VOLUME 72, No. 1 THE QUARTERLY REVIEW OF BIOLOGY MARCH 1997

INFERRING EVOLUTIONARY PROCESS FROM SHAPE

ARNE 0. MOOERS Departmentof Zoology, Universityof British Columbia 6270 UniversityBoulevard, Vancouver, V6T 1Z4 Canada

STEPHEN B. HEARD Departmentof Biological Sciences, Universityof Iowa 138 BiologyBuilding, Iowa City,Iowa 52242-1324 USA

ABSTRACT Inferencesabout macroevolutionary processes have traditionallydepended solely on thefossil record,but such inferencescan bestrengthened by also consideringthe shapes of the phylogenetic treesthat link extant taxa. The realizationthat phylogenies reflect macroevolutionary processes has led to a growingliterature of theoretical and comparativestudies of tree shape. Two aspects oftree shape are particularly important: tree balance and thedistribution of branch lengths. We examineand evaluaterecent developments in and connectionsbetween these two aspects, and suggestdirections forfuture research. Studiesof tree shape promise useful and powerfultests of macroevolutionary hypotheses. With appropriatefurther research, tree shape may help us detectmass and adaptiveradia- tions,measure continuous variation in speciationand extinctionrates, and associatechanges in theserates with ecological or biogeographical causes. The usefulnessof treeshape extendswell beyondthe study of .We discuss applicationsto otherareas ofbiology, including , phylogenetic inference, population biology,and developmentalbiology.

INTRODUCTION Why are there so many species of passerine HERE IS probably no greater nor more birds (e.g., Raikow1986; Kochmer and Wagner T 1988) or beetles (e.g., Evans 1975)?J B S Hal- fundamental problem in ecology and dane's famous quip about God's inordinate evolutionarybiology than explaining the di- fondnessfor beetles can onlybe partof the story. versityof life on Earth. A comprehensive ex- Questions about the relativediversity of evo- planation of this diversityshould account for lutionarygroups are often posed in termsof not onlythe regulation of diversity in extanteco- taxonomies (see literaturereviewed byAnder- logical communities (Ricklefs and Schluter son 1974). Ultimately, however, these are 1993), but also provide an understanding of questions aboutvariationin and ex- what factorshave determined historical pat- tinction rates, and their signatures in the terns of diversificationamong evolutionary shapes of phylogenetic trees. The recent ex- groups. This latterquestion is a familiarone: plosion in the availabilityof phylogeneticdata

The QuarterlyReview of Bzology, March 1997, Vol. 72, No. 1 Copyright? 1997 by The Universityof Chicago. All rightsreserved. 0033-5770/97/7201-0002$1 .00

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(fueled in part by the molecular revolution) 450' has given us a new and powerfulapproach for Leaf beetles studyingtempo and mode in :phylo- 350 - genetic trees as historiesof the diversification of . The availabilityof these data has in turn led to dramatic growthin the study of , 250- phylogenetictree shape, whichprovides a pos- sible new approach to the studyof evolution and diversification(there are other applica- g 150- tions of tree shape, but we touch on them only z briefly).The time is ripe for an appraisal of the power and prospects of the studyof tree 50 shape. Here we outline the historybehind the use of tree shape, provide some necessary 00 10 20 30 40 50 60 70 80 90 100 technical background, and consider current Numberof speciesper genus descriptionsof and proposed explanations for FIGURE 1. A HOLLOW CURVE DISTRIBUTION OF the shapes we observe.We then conclude with THE NUMBER OF GENERA CONTAINING suggestionsfor future study. VARIOUS NUMBERS OF SPECIES OF LEAF BEETLE (CHRYSOMELIDAE). HISTORICAL SKETCH Data fromWilliams (1964, Table 50). Branching diagrams were considered fit- ting representations of organismal affinities long before Darwin (Panchen 1992). How- (Fisher et al. 1943), or log-normalseries (Wil- ever, Darwin is usually recognized as the first liams 1964), and saw in them the stamp of de- to consider trees explicitlyas representations terministicprocesses (Williams 1964; Ander- ofactual genealogies ofspecies, and his theory son 1974). Walters (1961; see also Cronk of gave him definiteideas as 1989) considered them merelypsychohistori- to theirshape (Darwin 1859:110). Faced with cal artifacts.Yule (1924) and Wright (1941) limited data, however, Darwin turned to pointed to a stochasticor probabilisticexpla- taxonomies instead of phylogenies for evi- nation for the hollow curve pattern.Ecologi- dence to support his hypotheses (Darwin cal theory-e.g., MacArthur's(1957) "broken- 1859:110). The use of taxonomies as reflec- stick" model of ecological diversity,which is tions of phylogeneticpattern continues up to also probabilistic-was adapted to explain the present. hollow curves,most prominentlybyAnderson Willis (1922) noted the concave shape of (1974). Recent investigatorshave even de- many frequency distributionsof taxonomic scribed the hollow curves in terms of fractal units containingvarious numbers of subunits geometry(Burlando 1990; Minelli et al. 1991; (e.g., species per genus), when units are or- see also Nee et al. 1992). Information-rich,rig- dered fromthose withthe greatestnumber to orous phylogenies have now largelyreplaced those withfewest subunits, and called this the the use of taxonomic listsin the studyof mac- "hollow curve"distribution. For example, Fig- roevolution (but see exceptions in Dial and ure 1 shows the sizes of chrysomelidbeetle Marzluff1989; Ricklefsand Renner 1994; Tiff- genera (from Williams 1964; based on data ney and Mazer 1995). collected by Willis). It plots the number of The modern study of phylogenetic tree chrysomelidbeetle genera withvarying num- shape and macroevolution can be traced to a bers of species. The hollow curve phenome- set of meetingsof paleontologistsand popula- non is familiarto anyone who has noticed the tion biologists at Woods Hole in the early conspicuous abundance of,for example, bee- 1970s (Raup et al. 1973; Gould et al. 1977; tles among insects,passerines among birds,or Schopf 1979), and to a biogeographic study teleostsamong fish. (Rosen 1978; Simberloffet al. 1981; Simber- Earlyauthors described these hollow curves loff1987). Both setsof investigatorswere seek- as hyperbolic(Chamberlin 1924), logarithmic ing falsifiablehypotheses of phylogenetictree

This content downloaded from 131.202.42.30 on Fri, 26 Apr 2013 09:59:50 AM All use subject to JSTOR Terms and Conditions MARCH 1997 PHYLOGENETIC TREE SHAPE 33 shape. The "Woods Hole group" (coined by and unsupported null expectation that all la- Slowinski and Guyer 1989) was concerned beled cladograms were equally likely,and pre- thatpaleontologists took an overlydescriptive sented two other null distributions(see the and deterministicapproach when consider- section below on null models fortree balance, ing the patternsof fossildiversity. The group p 35). Simberloffet al. (1981) highlightedthe felt that some deductive methodology was necessity of using clear null models when needed, with a view to formulatinggeneral studyingcongruence among phylogenies,and evolutionarylaws (Raup et al. 1973). Taking showed how certain shapes of trees mightbe their cue from ecology (Simberloff 1972), expected to arise in nature. Together, the theycreated a simple stochasticmodel of mac- Woods Hole group's agenda of a quantitative roevolution (with lineages splittingand be- approach to paleontological studies of tempo coming extinct) and used it to simulate phy- and mode, and the response to the use of null logenies evolving through geological time. models in testsof ,set the stage Because the distribution of shapes of real forthe modern use ofphylogenetic tree shape clades fromthe literatureresembled the simu- in the studyof macroevolution. The two ap- lated random clades, Raup et al. (1973; Gould proaches also highlight two differentbut et al. 1977) held that deterministicexplana- closely related aspects of tree shape: changes tions for shape were unnecessary.How- in diversificationrates through time,and dif- ever, Stanley et al. (1981) found that with ferences in diversificationpatterns among more realistic parameter values the histories contemporaryclades. These mightbe thought of clades fromthe fossil record could not be of as two differentaxes of variation.We con- reproduced with simple stochastic models. sider the latter aspect first,beginning with a The Woods Hole studiesare partof a richliter- briefsummary of terminologyand the statisti- ature concerning the course of diversityin the cal approaches used. fossil record, but we will not review it here. Currentstudies of phylogenetic tree shape are TERMINOLOGY FOR PHYLOGENETIC generally intellectual descendants of the TREE SHAPE Woods Hole group and itsuse of a simulation- Most biological taxa have arisenby a branch- driven,stochastic model of tree production. ing evolutionaryprocess of descent withmodi- The biogeographic approach owes much to fication (we are stilla long wayfrom a proper Hennig (1966), who postulated a series of bio- account of reticulation in phylogenetic the- geographic "rules" (summarized by Ashlock ory). While taxonomies generally reflect (to 1974) by which cladograms could be used to various degrees) historical relationships be- infer past biogeographic events. In order to tween taxa, phylogenetic trees are explicit give these rules a quantitative basis, Rosen statementsof those relationships. That is, a (1978; see also Platnickand Nelson 1978) con- phylogenetictree is an estimate of the evolu- sidered the probabilitythat two area clado- tionaryhistory of the group in question. We grams (i.e., twocladograms of differentgroups will use the term estimatedtree to denote a par- with the common areas of occurrence substi- ticular phylogenetic tree inferredfrom real tuted for species) were congruent by chance data; this contrastswith the unknowable true alone. For instance, Rosen considered per- treewe are tryingto retrieve.The estimation fectly congruent area cladograms for two may have involved any of a number of tech- groups of fivespecies of fish,and pointed out niques, either phenetic or cladistic; despite that, given the 105 possible labeled clado- differences among techniques, in current gramshaving five tips, the chance thattwo five- practice all are normallyintended to retrieve tipped trees would match perfectlyowing to evolutionaryrelationships. chance would be (1/105) = 0.0095. This was Some furtherdefinitions will be useful.Any unlikely enough to justifyappeals to similar phylogenetic tree (Figure 2A) is made up of biogeographic trajectoriesfor the twogroups. tips,nodes, and branches.A nodeisa point where Simberloffand coworkers (Simberloffet al. twoor more branchesmeet, and each node ulti- 1981; Simberloff1987) pointed out that Ro- mately represents a speciation event whose sen's statisticswere based on the particular age may or may not be estimated; the oldest

