, assumption 1 (Nelson and b
e
rated, and area B, which was not part of the Platnick,1981).Incontrast to the result ofthe r 8
ancestral area of clade 26, is intercalated weighted ancestral area analysis (Fig. 2), the , 2
0
1
betweenthem.Therefore,itisveryimprobable primary vicariance event was between areas 6
thatareaIwaspartoftheancestralareaofclade I1 IIandareasA 1 B1 C 1 D,according to
26.Nevertheless, one shouldbearin mindthe the general area cladogram of Platnick and
possibilityofarelationshipofareasAandI.Ifa Nelson (1984) (Fig. 3b). However, the com-
similar disjunction is found in many groups, bined area I1 IIis inhabited by one position-
this might haveageneralcause.But ifthe dis- ally apomorphicgrouponly andtherefore itis
junction remains an individual case,it is more very unlikely that there was a primary vicar-
probably attributable to dispersal than to an iance event between areas I1 II and areas
unknowntectonic plate event. A1 B1 C 1 D.
Because Brooks parsimony analysis and
component analysis assume a single general
WEIGHTED ANCESTRAL AREA ANALYSIS IN THE
patternofarearelationshipsanddonotinclude
FRAMEWORK OF CLADISTIC BIOGEOGRAPHY
thepossibilityofdispersals,thestructureofthe
Using the same data, one can construct a general area cladograms generated with these
general area cladogram for the polypterid methodsisalreadystronglyconstrainedbythe
1998 HAUSDORFÐ WEIGHTED ANCESTRALAREA ANALYSIS 453
scenario (Fig. 4b), one must assume that the
stem species 1 speciated in the area ABC. As
aresult ofthe allopatricspeciation,eachofthe
two species2 and8 originally occupiedonly a
restrictedrangewithintheareaABC.However,
before the next speciations happened, both
species hadto colonize the range of the other
species. Thus, this scenario requires two addi-
tionaldispersalevents.Furthermore,itrequires
FIGURE3. Generalareacladogramderivedfrom the two additionalextinctionevents(ofspecies10
cladogramofthePolypteridae(Fig.2)byusing(a)Brooks
and11).
parsimony analysis (assumption 0) and (b) component
analysis,assumption1 (afterPlatnickandNelson,1984; Under their assumption 2, Nelson and
theirFig.3 right). Platnick (1981:432) proposed, ``that whatever
istrueoftheoneoccurrencemight notbetrue D
® rst vicariance event in the tree. Therefore, a ofthe otheroccurrence.’’Thus,one ofthetwo ow
n
comparison of the following nodes in those occurrencesofspeciesinareaCisconsideredan lo
a
general area cladograms with the vicariance- item of errorandis deleted. This results in two d
e
d
dispersal scenario constructed by weighted di(cid:128)erent area cladograms (Figs. 4c, 4d). The fro
ancestralareaanalysisis not meaningful. cladogram in Figure 4c implies that species 2 m
The operation of component analysis con- was present in area ABC and that the species http
cerningredundantdistributions(morethanone 5, 6, and 7 originated by vicariance events. ://s
member of a clade in the same area)has to be However, it is unclear where species 4 origi- ys
b
examined more closely. Nelson and Platnick nated. Although endemic to area C, species 4 io
.o
(1981)haveproposedtwoalternativesolutions could not have originated there because this x
fo
of redundancy. These solutions will be dis- areawasoccupiedbyspecies2.Fortheassump- rd
cussed on the basis of the cladogram in Fig- tionthatspecies4originatedelsewhere(inarea jou
rn
ure 4a (Page, 1988). For the generation of a X), two additional ad hoc hypotheses would a
ls
pattern with three separate areas, two vicar- be necessary: (1)Species4 is assumed to have .o
rg
iance or dispersal events are necessary in any dispersedfromareaXtoareaC,and(2)species b/
case.Foreachsolutionof the redundancy, the 4 isassumedto havebecomeextinct inareaX. y g
u
necessary additionaladhochypotheseswillbe ThecladograminFigure4dimpliesthatspecies e
s
investigated. In the following, all speciations 1 split into species4 inareaC andspecies 2 in t o
n
areassumedto beallopatric. area AB.This scenario requires that area C be N
o
Under their assumption 1, Nelson and colonizedby species 2,3,or7. ve
m
Platnick (1981:421) proposed ``that whatever Applying weighted ancestral area analysis b
e
is true of the one occurrence is true of the to the cladogram in Figure 4a suggests that r 8
other occurrence.’’ To explain the resulting species 4 originatedinareaC (thePIvaluefor , 2
0
1
6
FIGURE4. Interpretingredundantdistributions.(a)A four-taxoncladogram,withtwotaxaoccurringinthesame
area.(b)Theinterpretationunderassumption1.(c)and(d)Thetwoalternativeinterpretationsunderassumption2(after
Page,1988;hisFig.5).
