ARTICLES - Boston University and Barton 2001...ARTICLES Comparative Methods for Studying Primate Adaptation and Allometry CHARLES L. NUNN AND ROBERT A. BARTON In this article, we review

ARTICLES

Comparative Methods for Studying PrimateAdaptation and AllometryCHARLES L. NUNN AND ROBERT A. BARTON

In this article, we review develop-ments in comparative methodologythat have emerged in the last fifteenyears, with particular emphasis on theimportance of incorporating phylog-eny into comparative studies. We de-fine “comparative study” as meaninganalysis of trait variation acrossrather than within species, with theaim of testing hypotheses or generat-ing new ones.11 We provide informa-tion on how to implement phyloge-netic comparative methods, includingavailable computer programs (Box 1).

For reasons of space, this review fo-cuses mainly on the most commonlyused methods, namely the method ofindependent contrasts12 and the con-centrated changes test.13 Readers in-terested in other methods may wish toconsult longer or more focused re-views.10,14,15

WHY INCORPORATEPHYLOGENY IN COMPARATIVE

STUDIES?

In recent years, biologists haveidentified many possible methods forthe analysis of comparative data.5,10,15–19

There has been much debate aboutthe validity of these different methodsin biological anthropology20,21 andother fields such as ecology.22–24 Al-though this debate has provided im-portant insights, a consensus hasemerged that comparisons must in-corporate information about the phy-logenetic relationships among thespecies under consideration.

Why is phylogeny necessary? Thereare three interrelated answers to thisquestion. First, phylogeny allows theidentification of independent data

points. The concept of independenceis as important for comparisonsacross species as it is for experimentaland observational studies within spe-cies.25,26 Closely related species tendto share traits because of their recentcommon ancestry,10,27 but we can bemore confident that a trait is an adap-tation if it has evolved repeatedly,rather than once, in association withsome other trait or environmental at-tribute.28 Thus, it may be incorrect toconsider a trait shared by multiple ex-tant species as independent, andcounted as multiple degrees of free-dom, if it is shared among speciesthrough common descent rather thanindependent origin.10

Second, the usual aim of a compar-ative study is to document correlatedtrait evolution.10 Hypothesizing that adependent variable Y, such as brainsize, is adaptively linked to an inde-pendent variable X, such as socialgroup size, implies that the two vari-ables have evolved together. Phyloge-netic information allows us to test thishypothesis directly.

Finally, incorporation of phylogenyreduces the effects of unmeasuredconfounding variables. Such variablesare particularly problematic whenshared through common descent.Felsenstein12 provided a hypotheticalexample to illustrate how ignoringphylogeny can lead to spurious results(his Figs. 5–7). We provide a real ex-ample in primates involving the rela-tionship between body mass andgroup size,2,29 which we also use toillustrate the methods discussed be-low. Conducting the analysis with spe-cies data points, there is a strong, pos-itive relationship between group sizeand body mass in primates, withlarger-bodied species living in larger

Charles Nunn is a Research Associate inthe Department of Biology at the Univer-sity of Virginia. His current research fo-cuses on the macroevolutionary correlatesof disease risk in mammals and methodsfor analyzing host-parasite trait evolution(http://faculty.virginia.edu/charlienunn).Email: [email protected] Barton is a Reader in Anthropol-ogy, and convenor of the EvolutionaryAnthropology Research Group at the Uni-versity of Durham, UK. His recent re-search uses comparative methods tostudy brain evolution. Email: [email protected]

Evolutionary Anthropology 10:81–98 (2001)

A well-known comparative biologist was once asked by a field biologist whetherthe latter’s detailed and painstaking field study of orangutan behavior, carried outover many years, qualified as an example of the comparative method. “No,” repliedthe comparative biologist, “that’s an anecdote.” The reply is somewhat harsh, asuseful comparisons can be conducted both within and across species. The replydoes emphasize, however, that analysis of patterns across species is fundamentalto the study of adaptive evolution, particularly when variation needed to testhypotheses is present only at this interspecific level.1–5 Examples in primatologyinclude the occurrence of female sexual swellings in species with habitually mul-timale, rather than single-male, breeding systems,6,7 the relationship betweenpolygynandrous mating and relatively large testes size,3,8 and the associationbetween brain size and social group size.9 Thus, in many cases, interspecificvariation is required to test adaptive hypotheses.10

Evolutionary Anthropology 81

groups (b 5 0.326, F1,105 5 29.4,P , 0.0001; data from Nunn andBarton30 and Smith and Jungers31).However, this relationship is con-founded by activity period and sub-strate use, as shown in Figure 1. Thus,within activity-substrate categories, norelationship is found between femalebody mass and group size (nocturnalspecies: F1,10 5 0.10, P 5 0.76;diurnal-arboreal species: F1,70 5 0.30,P 5 0.58; diurnal-terrestrial spe-cies: F1,21 5 0.32, P 5 0.58; data

on activity period and substrateuse updated from Nunn and vanSchaik29).