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tip balanced trees have been called pectinate, A # chained, or comblike ("unbalanced" is also ...... node used, and is identical in meaning). We use tree shapeas a general termthat includes both bal- ance and the distributionof branch lengthsin ...... branch the tree.

...... root TREE BALANCE B MEASURES OF TREE BALANCE Although it is possible to examine patterns in the frequencies of all possible tree topolo- gies (Savage 1983; Brown 1994), this quickly becomes unwieldywith trees larger than a few time species. An alternativeis to use a summaryin- dex of overall tree balance. Many differentin- FIGURE 2. Two HYPOTHETICAL 8-TIPPED dices have been proposed; theydiffer in calcu- PHYLOGENETIC TREES. lation and to some minor extent in behavior These treesillustrate the range of possibilities (Shao and Sokal 1990; Kirkpatrickand Slatkin for tree balance and some basic terminology for 1993). Most have in common the fact that elementsof trees. Tree (A) is completelybalanced; each summarizes,in a single number, the de- tree (B) is completelyimbalanced. gree to which a treeis balanced or imbalanced (but see Sackin 1972; Fusco and Cronk 1995; and the use of only a single node by Slowinski and Guyer 1989, 1993; Guyer and Slowinski node is the root.Tips are the smallest taxo- 1993). Balance indices ignore any informa- nomic unitsshown in a tree.A branchconnects tion about branch lengths (Figure 2) and con- a tip or node to the next nearest node, and its sider onlythe distributionof tipsacross nodes. length may reflectinferred amounts of time, We assume for the moment that the trees un- genetic change, or morphological change be- der consideration are binary. tweennodes or between nodes and tips.Binary The most widely used index is Colless' treeshave no more than three branches meet- (1982) index ofimbalance Ic (Cin Kirkpatrick ing at any node: an ancestral branch and two and Slatkin 1993). Ic sums, over all (n - 1) daughter branches. A tree is labeled if each nodes in a tree with n tips, the differencein tipis uniquely identified(normally as a species the numbers of tips subtended by the right- or other taxonomic group); it is unlabeled hand and left-handbranches arising at each otherwise.A tree is completeif it includes all node, and then normalizes by dividingby the extant taxa in a given group (for instance, all largestpossible score. That is, seven recent species in the horse family). treesare because are I TR-TL I Many incomplete species (all intenorI nodes) unknown,or eitherunavailable to or omitted Ic = (1) by the systematist. (n- 1)(n- 2) Treetopology refers to the branchingpattern 2 of a tree, but ignores branch length informa- where at each node the rightand leftbranches tion and labels on the tips. Two unlabeled subtend TRand TLtips. Ic = 0 fora completely trees have the same topology if they can be balanced tree and Ic = 1 for a completelyim- made identical (ignoring branch lengths) by balanced one. Kirkpatrickand Slatkin (1993) swapping the positions of the right-handand point out that Ic gives more weight to nodes left-handbranches at anyset ofnodes. Balance, close to the root (for which I TR- TL I can be or the extentto whichnodes definesubgroups largest). This is reasonable because those of equal sizes (Figure 2B), is the most widely nodes are the most informative,as the sub- considered aspect of topology.Balanced trees clades they define are older and therefore have also been called symmetrical,while im- sample longer periods of evolutionarytime. It

This content downloaded from 131.202.42.30 on Fri, 26 Apr 2013 09:59:50 AM All use subject to JSTOR Terms and Conditions MARCH 1997 PHYLOGENETIC TREE SHAPE 35 is possible to constructan alternativemeasure including polytomies,but for such trees ex- thatweights all nodes equally: pected values and moments of the indices are much less easyto derive.In manyor mostcases, ,I - I TR TL trees with polytomiesreflect only our incom- (1-nodes, j>2) j - 2 plete knowledge; for instance,a wide-ranging '2= (n-2) (2) species, budding new species fromperipheral isolates but not itself changing phenotype, where j is the number of tips subtended by could produce a clade we would estimateun- each interiornode. The cost of thisalternative der maximum parsimonyas a polytomy(Wag- is thatI2 is a less familiarindex and itsbehavior ner and Erwin 1995). The balance of such un- has yetto be characterized. resolved trees may have little to tell us. Five other indices have been examined in However, "hard" (true) polytomiescan result some detail byKirkpatrick and Slatkin (1993): fromsimultaneous speciation events in a sin- N, uN,B1, B2, and R N and uNderivefrom Sack- gle lineage (Hoelzer and Melnick 1994); such in's (1972) vector measure of tree balance: If cases are difficultto accommodate with cur- is the number of nodes between tip i and N rent methods. The usual practice is to con- the root,then the mean and variance of Nover sider only binarytrees. all i (i.e., N and cN2) are two slightlydifferent How are we to choose among the alternative measures of tree shape [Shao and Sokal measures of balance? Kirkpatrickand Slatkin (1990) used INinstead of N]. Both increase (1993) compared the power of six statisticsfor with increasing imbalance. A third related discriminatingbetween two simple models of measure is B2 = (N/2N,),which is related to evolution. R and B2 low the Shannon-Wiener information function N, showed relatively o2, B1 [note thatB2 in Kirkpatrickand Slatkin (1993) power, but I, and all performedfairly is equal to B2 divided by log(2) in Shao and well. Of the latterthree, I, is computationally Sokal (1990)]. B2is larger for more balanced the simplest,and is the onlyone whose expec- trees. B1is more complicated: For each of the tation and variance (under a simple null interiornodes except the root, determine Ml, model; see below) are known analytically the maximum number of other nodes be- (Heard 1992; Rogers 1994). For these reasons tweenthat node and a tipit subtends. Then B1= we expect that I, will be, for most purposes, the most useful measure of balance, despite a E 1/Ml (Shao and Sokal 1990); B1 is larger formore balanced trees.Finally, Page (1993b) slightedge in power reported forB1 (Kirkpat- developed an alternativemeasure, which re- rick and Slatkin 1993). quires an ordering of all possible trees of size n by Furnas' (1984) "left-lightrooting" rules. NULL MODELS FOR TREE BALANCE These rules place a perfectlyimbalanced tree Given that we can calculate a measure of first,and a perfectlybalanced one last,and the balance fora phylogenetictree, what do we do balance index Rfor a particulartree isjust the with this information?Balance was firstdis- position of the tree in that order. cussed withreference to the informationcon- There seems to be no end to the number of tent of a taxonomy (e.g., Mayr 1969; Sackin balance indices that can be derived. Rogers 1972), but the recent surge of interestin bal- (1996) has suggested counting the number of ance reflectsinstead the realization thatit can nodes in a treethat are imbalanced (J). Other be used to study the evolutionary process. variations on the indices discussed here ap- Such studyinvolves seeking biological (evolu- pear in Shao and Sokal (1990). Furthermore, tionaryor other) explanations forpatterns in tree topologyis of interestin other fields,and balance. A usefulbaseline forthis sort of enter- analogous approaches can be found (e.g., in prise is provided by null modelsfor tree bal- hydrology,Smart 1972; in cell morphology, ance: that is, simple models forwhich we can Van Pelt et al. 1989). predictthe distributionof tree topologies, and Trees that include polytomies (i.e., which against which we can evaluate samples of esti- are not binary) pose problems for the mea- mated trees or the results of more sophisti- surement of balance. Shao and Sokal (1990) cated evolutionarymodels. discussthe application of several indices to trees Three rather differentnull models have