454 SYSTEMATIC BIOLOGY VOL. 47
thatareaisin® nite).ThePIvaluesforspecies2 binedareasofitsdescendants.Using weighted
are 1.0 forarea A and 0.33 forareas B andC. ancestral area analysis allows the ancestral
Because the PI value of area C is higher for areas to be con® ned. Neither component nor
species 4, the original range of species 2 in- Brooksparsimonyanalysisnoranyotheravail-
cludedonly the areasA andB.Like the clado- able method for the construction of general
gram in Figure 4d, the result of the weighted area cladograms can resolve the redundant
ancestral area analysis implies that area C has areaproblem,becausethey ignore the sympa-
beencolonizedeither by species2,3,or7. try criterionandthey do not use the informa-
The result of the weighted ancestral area tionabouttheancestralareasinthecladogram.
analysis requires only one additional ad hoc Component methods treat all components
hypothesistoexplaintheredundancy,whereas equally, although it can be inferred from the
under assumption 1 of Nelson and Platnick cladogramwhichgroupsofareasareprobably
(1981) four additional ad hoc hypotheses are nottheresultofvicarianceeventsbutratherof
necessary. The outcome of one of the two dispersal events. Brooks parsimony analysis D
cladograms generated under assumption 2 of does not take into account that the character ow
n
Nelson and Platnick (1981) is identical to the statesofcertaincharactersarenotindependent; lo
a
result of the weighted ancestral area analysis, i.e.,ifacladewasoriginally present inanarea, d
e
d
whereas the other cladogram requires two its sister group must have been originally fro
additional ad hoc hypotheses. Their assump- absent inthat area. m
tion 2 does not distinguish between the two http
calraedaoagnraalmyssi.sCiosnssuepqeureionrtlyto,wbeoitghhtaesdsuamncpetsiotrnasl DISPERSAL-VICARIANCE ANALYSIS AND ://sys
of Nelson and Platnick (1981) in resolving WEIGHTED ANCESTRAL AREA ANALYSIS bio
.o
redundancies. Afterthe present paperhadbeensubmitted x
fo
There is no information in the initial clado- for publication, Ronquist (1997) proposed a rd
jo
gram (Fig. 4a)orthe ancestralarea cladogram newmethodforthereconstructionofancestral u
rn
(Fig.4d)thatindicateswhetherareaChasbeen distributionsandtheanalysisofvicariance-dis- a
ls
colonized by species 2, 3 or 7. However, this persal scenarios: dispersal-vicariance analysis .o
rg
questionmight tentatively besolvedifawell- (see also Ronquist,1996). b/
corroborated general area cladogram is avail- There is a minor di(cid:128)erence between the y g
u
able. If there is a component BC or ABC in a ancestraldistributions calculatedby dispersal- e
s
generalareacladogram,itisprobablethatarea vicariance analysis and by comparison of PI t o
n
C wascolonizedby species3 or2. values.Whereasthedistributionofanancestral N
o
Brooks (1990) suggested recoding redun- species immediately after its origin is inferred ve
m
dant areas as di(cid:128)erent areas a posteriori and by comparing the PI values, dispersal-vicar- b
e
deciding which of the recoded areas are mis- iance analysis gives the distribution of the r 8
placedintheareacladogrambycomparingthe ancestral species immediately before the next , 2
0
1
biogeographicalareacladogramwithageolog- speciation. Therefore, the results of the two 6
ical hypothesis. This procedure results in an methods should di(cid:128)er, if the ancestral species
adjustment ofthebiogeographicalhypotheses dispersed into additional areas afterits origin.
to current geological hypotheses. However, Thedistributionoftheancestralspeciesimme-
most biogeographers aim at the formulation diately before the next speciation can also be
of independent hypotheses of area relation- inferredfromtheresultsofthecomparisonofPI
ships, basedonly on the biogeographicaldata values by summing the ancestral areas of the
(e.g.,Humphries andParenti,1986). twodescendantspeciesoftheancestralspecies.
Under the assumption of allopatric specia- More important is that the results of the
tion, redundant distributions in a cladogram, two methods may di(cid:128)er because of di(cid:128)erent
or in other words, sympatry of sister groups, assumptions.Thecriticalassumptionofdisper-
isthecorollaryofdispersal(Croizatetal.,1974; sal-vicariance analysis is that allopatric spec-
Platnick and Nelson, 1978). That means that iationwithinasingle unit areaandthe follow-
the areaofatleast one ofthe ancestralspecies ing dispersal within that unit area costs zero,
ofthe sistergroupswassmallerthanthe com- whereasotherwise dispersalcostsone perunit