A plausible adaptive hypothesisfor the pattern in Figure 1 is thatdiurnal primates reduce predationrisk through gregariousness andtherefore live in larger groups thando nocturnal species, which avoidpredation through crypsis. Terres-trial species experience increasedpredation risk and are thereforelarger in body size and live in even

larger groups.2,29 Hence, the truecausal variables are likely to be ac-tivity period, substrate use, and bothof these variables’ interactions withpredation risk. All of these variablestend to be shared through commondescent (for example, all baboonspecies are terrestrial, have largerbodies, and probably experiencegreater risk of predation, yet thesetraits have not been acquired inde-pendently among these species). Infact, as we show below, there is nosignificant relationship betweenbody mass and group size once phy-logeny is taken into account. Be-cause so many variables interact inbehavioral, ecological, and morpho-logical studies, confounding vari-ables are a common problem incomparative biology.

Computer simulation studies havedocumented the magnitude of statis-tical errors that result when phyloge-netic information is ignored.32–37 Theeffects are staggering. A recent simu-lation study, for example, showed thatType I error rates (the probability of

rejecting a true null hypothesis) canbe as high as 44% when phylogeny isignored, compared to an expected er-ror rate of 5%.37 In other words, anaıve comparative analysis, as in Fig-ure 1, can be up to nine times morelikely to detect a significant patternwhen, in fact, no relationship exists. Itis even theoretically possible for anonphylogenetic analysis to indicate astatistical relationship that is in theopposite direction from the true evo-lutionary relationship.38 Moreover,

Box 1. Implementing Phylogenetic Comparative Methods

Many computer programs have been developed to implement phylogeneticcomparative methods. In searching for the latest programs, a good place tostart is Joe Felsenstein’s web page (http://evolution.genetics.washington.edu/phylip/software.html). The CAIC computer program,53 which runs on a Macin-tosh, calculates contrasts for continuous traits and also allows analysis ofmixed data using the BRUNCH algorithm (see Box 3). The latest version ofCAIC (v. 2.6.2) is available from http://www.bio.ic.ac.uk/evolve/software/caic/index.html. Options for non-Macintosh platforms include PDAP44 (informationavailable at: http://www.wisc.edu/zoology/faculty/fac/Garland/PDAP.html),which runs on a PC, and COMPARE (http://darkwing.uoregon.edu/;compare4/), which is web-based and therefore runs on multiple platforms.Finally, PHYLIP also runs on a wide range of machines, and it providestree-building methods (http://evolution.genetics.washington.edu/phylip.html).

Readers may find a variety of other methods useful for particular ques-tions.10 Phylogenetic autocorrelation methods can be used to assess whethera trait is correlated with phylogeny and can generate “phylogeny-free” valuesfor comparative studies.92,108 This approach can be implemented in the com-puter package COMPARE or by using the program Phylogenetic Autocorre-lation (ftp://ftp.math.utk.edu/pub/luh/PA.hqx). Grafen’s54 Phylogenetic Re-gression program may be useful for some comparative studies (http://users.ox.ac.uk/;grafen/phylo/). Moreover, similar approaches have beendeveloped.15,18,67 Pagel’s program Discrete66 can be used to test for corre-lations among discrete variables. Finally, new methods of reconstructingancestral character states with confidence limits, for example, using maxi-mum likelihood, can be implemented using several programs, among themCOMPARE, PDAP, or Schluter’s81 program ANCML, available from http://www.zoology.ubc.ca/;schluter/ancml.html).

All of these methods require as input a phylogenetic hypothesis. At present,many consider the composite estimate of phylogeny given by Purvis26,55 to bethe best option for primate comparative studies. One important advantage ofthis primate “supertree”109 is that branch length estimates are provided, arequirement of many methods. For 203 species of primates in the Corbet andHill110 primate taxomony, the Purvis phylogeny has 160 resolved nodes. Moregeneral information on supertrees is available.109,111 Web sites for recentphylogenies are TreeBase (http://www.herbaria.harvard.edu/treebase/) andthe Tree of Life (http://phylogeny.arizona.edu/tree/phylogeny.html). Sequenceinformation for primates and other species can be obtained from GenBank(http://www.ncbi.nlm.nih.gov/Genbank/GenbankOverview.html). The data-sets used in this paper, along with links to many of the web sites providedhere, can be obtained from the first author’s web site: http://faculty.virginia.edu/charlienunn.

Computer simulationstudies havedocumented themagnitude of statisticalerrors that result whenphylogeneticinformation is ignored.The effects arestaggering.