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A D B C B D A C A B D C it is an appropriate null model for studies in which one is interestedin balance for evolu- tionaryreasons. Analyticaltreatments of the imbalance index Ic under the Markov model are available (Heard 1992; Rogers 1994).

j L Notice that the Markov model does not ex- A B C plicitlyinclude . This is normally justified by considering the modeled (or cal- culated) speciation rate as the "net rate of di- versification,"the actual rate of speciation mi- FIGURE 3. THREE POSSIBLE WAYS A 3-TIPPED nus the rate of extinction. If extinction is TREE CAN GIVE RISE TO A random across lineages it does not affecttree 4-TIPPED TREE THROUGH balance (Slowinskiand Guyer 1989), and so a SPECIATION OF ONE LINEAGE. model withnet diversificationis sufficient.For Notethat there are onlytwo different topologies; thisreason we and othersoften use "diversifica- thetwo trees on theleft are identicalif unlabeled, tion"and "speciation"as ifthey were equivalent. but differentif labeled. We caution,however, that this equivalency does not hold ifbranch lengthinformation is taken into account (see the section on estimating been proposed for tree balance: the equal- branch length, p 41). Also, because the two rates-Markovmodel, the proportional-to-dis- ratesare considered together,their effects are tinguishable-arrangementsmodel, and the conflated; while patterns in extinction rates equiprobable-typesmodel. No null model is could play as importanta role in shaping tree completelyfree of assumptions and different balance as patternsin speciation rates,we can- (even ifminimal) setsof assumptionsyield dif- not normallyseparate the twoprocesses using ferentnull models. balance alone. The equal-rates-Markov(often just "Mar- Under the proportional-to-distinguishable- kov") model is attributedto Harding (1971) arrangements (PDA) model (Rosen 1978; and to Cavalli-Sforzaand Edwards (1967), but originally described for area cladograms), is based on models of the diversificationpro- there is no explicit model of growing trees. cess that date at least to Yule (1924). Under Instead, each possible arrangementof n taxa this model, trees are generated by an evolu- into a tree-that is, each possible estimateof tionaryprocess under which,at any time t,all the phylogenyof the n taxa-is equally likely. extant lineages have equal probabilities (de- Within this larger set, the frequencyof each noted X) of speciating in the interval (t, t + topologyis proportional to the number of dis- At). "Equal rates" here refersto the equality tinguishabletrees sharing that topology [Rog- ofspeciation probabilitiesacross lineages; spe- ers (1994) gives recursion equations for the ciation rates are often considered constant number of topologies forany tree size n]. For through time as well, but thisis not necessary four-tippedtrees, there are 12 differentimbal- provided that when they vary, they vary to- anced trees and 3 differentbalanced ones gether in all lineages. To see how the Markov (shufflethe labels on the tips in Figure 3, re- model works, consider a four-tippedtree; it membering that any clade can be rotated at must be the result of three speciation events the node that subtends it withoutproducing (of which onlythe last can produce more than a new distinguishabletree). The imbalanced one topology). This last speciation event can and balanced topologies thereforehave fre- happen withequal probabilityto threespecies quencies 0.8 and 0.2 respectively.The PDA (see Figure 3); two of these eventsgive an im- model produces trees that are more imbal- balanced topologyand one a balanced one, so anced than the equal-ratesMarkov, and mim- the probabilities of the imbalanced and bal- ics the action ofsystematists who choose at ran- anced topologies are 2 and '/3,respectively. Be- dom among all possible phylogenetic trees cause the Markovmodel explicitlyconsiders a (all possible labeled trees;Slowinski 1990). As simple model of evolutionarydiversification, such, it is not of much interestfrom an evolu-

This content downloaded from 131.202.42.30 on Fri, 26 Apr 2013 09:59:50 AM All use subject to JSTOR Terms and Conditions MARCH 1997 PHYLOGENETIC TREE SHAPE 37 tionarypoint of view,but whenever tree esti- trees, either in large samples (e.g., Savage mation is imperfectwe can consider the likeli- 1983; Heard 1992) or one tree at a time (e.g., hood of a bias in treebalance towardsthe PDA Guyer and Slowinski 1993), and compared expectation(Rogers 1994; Cunningham1995). them with the expectations based on null Finally,the equiprobable-types(EPT) model models. Others have produced simulated (Simberloffet al. 1981) holds thateach differ- trees under a varietyof simple evolutionary ent topologyfor a given tree is equiprobable. models. The twoapproaches can then be com- For instance, there are two differentfour- bined in hopes of understandingwhich evolu- tipped topologies (Figure 3), whichunder the tionarymodels are, and are not, consistent EPT model should each occur in a sample of withdata fromthe literature. treeswith frequency 0.5. This model produces Imbalance has been examined for fivema- the mostbalanced treesof the three.However, jor compilations of estimated trees. Savage no credible model either of the evolutionary (1983) collected over 1,000 estimatedtrees of process or of the action of systematistsleads sizes 4 to 7 (although manysmaller treeswere to the EPT balance distribution.We therefore subsets of the larger ones) and found that concur with Rogers (1993) that neither these largelyfit the Markov model (trees with agreement nor disagreement with the EPT 4, 6, and 7 tips,but not those with5 tips). Sav- null model is interesting,and it can safelybe age interpretedthis result as indicating that disregarded. among lower taxa "lineage diversification.. . withina group ... is largelystochastic" (Savage PATTERNS IN TREE BALANCE 1983:236), although he did not expect his re- Patternsin tree balance may arise fromsev- sult to hold for higher taxa (roughly,above eral sources. First,all reasonable models of the familylevel). evolution include stochasticity;any observed In contrast,the consensus of four more re- patternin balance can thereforereflect purely cent studies is that even small estimated trees stochasticeffects. Second, because estimated are consistentlyand significantlymore imbal- treesare not alwaysidentical to the underlying anced than expected under the Markov null true trees, patterns in balance might reflect model (Figure 4): Guyerand Slowinski(1991) propertiesof the estimationalgorithms or de- examined 120 complete trees of 5 species; cisions of systematistsin the definitionand in- Guyer and Slowinski (1993) examined 30 clusion of taxa. Third, and most interesting, trees of 100 to 20,000 species; Heard (1992) patterns in balance reflect the macroevolu- examined 196 treesof 4 to 14 tips;and Mooers tionaryprocesses throughwhich the diversity (1995) examined 39 complete trees of 8 to 14 of life on Earth has been generated. The task tips. Each studyrejected the Markov model, of balance studies is to determine to what ex- although none could account forthe disagree- tent the signal (the third source of balance mentwith Savage (1983). The rejection of the patterns) comes through the noise and bias Markovmodel was veryrobust: it held fortrees (the firstand second sources, respectively), of species or of higher taxa, for phenetic or and to draw conclusions fromdata appropri- cladistic trees, and for complete and incom- atelyfiltered or statisticallycontrolled to leave plete trees (furtherdiscussion of treecomplete- only the evolutionarysignal. We discuss first ness below). If this "excess imbalance" can be patternsin the available data and possible bio- taken at face value, it documents the existence logical explanations, deferringconsideration of substantialvariation in speciation and/or of possible biases until the section on nonevo- extinction rates among lineages within even lutionaryexplanations forimbalance (p 38). quite small phylogenetictrees. Rejection of the Markovmodel tellsus only Balancein EstimatedTrees and Simulations thatlineages vary in theirspeciation/extinction Two complementary approaches to the rates,but we would obviouslylike to know how study of patterns in tree balance have been much and what kind of variation would be taken: mining the literature for estimated needed to produce treeslike those in the liter- trees, and computer simulations. Several au- ature. Computer simulations have recently thorshave examined the balance of estimated been applied to this problem, although the

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1.0 limit exists for punctuated evolution. This contrast could potentiallyhelp to illuminate the relativeroles of these two major modes of 0.8 macroevolution, but more detailed and so- phisticated evolutionarymodels will have to be explored first. Losos and Adler (1995) modeled a verydif- 0.6 j j ferentform of speciation-ratevariation; one thatarises because a newlyformedspecies passes througha "refractoryperiod" during which it 0.4 cannot speciate further-perhaps as it ex- pands in density and range from a small founder population. Short refractoryperiods 0.21 tend to produce treesmore balanced than the Markov expectation, because they dampen 4 6 8 10 12 14 the activityof the most activelyspeciating lin- Tree size eages. However, Rogers (1996) has recently shown thatvery long (but perhaps unreason- FIGURE 4. A SUMMARY OF DATA ON THE BALANCE ably long) refractoryperiods can produce OF ESTIMATED PHYLOGENIES. stronglyimbalanced trees. Solid triangles:Heard 1992 (errorbars are ? twostandard errors); open triangles:Mooers 1995; NonevolutionaryExplanations for Imbalance open circle:Guyer and Slowinski1991; dashed line is theMarkov expectation. The figureincludes all We should not interpretpatterns in treebal- availablecompilations measuring balance forsys- ance solely in terms of evolutionaryprocess. tematicsamples of literaturetrees, except Savage We must also consider the possibilitythat the (1983), whichwe excludedbecause his smalltrees trees we make give biased or inaccurate esti- are subsetsof largertrees, and thereforethe tree mates of the balance of the true treesunderly- sizesare not independentsamples. ing them (this is not an issue for patternsin computersimulations). Several possible sources of such bias have been identified. Three in evolutionarymodels underlyingthem are not particularhave seen considerable discussion: yet verysophisticated. Heard (1996) consid- bias in poorly supported trees,bias in system- ered a model where diversificationrates de- atic methodology, and bias in incomplete pend on the value of a trait(such as body size) trees. Recent work indicates that at least the evolvingin a random walk,and are also subject firsttwo are actuallyclosely related. to random variation.Rate variationrelated to PoorlySupported Trees. Several studies have heritable traits("heritable" at the level of an- examined the effectsof tree accuracy. Esti- cestorto daughterspecies), and some formsof mated trees are not always identical to the ratevariation unrelated to anythingheritable, (usually unknown) true trees. Several studies produced trees with increased imbalance. have also examined how estimation errors However, extremely large amounts of rate might affect tree balance. Work with simu- variationwere required to produce treesas im- lated data suggests that differentmethods balanced as the estimated trees discussed make differentkinds of estimation errors, with above. Kirkpatrickand Slatkin (1993) reached differentconsequences forbalance. a similar conclusion froma related model of Mooers et al. (1995) found by simulation evolving speciation rates. Heard (1996) also (for trees with 10 tips) that incorrect maxi- found thatgradual and punctuated models of mum parsimonyestimates tended to be more macroevolutionproduce differentpatterns in imbalanced than the underlying true trees, tree balance. Specifically,under gradualism and Zarkikhand Li (1993) documented con- there appears to be an upper limit to imbal- ditions under which balanced 5-tipped trees ance no matter how fast the traitson which were incorrectlyestimated as imbalanced, us- diversificationrates are based evolve; no such ing maximum parsimony.Heijerman (1992,

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1993) undertook a large simulation studyin- data sets;Heard and Mooers 1996). It appears volvingtrees with 20 tips,and found thatgen- thatUPGMA estimateswith random data may erally,under a Markov model of tree produc- be biased (Heard and Mooers 1996; see also tion, balanced estimates were closer to the Colless 1996). underlying true tree than imbalanced esti- Documenting these effectswith trees esti- mates. The parametersthat Heijerman chose, mated fromreal data is more difficult,as there however,made the true treesvery hard to re- is no good method for measuring how well cover, so his resultsare hard to interpret.In- an estimatedtree reflectsthe (unknown) true terestingly,Heijerman found no relationship tree. There are manyindices of how well data between tree balance and accuracy of recon- agree withina single tree: forinstance, consis- structionfor an equilibriummodel of treepro- tencyand retentionindices (Farris 1989), ho- duction; thismay serve as a caution thatdiffer- moplasy-sloperatios (Meier et al. 1991), deci- ent underlyingmodels may lead to different siveness ratios (Goloboff 1991), skew in the biases. distributionof treelengths (Le Quesne 1989), Related workby Huelsenbeck and Kirkpat- and permutation tests (tree support values; rick (1996) shows thatas data deteriorates(as K.allersjoet al. 1992) or resamplingmeasures sequence data accumulates very large num- (bootstrapvalues; Felsenstein1985a) of agree- bers of site changes and corresponding tree ment. We might consider these as surrogate estimates contain more errors), maximum measures of reliability,although they are of- parsimony phylogenies become increasingly ten poorly intercorrelated (Goloboff 1991; imbalanced; simulationsby Colless (1995) us- Mooers et al. 1995; Sanderson and Donoghue ing artificiallyevolved data withvery few char- 1989) and so we warn thatrecognition of reli- acters per show similar results. In the able and unreliabletrees may often be difficult. extreme,when data are entirelyrandom (so There have been a few studies of the bal- there is no true tree to estimate), cladistic ance effectsof estimation errors in real data methods produce random guesses from the sets. Guyer and Slowinski (1991) found that set of all possible trees (Heard and Mooers maximum parsimonytrees with more charac- 1996). The expectation under the PDA null ters defining interior nodes were more bal- model (defined in the section on null models anced than trees withfewer characters defin- a for tree balance, p 35) is stronglyimbalanced ing nodes, and Mooers et al. (1995) found negative correlation between measures of compared to both the Markovmodel and col- characteragreement and treebalance. Colless lections of estimatedtrees. For maximum par- (1995) examined a set of unreliable (Heard simonymethods, therefore, increasing amounts and Mooers 1996) data matrices and found of error in tree estimation produce increas- that cladistic estimated trees were highlyim- ingly imbalanced trees until, with random balanced while phenetic estimateswere quite data, imbalance reaches that of the PDA null balanced. The empiricalresults therefore sup- model. Markov and Combined models with port the expectationsfrom simulation studies, PDA components can be developed in an at- despite being hampered by problems in mea- tempt to accommodate contributions from suring tree accuracy. both models, although a difficultyarises in dis- SystematicMethodology. The question of bias tinguishingimbalance generated by macro- in tree shape arisingfrom systematic method- evolution from imbalance generated by sys- ologyhas been contentious.Recent discussion tematicerror. has centered on possible differences(in bal- Phenetic methods treat poor data differ- ance) between phenetic (almost always UP- ently. Huelsenbeck and Kirkpatrick (1996) GMA) and maximumparsimony trees. Colless found thatas data deteriorated,UPGMA (un- (1982) suggested that published cladograms weightedpair-group method using arithmetic were more imbalanced than phenograms,but averages) estimates did not change much in produced only anecdotal evidence. Savage balance, despite containing roughlyas many (1983) suggestedthat phenograms were more errors as cladistic estimates. Colless (1995) imbalanced than cladograms, but recognized found quite balanced phenetic treeswith ran- that the differenceswere of uncertain statisti- dom data (and also withvery unreliable real cal significance.

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More recently,Colless (1995) claimed that Mooers 1995) have found that trees that are cladograms and phenograms produced from incomplete because theyhave genera or fami- the same data differdramatically in balance lies as tips do not differin balance fromtrees (the cladograms being more imbalanced). In of species. Mooers (1995) has shown by simu- contrast, Heard (1992) and Mooers (1995) lation that some, but not all, other plausible analysed large and systematiccompilations of kinds of sampling (for instance, selection or literaturetrees, and found no differencesin exclusion of taxa that have similarvalues for balance between cladistic and phenetic trees heritable traits)do affectbalance, oftenlead- aftercontrolling for tree size and the inclusion ing to incomplete trees that are more imbal- of outgroups. This apparent contradiction anced than their corresponding complete can be resolved (Heard and Mooers 1996) by trees. considering tree reliability:nearly all data sets Mooers (1995) also found a significantdif- used by Colless (1995) produced poorly sup- ference in balance between a set of complete ported trees,for which we have seen thatphe- trees assembled from the literature (hollow netic and cladisticmethods make differenter- trianglesin Figure 4), and a sample of incom- rors.For robusttrees, simulations have shown plete trees fromHeard's (1992) compilation: little disagreement between methods (see the complete trees were more balanced, Huelsenbeck and Kirkpatrick1996), which though still not as balanced (as a group) as lines up well withHeard's (1992) and Mooers' the Markov expectation. The opposite effect (1995) results. However, Huelsenbeck and is also possible: in some large phylogenies, Kirkpatrick(1996; theirFigure 2) found that smaller subclades may be omitted, and this even withvery good data, both methods (and can produce a more balanced incomplete tree other phylogenetic methods such as maxi- (Fusco and Cronk 1995). mum likelihood) seem to produce estimated It is possible that the differencebetween trees which are slightlybiased towardsimbal- Mooers' (1995) and Heard's (1992) resultsare ance. actuallydriven by treereliability, not complete- IncompleteTrees. Mooers (1995) has exam- ness. In making his compilation, Mooers in- ined the issue of tree completeness.The prob- cluded onlydatasets giving unique (or at most lem arises because we are interestedin the bal- two) most parsimonious treeswithout ad hoc ance of a real tree, but often we actually weighting.In contrast,Heard made no effort measure the balance of a subset of this tree: to assess tree quality,and so that dataset may the sample of taxa available, or of interest,to have included some less robust trees, which the systematist.While balance is unaffectedby we might expect to be more imbalanced. In random omission (or extinction) of taxa from support of this interpretationis Guyer and a tree (Slowinski and Guyer 1989), this need Slowinski's (1991) compilation of 120 com- not be true for nonrandom omission of taxa. plete 5-tipped trees (hollow circle in Figure Brown's (1994) argument that the frequen- 4). Guyer and Slowinski,like Heard, did not cies of tree shapes are "independent of the attemptto assess tree quality,and theyfound extinctionprocess and even of the process by imbalance slightly(but not significantly)higher which a scientistselects the species to be stud- than Heard's compilation. It remainsunclear, ied" (p 79), appears in fact to apply only to then,whether the differencesbetween Mooers' random extinctionor selection on equal-rates and Heard's compilations (Figure 4) can be Markov trees. laid to completeness, tree quality, or some One can imagine many ways in which the combination of the two. taxa under studycould be a nonrandom sub- We emphasize that the conclusions pre- set of all possible taxa. Some extant taxa may sented here are based on a distributionof true be unknown or some specimens unavailable treesthat can be mimickedwith an equal-rates to a systematist.A particularlycommon case Markov model of diversification.We do not is when a systematistchooses to include only know how noise in character data sets, tree representativetaxa (for instance, one from reconstructionmethods, or sampling biases each species group, genus or family). Two affecttree balances when the true treesbeing studies of large sets of trees (Heard 1992; estimated deviate stronglyfrom the Markov

This content downloaded from 131.202.42.30 on Fri, 26 Apr 2013 09:59:50 AM All use subject to JSTOR Terms and Conditions MARCH 1997 PHYLOGENETIC TREE SHAPE 41 expectation (except forthe trivialcases where branch is given a length equal to the number the true trees are all perfectlybalanced or all of changes inferredto occur on it. However, perfectlyimbalanced: error then could only thereneed be no unique wayof mapping char- be in one direction). The equal-rates Markov acters onto most parsimonious trees (Swof- treesare, on average, more balanced than the ford and Maddison 1987), and so other infor- PDA expectation and less balanced than the mation is needed to choose among alterna- EPT expectation, and so would seem a good tive mappings. With few models for rates of baseline for studyingbias, but they may not change in differentmorphological characters properlyrepresent the universe of true trees available, inferred morphological change is we ultimatelywant to study. rarelyused to estimatebranch lengthson phy- In summary, imbalance indices for esti- logenetic trees (Ross 1974; Felsenstein1985b), mated trees are subject to some bias. Unrelia- and this extends to phenograms made from ble cladistictrees tend to be more imbalanced morphological data. However, if nodal dates than reliable ones, all estimatedtrees may err can be inferred from geological data, mor- slightlytowards imbalance, and incomplete phology-based cladograms and phenograms trees can be more imbalanced than full trees. can be used to make inferencesabout macro- We do notyetknow to whatextent these biases evolution. Cloutier (1991) offersan interest- account for patternsin sets of literaturetrees ing example based on a cladogram of the co- (e.g., Heard 1992; Mooers 1995; Mooers et al. elacanth and related fossilActinistian fishes. 1995; see also the section on biases in tree Branch length data frommolecular phylog- shape, p 48), but the best evidence suggests enies are routinelybased on some model of that they are usually mild. Therefore, we do that assumes clock-like not believe that the biases are responsible for behavior (forearly evidence of rate constancy all (or even most) of the differencebetween in molecular evolution, see Zuckercandl and estimated trees and the Markov null model. Pauling 1965; for a review of the theoretical basis for clocks, see Kimura 1983; Chao and TREE SHAPEAND BRANCH Carr 1993; see also Gillespie 1991). These al- LENGTHDISTRIBUTIONS gorithms include the common UPGMA ESTIMATINGBRANCH LENGTH method (Sokal and Michener 1958), and the in PHY- Until recently, most phylogenetic trees KITCH and the DNAMLK algorithms a were presented without estimates of branch LIP (Felsenstein 1993; who also offers con- lengths (see Figure 2); thisgives only half the cise explanation of these methods). The as- storyof evolution.A time axis allows us to ask sumption of a molecular clock means that more precise questions about the variationin inferredbranch lengths can be read as time diversificationrates among extant lineages intervals;i.e., a time axis can be placed on the (i.e., looking at variationwithin a horizontal tree (see Figure 2). If the branch length data slice throughthe tree in Figure 2), and also to are reliable,various comparisons can be made ask about variation in rates as a whole clade between these inferredtrees and expectations diversifies (i.e., variation along the vertical based on null models [see, however, Felsen- axis of the tree in Figure 2). In either case, by stein (1988:542), Nei et al. (1985), Hasegawa comparing observed patterns with expecta- et al. (1993), and the section below on biases tions from null models, we may gain insight in tree shape (p 48) for discussions of the er- into the processes drivingdiversity patterns. rors associated withinferred branch lengths, Inferringbranch lengthson a tree requires which can oftenbe substantial]. either some knowledge of (or guess at) the rates of change in the charactersused to con- TREE SHAPE MODELS WHICH INCLUDE TIME structthe tree, or recourse to fossilevidence. The equal-rates-Markovnull model of tree Cladistic trees inferredfrom morphological shape is also the startingpoint for tests that data and parsimony algorithmscontain lim- incorporatebranch-length information. How- ited informationabout distancesbetween suc- ever, the actual values of the speciation rate cessive nodes. Character changes can be [X, or birthrate, estimatedby b,the probabil- "mapped" onto a topology, such that each itythat a lineage will splitbetween time t and

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(t + At)] and the extinctionrate [p, or al. 1992; Figure 5). These are semilogarithmic rate, estimatedby d, the probabilitythat a lin- plots of the number of lineages in existence eage willgo extinctbetween time tand (t + At)] as a functionof time since the firstbranching now play prominent roles. The simplestcase of the tree at its root. Figure 5 highlightsthe is one which sets p to zero, and models A as various parameters that are depicted in such unchanging throughtime (Yule 1924), which a plot. First,under the simplestMarkov model sets a probabilitydistribution for the time to witha constantand positivenet rate of diversi- speciation for any extant lineage as (Hey fication [ (A - p) > 0; for simplicity,we refer 1992): to this also as a constant-rateMarkov model, P(t) = Xe" . (3) and rate is understood to be net], there will be exponential increase in the actual number For n extantlineages, the probabilitydistri- of lineages, resultingin a straightline, with bution for the time until the next speciation stochasticwiggles, on a semilog plot (Harvey event will be the same withparameter nA: et al. 1994; top line in Figure 5). Second, if there has been extinction > 0), there will P (t) n= nXe . (4) (p be a differencebetween the actual number of The waiting times between speciation lineages presentat any one timeand the num- events in the tree decrease as n increases, be- ber thatare estimated (the bottom line in Fig- cause there are more lineages that are free ure 5): the phylogenyderived from extant taxa to speciate. Whereas the equal-rates-Markov can onlyrecover lineages thatleft descendants model (see the earlier section on null models to the present day.At the end-point (the pres- for tree balance, p 35) stipulates that at any ent) the twolines converge on the actual num- one time,all extantlineages have the same A, ber of lineages in existence. Over most of the this "constant-rateMarkov" model goes one historyof an expanding clade, the slope of the step further,specifying that A does not change lineages-over-timeplot is an estimate of (A - through time. In fact,the speciation parame- p) (Nee et al. 1992). [If there is no error in ter A is specified in many simulation studies the branch length data, the slope is in factthe of tree topology (e.g., Kirkpatrickand Slatkin realized rate of diversification(b - d) (Purvis 1993; Heard 1992, 1996; Losos and Adler 1996) ]. If there is no extinction,then the ac- 1995; Mooers 1995; Rogers 1996), but the re- tual and reconstructed lines will be coinci- sulting branch lengths are not analysed fur- dent, and the slope estimates A. Computer ther.Below, we consider some applications. packages are available,which allow estimation The addition of an extinction parameter of these various parameters (Harvey et al. (p) expands the versatilityof the models, 1995b; Rambaut and Harvey 1996). allowing two classes of processes to be consid- The lineages-through-timeplots make ex- ered. With A greaterthan p, the model is one plicit several other features of the constant- of nonequilibrium growth. An equilibrium rate Markovmodel. First,the model produces model, on the other hand, begins witha tree a steep slope of actual lineage production of a certain size, perhaps produced by way of earlyon in the diversificationof a clade. This a nonequilibrium model, and then regulates "push of the past" (Nee et al. 1994b) is due A and p, so that the tree is maintained at this to the fact thatwe confine ourselves to clades size (except perhaps for stochastic fluctua- thathave leftat least one livingdescendant (in tions). More complex models can specifydif- fact,we studyonly clades that have leftmany ferent relationships between speciation and descendants): even when A is higher than p, extinction that produce differentexpecta- some entiregroups will become extinctbefore tions of tree shape-for instance, they may we sample the tree, owing to chance alone. allow the tree to firstgrow and then shrink This means we tend to observe the nonran- through time. dom sample of clades that got offto a flying In order to compare the shapes of phyloge- start; such clades should show an increased netic treeswith expectations from the various number of fossilspecies early on in their his- models, the phylogenies are often repre- tory.Second, because the actual and recon- sented as lineages-through-timeplots (Nee et structednumbers of species must coincide at

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1000-

actualnumber of lineagel's

10| qf < lineages l

AA . 0m(00)

1

0 10 20 30 40 50 60 70 80 90 1+00

Time present

FIGURE 5. LINEAGES-THROUGH-TIME PLOTS FOR A SIMULATED PHYLOGENY. A constant-rateMarkov process has given rise to a phylogeny,depicted here as a semilogarithmicplot of the number of extant lineages as function of time since the firstsplit in the tree at its root. The top dashed line is the actual number of lineages, and the bottom dashed line is the reconstructednumber (the top line minus extinctlineages). The slope of the two lines in theg-. mid time range estimates Near the present, the bottom line steepens, and estimates A. Time units are arbitrary.The simulation was done using the Bi-De simulation package (Rambaut and Harvey 1996) withe = 0.3is and = 0.25.

the present day and the reconstructed line d, the extinction rate, can also be estimated. mustlie below the actual line when d > 0, the Maximum likelihood techniques can be ap- reconstructedcurve will show an upswing at plied for any given tree (Nee et al. 1994a,b, the present, and the slope of the recon- 1995a). structed curve near the present (its tangent at the present) will be b. This is owing to the APPROACHES USING THE NULL MODELS inevitable time lag between the birthof a lin- Hey (1992) presented two new approaches eage and its possible death; close to the pres- to the studyof phylogenetictree shape using ent we sample manylineages thatwill become branch lengths. The firstis a time-basedver- extinct,but haven't yet done so. Under the sion of the balance testsconsidered in the sec- constant-rateMarkov model, we can therefore tion on tree balance (p 34) for the Markov measure both (b - d), the slope of the middle model, and is referredto as a Links test.It com- part of the plot, and of b, which means that bines the probabilities that successive specia-

This content downloaded from 131.202.42.30 on Fri, 26 Apr 2013 09:59:50 AM All use subject to JSTOR Terms and Conditions 44 THE QUARTERLY REVIEW OF BIOLOGY VOLUME 72 tion eventsoccur along the same lineage over cies. This might model the situation where all the speciation eventsin a given tree,and is niche space is completelysaturated by a clade. sensitiveto both an excess of speciation events The expected internode times are less easily along one lineage (leading to imbalanced to- derived than those fromEquation 4, but both pologies) and the sort of repulsion of succes- the most likelyvalue for the replacement pa- sive events envisioned by Losos and Adler rametergoverning the process and the likeli- (1995). Hey found that the test was much hood of observing a given tree if the most more sensitiveto the formerpattern than to likely value is fit can be calculated directly. the latter.Harvey et al. (1991) presented an- Again, we can compare the fitwith that from other version of this testthat considered only a model where a new value is calculated for the differencesin splittingprobabilities be- each internode in a given tree, using the chi- tween nested sets of sisterlineages. Mooers et square distribution. al. (1994; followinga suggestion made by A Note thatthe formalrejection of these sim- Burt) carried this test further, and asked ple models does not on itsown implythe rejec- whether,over a whole tree, the propensityto tion of a stochasticprocess, but simplya rejec- split was heritable among lineages: Did lin- tion of those processes that include only one eages that splitquickly produce daughter lin- speciation or replacement parameter when eages thatalso splitquickly? All these testsuse compared with a more general model. Hey the time axis to ask questions about the varia- (1992) found thatneither model could be re- tion in diversificationrates among extant lin- jected for any of eight trees taken from the eages, as do the topologytests presented in the literature,suggesting that simple one-parame- section on tree balance (p 34). ter models were sufficient.For each of the Hey's (1992) second approach compares eight cases, the simple growthmodel offered the timeintervals between successive branching a better fit to the data than did the second, events (the distributionof t's in Equations 3 constantreplacement model. Hey interpreted and 4) withthe expectation based on twosim- this as evidence against extinction in the ple theoretical models. The firstis the con- eight clades. stant-rateMarkov model with no extinction. Harveyet al. (1991; see also Harveyand Nee The maximum likelihood parameter for the 1994a) also compared time intervalsbetween speciation rate (the value of b which maxi- successivebranching events on a phylogenetic mizes the fitbetween the observed times t on tree, presentinga lineages-through-timeplot a tree and those generated byEquation 4) and of the earlyportion of the infamoustree of the the actual likelihood of the data arisingunder birds (Sibley and Ahlquist 1990). Rather than the simple one-parameterprocess can be cal- a straightline, as expected under the equal- culated directly.Hey suggests that this likeli- ratesMarkov model withconstant (A - pt)(Fig- hood be compared withthat in which the spe- ure 5), Harveyet al. (1991) reporteda distinct ciation rate is allowed to varyfreely for each downward curvature,evidence of a deficitof of the (n- 2) internodes.The likelihood ratio new lineages as one moved towards the tips. for this comparison is distributed as a chi- Nee etal. (1992) were able to statisticallyreject square, allowingquick assessmentof the prob- the simplest constant-ratemodel, but not a abilityof a particulartree havingarisen under two-parametermodel withdeclining diversifi- the simple model versus the more complex cation rates. Nee et al. (1992) interpreted scenario. theirmodel as consistentwith a scenario (out- The second model considered by Hey is a lined in a paleontological context by Valen- special case of the equilibrium model, where tine 1973; and modeled by Sepkoski 1978) of clades remain at a constantsize throughtime. initialrapid diversificationof birdsinto empty A monophyleticgroup of n species firstarises adaptive zones (aerial carnivores,aerial grani- under an unspecifiedprocess. Then, forevery vores, shorebirds), followed by a more stately speciation event, governed by some diversifi- process of speciation and extinction within cation parameter,there is a simultaneous ex- these zones. The same patternwas found for tinction event somewhere in the tree, such much more recentlydiverged groups of birds that the phylogenyis maintained with n spe- byZink and Slowinski(1995). They found that

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9 of 10 phylogeniesof recentNorth American bird genera also showed a downward curva- Cranes ture in lineages-through-timeplots. Zink and 10 Slowinski (1995) suggested that the deficitof new lineages was owing to increased extinc- tion rates during the Pleistocene. Purviset al. (1995) tested various scenarios with a tree of the primates,and found that the shape of the lineages-through-timeplot of the treewas con- sistentwith a constant-rateMarkov model. Lineages-through-timeplots can also sup- 2 plyinformation about mass extinctionevents. Harveyand Nee (1993) reported that certain 0 .1 .2 .3 .4 .5 .6 A formsof severe mass extinctionsmight leave a signaturein the formof an S-shaped curve, Time present and this was formalized by Harvey et al. (1994). Kubo and Iwasa (1995) point out that FIGURE 6. RECONSTRUCTED LINEAGES-THROUGH- while mass extinctionevents will be veryhard TIME PLOT FOR THE CRANES. to detect in real data sets (a point made by The curve is S-shaped, suggesting a decreasing Harveyand Nee 1993), suddenjumps in speci- rate of diversificationthrough time. Data fromKra- ation rates will leave a measurable footprint jewski (1990). on the lineages-through-timeplot. Kubo and Iwasa reasoned that the two processes might be linked (a mass extinctionallowing a subse- nodes in the tree near the present,causing a quent radiation), and so evidence for the lat- deficitof new nodes and a flatteningof the ter may suggest looking for independent evi- curve near the present. A tree of HIV-1 lin- dence for the former. eages (Harvey et al. 1995a) showed just this sampling effect,while a tree of poliovirus 1, INTERPRETATION OF BRANCH-LENGTH DATA also made from a subsample of extant lin- Care mustbe takenin interpretinglineages- eages, showed an S-shaped curve, consistent through-timeplots. Nee et al. (1994b) high- witha mass-extinctionevent. lighted how a model of a smooth decline in Figures 6 and 7 offerexamples of a related global splittingrate over time (Strathmann problem. Recall that Hey (1992) had no rea- and Slatkin 1983), wherebya clade firstgrows son to reject a simple growthmodel (having and then shrinks,could be interpretedas a a single parameter b), in favorof his general sporadic historyof boom and stasiswhen con- model forany of eight clades. However,Hey's verted to a lineages-through-timeplot of ex- general model [with (n - 2) parameters] is tant lineages. Similarly,a tree with a large much more complex than a scenario of a sin- number of nodes near the present, which gle b and a single d (e.g., Harveyet al. 1994); would correspond to a steep upswing in the the many extra degrees of freedom used by curve near the present,appears to suggestan Hey for his general model demanded that it increased rate of diversification;however, a offera much better fit to the data before it constantrate of net diversificationwith a high could be preferredover the simplerscenario. extinctionrate is another simple explanation Fairlysimple models that include extinction [if b > (b - d), then d must be large; Nee et mightoffer better fits to these trees than that al. 1994a]. Nee et al. (1994b) also pointed out supplied by Equations 3 and 4. The plots in thatwhen only a random subset of extant lin- Figures 6 and 7 are of twoof the clades consid- eages is sampled under a nonequilibrium ered by Hey. The Crane phylogeny(Figure 6) model, the resultingplot could mirrorthe de- seems compatible withvarious models of den- creasing per-lineage diversificationrate sce- sity-dependentcladogenesis (i.e., a changing nario attributedto the birds. Extant lineages rate of diversification),while the Plethodonphy- not present in a sample cannot contributeto logeny (Figure 7) is consistentwith a scenario

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true extinctionrate, even when the presumed Plethodon model is true,owing to the stochasticityin the realized diversificationprocess (see also Nee 10 et al. 1994a). Purvis (1996) has even suggested using the fossilrecord to check on the plausibilityof var- ious models. Lineages-through-time plots allow the total number of extinctspecies to be estimated: if more extinctspecies are known than predicted, we would do well to recon- sider our model. In summary,lineages-over-time plots offer 0 2 4 6 8 10 a powerfulapproach to testingnull models of macroevolution,having been successfullyap- Time + present plied to both large trees (e.g., of the primates and of the birds) as well as small trees, such FIGURE 7. RECONSTRUCTED LINEAGES-THROUGH- as thatof Plethodonsalamanders. As molecular TIME PLOT FOR PLETHODON data continue to accumulate, so will the op- SALAMANDERS. portunitiesfor testsof various models. How- The steeprise near thepresent can be interpre- ever,the fitfor any one model should be seen ted as evidencefor a high rate of extinctionin as the startingpoint forfurther research, not this group. Time is measuredin arbitraryunits (adaptedfrom Nee et al. 1994a). as an explanation of the data.

TREE SHAPE AND KEY INNOVATION HYPOTHESES of a constantbut high extinctionrate and was We turnnow to a specificapplication of the presented as an example of such a process studyof tree shape: the search for the causes (Nee et al. 1994a). The plot is also superficially of radiations. One approach, that of testing similarto the expectation froma more sophis- individual phylogenies for agreement with a ticated equilibrium model of diversification simple Markovmodel, can be extended to par- [equivalent to Hey's (1992) replacement ticular clades within a phylogeny. For in- model], adapted fromcoalescent theoryto de- stance, under the Markovmodel, at any single scribe endemic population processes (Nee et node, all possible partitionsof n species into al. 1995a,b). However, such a model for re- subgroups of size r and (r - n) (all vectorsof placement of species mightbe hard tojustify; progeny numbers) are equally likely (Farris there is ample evidence in nature that niche 1976). This propertymeans that sisterclades space maybe eitherundersaturated (e.g., Cor- of the same size are no more likelythan sister nell and Lawton 1992; Ricklefsand Schluter clades of greatlydifferent sizes. More impor- 1993) or oversaturated (e.g., Sale 1978). tantly,individual clades can be identifiedthat These examples serve to emphasize that the are bigger than expected under the null model to be testedshould be based on knowl- model (i.e., a split of 41 species into sister edge of the clade at hand; a population of en- clades of 1 and 40 species would only occur demic virusstrains and a group of salamander 5% of the timeunder the Markovmodel). Un- species may yield similar phylogenetic pat- fortunately,the flat probabilitydensity func- ternsfor very different reasons. Many models tion forsplits means thattests for single nodes can be rejected by (or fit) the same data. are of verylow power. Kubo and Iwasa (1995) expand on this Nee et al. (1992) presented a generalized theme. They point out thatmany functions of case for an arbitrarynumber of ancestor lin- b and d may produce the same phylogenetic eages when a time axis can be added to the patternunder a simple Markovmodel. As well, tree. If we draw a horizontal slice through a theyshow thatwhile bmay accurately estimate tree at a single point in time,thereby defining the true X, d will be a poor measure of the n ancestral lineages, we can model the distri-

This content downloaded from 131.202.42.30 on Fri, 26 Apr 2013 09:59:50 AM All use subject to JSTOR Terms and Conditions MARCH 1997 PHYLOGENETIC TREE SHAPE 47 bution of the sizes of the clades that result abilitycoming froma comparison in clade size fromthese ancestral lineages at any time later between a group exhibitinga putativekey in- in the tree by randomlyand repeatedlybreak- novation and itssister-group (for an example, ing a stickwith the same lengthas the number see Hodges and Arnold 1995). Sanderson and of descendent species into n fragments.This Donoghue (1996) survey a range of tech- allows us to identifysubclades that are signifi- niques available for pin-pointingchanges in cantlylarger than we would expect, a possible diversificationrates. Barraclough et al. (1996) firststep when looking for evidence of keyin- presented a novel analysis,which correlates novations.Another, related, approach is to es- higher rates of angiosperm diversification timate speciation and extinction rates sepa- with higher rates of genetic change early in rately for differentclades, and then to ask thatdiversification. This analysiswas based in whether the estimates differamong clades. part on the equal-rates Markov null model. Purviset al. (1995) applied both of these tests However, if it turnsout that the Markov null to the tree of the primateshaving 203 species model is generallya poor predictor of actual (Purvis 1995) and were able to identifyclades tree shape, as it seems to be (see the section with higher than average diversificationpa- on patternsin tree balance, p 37), then tests rameters (e.g., the Old World monkeys), as that do not compare treeswith the equal-rate well as groupswith very different ecologies but Markov null model might be preferred (see similar diversificationparameters (e.g., the the section on sophisticated evolutionary hominoids and the New World monkeys). models, p 49). Nee et al. (1996; see also Bar- This result is particularlyinteresting, given raclough et al. 1995; Mooers and M0ller 1996) that there was no evidence of a change in the offeran alternativetest that does not assume average diversificationrate across the entire a Markov null expectation. tree over time (Purvis et al. 1995), and serves to show how the two axes of variationthat we OTHER USES FOR TREE SHAPE have been considering (the one throughtime The shapes of phylogenetictrees are a rich and the other across lineages) may be inde- resource for many areas of studynot fullyex- pendent. plored in thisreview. One such area is in tech- Sanderson and Donoghue (1994) have ex- nical aspects of tree estimation:the shape of tended the search for differencesin diversifi- a true tree appears to affectthe possibilityof cation rates among contemporarylineages to estimatingit correctly.This is the inverseof the take into account uncertaintyin the timings problem of bias discussed in the section on of branching events.They found a change in patternsin tree balance (p 00). This issue has the rate of diversificationnear the base of the been explored through simulations by Rohlf angiosperm tree, but most likely occurring etal. (1990) andHeijerman (1992, 1993),and afterthe origination of angiosperms, sug- a biological investigationof the relationship gesting that characters that unite all angio- between shape and ease of estimation has sperms may not be sufficientto explain the been made byArnold (1990). All these studies clade's taxonomic success. This approach- suggest that the shape of the true tree can used by Hodges and Arnold (1995) to associ- stronglyaffect the probabilityof recoveringit ate nectar spurs with plant diversification- withdifferent estimation techniques. may prove useful when dealing with unique Another area is the comparison of particu- radiations,where statisticaltests for correlates lar treeswith one another. The connection be- of diversificationare inappropriate (Purvis tween the purelytopological null models pre- 1996). sented by Simberloffet al. (1981) and the Slowinski and Guyer (1993) present a time-based Markov null model of diversifica- method forusing the propertyof the flatdistri- tion (Page 1991; Brown 1994) allows branch bution of sister-cladesizes to studycorrelates length informationto be added to data from of radiationsacross manytaxa. Their testcom- topologies in comparisons of shapes of partic- bines the individuallyweak testsof differences ular trees. Page (1990) has pointed out that in sister-clade sizes across many taxa using both studies of biogeography and studies of Fisher's combined probabilitytest, each prob- host-parasitecospeciation askwhethertrees of

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differenttaxa are similar,and both make use gens are presented to the host), orwhere error ofthe same null models ofdiversification. This has more serious consequences for certain insighthas led to a common approach to these cells withinthe cell lineage. We are not aware questions, drawing directly on concepts of of any serious exploration of the use of tree tree shape (Page 1993a,c, 1996; Paterson et shape in this context, although it would cer- al. 1993). tainlyseem worthpursuing. Tree shape can also be applied to the study of population processes. Lineages-through- WHERE NEXT FOR TREE SHAPE? time plots can in theorybe used as an aid to Although the past decade has seen a flurry reconstructingthe population historyof a spe- of activityin studies of phylogenetic tree cies. This approach was pioneered by Nee et shape, we are not close to our ultimate goal: al. (1994b, 1995b), and has been applied to being able to account forat least some features data from virus populations (Harvey et al. of the diversityof life on Earth. This lack of 1995a; Holmes et al. 1995; Zanotto et al. 1996; answers does not, however, mean a lack of see also Holmes and Garnett1994; Harveyand progress. We are beginning to have a much Nee 1994b), and to data fromwhales (Nee et better idea of what the interestingquestions al. 1995b). Clough et al. (1996) used tree are, and how one might look for convincing shape to discriminatebetween possible repli- data to address them. We here consider some cation mechanisms in "populations" of retro- potentiallyfruitful avenues forfuture work on transposonswithin mammalian genomes. tree shape. Finally,cell lineage diagrams are close rela- tives of phylogenetic trees, and their shapes BIASES IN TREE SHAPE may be of considerable interest. Such trees Despite recent advances (see the section on show the historyof cells dividing and dying, patternsin tree balance, p 37), we do not have and the parallel to speciation and extinction a thoroughenough understandingof the vari- of lineages is obvious. Recent progress in de- ous biases that affectthe shape of estimated velopmental biology means that cell lineage trees. This is important,because we need to data are rapidlyimproving; a complete cell lin- know how much of the deviation of estimated eage tree is available for Caenorhabditiselegans trees from the Markov model needs macro- (Sulston et al. 1988), and smaller trees (show- evolutionaryexplanation and how much can ing descendants of particularcells) are being be laid to methodological problems. In a nut- worked out in organismssuch as leeches (e.g., shell,it seems thatfor well-supported trees the Shankland and Martindale 1992), zebrafish choice of estimation algorithmsis unimpor- (e.g., Eisen 1992), and Drosophila(e.g., Good- tant, but unreliable maximum parsimony man and Doe 1993). Here treeshape relatesto trees and possibly incomplete trees will be variation in the numbers of descendent cells more imbalanced than the underlying true traceable to differentmother cells (e.g., Stern- and complete trees. But how much, forwhat berg et al. 1992). The balance measures N levels of reliability,and what kinds of incom- and cr2 have important and straightforward pleteness? Existing compilations of complete biological implications for these trees, be- trees (Mooers 1995; Guyer and Slowinski cause they represent mean and variance in 1991) are few,and the assessmentof treerelia- numbers of cell divisionsper "adult" cell. Bal- bilityis currentlyvery difficult. So although in anced cell lineage trees minimize N (and cr2) theorywe know how to produce a perfectdata and perhaps, therefore,the total exposure of set forthe studyof treebalance (use onlycom- the genome to replication error;this may be a plete and well-supportedtrees), no such data good developmental strategyin tissueswhere set has yet been compiled. It is also possible replication error is particularly damaging that reliable and unreliable trees are being (e.g., in the germ line). In contrast,imbal- sampled from differentunderlying distribu- anced trees might be a good developmental tions of true trees; the resultsto date assume strategywhere change through such error is that all the underlyingtrees can be modeled advantageous (perhaps where antibodies are as equal-rate Markov trees. produced, or in a parasite where surfaceanti- We also do not know how robust estimates

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of diversificationparameters (see the section Furthermore,the continued poor fitof the on tree shape models which include time, p equal-rates-Markovmodel to data sets of esti- 41) are to error in branch-lengthestimation. mated trees suggests that the model should The entire endeavor rests on the realityof a not be used indiscriminately.We have alluded molecular clock, which may not be veryreal to thiswith reference to the studies of bias, as (Gillespie 1991). More molecular data, more well as to the studyof keyinnovation hypothe- realisticmodels of molecular change (Felsen- ses. This caution may also be extended to all stein 1993; Yang 1994), and more calibrations other areas of comparative biology that use withfossil data are needed in order to increase the Markovnull model to generate null distri- our confidence in the trees we use. Random butions of tree shapes (e.g., Losos 1994; Mar- errorin molecular data, even when the model tins 1996; Sanderson and Donoghue 1994). is correct and a clock is in effect,must surely affectdistributions of branch lengthsas itdoes TREE SHAPE, ECOLOGY, AND BIOGEOGRAPHY topologies (cf. Huelsenbeck and Kirkpatrick 1996). Incorporating branch-lengtherror es- We should soon be in a position to use pat- timates(Nei et al. 1985; Hasegawa et al. 1993) ternsin sets of estimatedtrees to testhypothe- into the tests of various macroevolutionary ses about ecology, biogeography,and specia- models is one possible avenue (Nee et al. tion. For instance, predictions about tree 1995b). We do not yet know whetherbranch balance could be drawnfromJablonski et al.'s lengtherrors will only make itmore difficultto (1983) onshore-offshorehypothesis. This hy- choose among alternativemodels (since many pothesis holds that for marine invertebrates, more may fitthe poorer data) or will, more originationrates are highestin deep-wateren- seriously, produce biased parameter esti- vironments.If deep-watermembers of a clade mates. speciate more often than shallow-waterones, imbalanced phylogenetictrees should result. SOPHISTICATED EVOLUTIONARY MODELS Are phylogeniesof marine invertebratesmore The Markov model has been well studied, imbalanced than those of groups lacking this but we are onlyjust beginning to understand regional bias in speciation? We do not know, patternsin tree shape expected frommore so- but intriguinglyBurlando (1990) reportedthat phisticatedevolutionary models (Heard 1996; taxonomiesof marine organismswere more im- Kirkpatrickand Slatkin1993; Losos and Adler balanced than those of terrestrialones [but 1995; Rogers 1996). Such an understandingis see Minelli et al. (1991:93); furthermore,we essential ifwe are to say more about patterns caution thatsome terrestrialgroups mayshow in estimated trees than merely that they do patterns analogous to the onshore-offshore notfitthe null model. Realisticshape behavior hypothesis(DiMichele and Aronson 1992) ]. from a particular detailed model could lead Other biogeographical contrastsare possi- to hypotheses(but not conclusions) about fac- ble. For instance, consider a lowland species torsaffecting speciation and extinctionrates. whose range is sequentiallydivided by the up- Such models should consider both ecological liftingof multiple, parallel mountain ranges (Heard and Hauser 1995) and biogeographi- (or a species expanding along a linear island cal Uablonskiet al. 1983; Page 1991) influences chain). would then be on diversification.For instance,the effectsof expected to produce an imbalanced tree. Ex- natural selection, ecological opportunity,or tending this argument, recolonization after mass extinction have not yet been incorpo- glaciation on continents with north/south rated into models of tree balance, and the versuseast/west mountain chains should pro- studyof theireffects on branch lengths is still duce differenttree balance patterns.For a ma- in itsinfancy (Harvey et al. 1994). As the evolu- rine ancestor with populations isolated by tionarymodels we use improve,studies of tree postglacial isostatic rebound in similar-aged shape may have important things to tell us lakes along a coastline [e.g., the threespine about macroevolution; for instance, patterns stickleback Gasterosteusaculeatus complex in tree balance may help distinguishpunctu- (Schluter and McPhail 1992) ], we mighthave ated equilibriafrom gradualism (Heard 1996). yetanother expectation: ifthe ancestralpopu-

This content downloaded from 131.202.42.30 on Fri, 26 Apr 2013 09:59:50 AM All use subject to JSTOR Terms and Conditions 50 THE QUARTERLY REVIEW OF BIOLOGY VOLUME 72 lation gave rise to many descendants at the CONCLUSION same time,the historyof the separate lineages Nothing is more fundamental to biology is not one of consecutivebifurcations, and the than the search for the processes responsible PDA model may be the best representation. for the diversityof life on Earth. Historically, The same prediction could be made forareas the fossilrecord offeredthe main evidence of the workingsof these processes; Darwin de- of high reliefthat are affectedby cooling peri- cried the niggardlinesswith which it offered ods during Milankovitchcycles: high levels of up that account. However, the processes that allopatry owing to range contraction should generated the diversityof life on Earth have produce diversificationamong taxa, and the etched theirsignal not onlyin the fossilstrata resultingtrees may be indistinguishablefrom but also in the shapes of phylogenetictrees of the PDA expectation (since no tree-likepro- extant organisms. If the estimated trees that cess of diversificationactually occurred). Vrba we produce give a clear view of thissignal, we would do well to look thatway.More complete (1992) has presented a series of such hypothe- and more accurate treesare clearlyneeded, as ses concerning the effectof climatechange on is theoretical exploration of more sophisti- the tempo and mode of diversification,and cated evolutionarymodels. severalof these lead to tree shape predictions: her turnover-pulsehypothesis, for example, ACKNOWLEDGMENTS predicts that diversificationshould be rapid, We thankPaul Harvey,John Huelsenbeck, Andy Purvis,and Dolph Schluterfor perceptivecom- and hence reconstructed branches will be mentsand suggestions.Aixa Alfonso and Jeff Den- many and short during periods of climate burghelped orient us to thecell lineage literature. change. Comparisons of tree balance among We weresupported in partby Izaak WaltonKillam PostdoctoralFellowships at theUniversity of British groups withdifferent biogeographical histor- Columbia.AOM receivedadditional support from ies can be used to testvarious models of bio- an E B Eastburn(Hamilton Foundation) Postdoc- geographically-drivenallopatric speciation. toralFellowship.

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