82 Evolutionary Anthropology ARTICLES

the statistical power to detect associ-ations is reduced when phylogeny isignored.32,33,37 This conclusion runscounter to the commonly expressedopinion that nonindependence is sim-ply a “degrees of freedom” problem,one in which phylogenetic compara-tive methods are thought to reducethe number of data points for analysisand therefore result in lower statisti-cal power. Although some phyloge-netic comparative methods do appro-priately result in fewer degrees offreedom, the most commonly usedcomparative method, independentcontrasts, has the same degrees offreedom as a species analysis whenthe phylogeny is fully resolved.52

The computer simulations also il-lustrate an important assumption ofnonphylogenetic studies. When usingspecies values with no control fortheir historical relationships, the in-vestigator assumes that the datapoints in the study are statistically in-dependent. This is equivalent to as-suming that the species are all equallyrelated to one another and thereforelinked by a “star phylogeny,” with allbranches emanating from a single an-cestor.12 This assumption is clearly in-valid. Thus, it is not surprising thatimperfect phylogenetic informationoften provides better statistical per-formance than ignoring phylogeny en-tirely.33

PHYLOGENETIC COMPARATIVEMETHODS: AN OVERVIEW

Comparative analysis requiresinformation on phylogeny and ameans to reconstruct evolutionarychange.10,12,14,39,40 Our confidence in acomparative test is strengthenedwhen the phylogeny is well supportedor when alternative models of charac-ter evolution, using several plausiblephylogenies, give similar results.10,41

In many cases, it is important that thephylogeny be reconstructed based ontraits that are independent of thequestion at hand, although the effectof this should be considered on a case-by-case basis.42 Many phylogeneticapproaches to comparative testingalso make assumptions regardingbranch lengths, or the amount of timecorresponding to each branch on thephylogeny.12

Although it may sound obvious, thefirst step in a comparative study is tostate the hypothesis and its predic-tions. There is a good reason for em-phasizing this step in comparativebiology. Explicit formulation of pre-dictions distinguishes one use of com-parative methods, namely hypothesistesting, from another equally valid useof comparative methods to generatehypotheses.7,10,11 The danger is that inexploratory analyses aimed at gener-ating hypotheses, several comparativepatterns are likely turn up significant

and then inadvertently “become” apriori hypotheses, written up at a laterstage as if the investigator had explic-itly tested a hypothesis. Instead, if thestudy is exploratory, then the hypoth-eses that are formulated should bestated as such. These hypotheses canthen be tested independently, either incomparative study of another appro-priate group of organisms or by test-ing independent comparative, obser-vational, and experimental predictionsin the clade from which the hypothesiswas generated.43

After formulating the hypothesisand collecting relevant data, the nextstep is to decide on the type of methodto use. This is a critical step: it struc-tures the overview of methods that fol-low because some phylogenetic com-parative methods are appropriate fordiscrete data, others are appropriatefor continuous data, and yet othersare appropriate for a combination ofdiscrete and continuous data. Contin-uous data can take any quantitativevalue, subject to measurement preci-sion, and include variables such asbody mass, group size, and longevity.Regression, correlation, and principalcomponents analysis are statisticaltests commonly used to examine rela-tionships among continuous vari-ables. Discrete data are those thathave integer values. In phylogeneticcomparative studies, these values aretypically dichotomous, coded as 0 or1, although more than two characterstates are possible. For example, mostprimate species can be classified asnocturnal (5 0) or diurnal (5 1). How-ever, cathemerality could be added asan intermediate value to give three to-tal character states, with adjustmentof character states such that noctur-nality 5 0, cathemerality 5 1 and di-urnality 5 2. Discrete data commonlyare analyzed using tests of indepen-dence such as the Chi-square test, al-though different statistical tests areusually required when taking phylog-eny into account.

A final situation concerns a mix ofcontinuous and discrete data types.These data would normally be ana-lyzed using analysis of variance(ANOVA) or, if there is more than onecontinuous variable, analysis of co-variance (ANCOVA). Although some ofthese specific tests can be used in com-

Figure 1. Association between body mass and group size in primates. Each data pointrepresents a different species and is identified according to activity pattern and substrateuse. A single three-value discrete variable is possible in this case, as all nocturnal primatespecies are arboreal.29 We used female body mass rather than averaging sometimesmarkedly different values for males and females in dimorphic species.

ARTICLES Evolutionary Anthropology 83

parative tests, for example by generat-ing null distributions using computersimulation,44 alternative approachesbased on independent contrasts areavailable.

This discussion brings up the issueof data collection and scoring of char-acters because discrete data often, butnot always, represent an underlyingcontinuous distribution of trait valuesin a discontinuous way.44,45 Compar-ative tests using continuous measuresare often better able to detect cross-species patterns because they providemore fine-grained variation to detectpatterns.44,46 Moreover, continuousvariables are more likely to meet para-

metric statistical assumptions thanare discrete categorizations. When-ever possible, then, continuous datashould be used to test comparativepredictions. In what follows, we con-sider methods that are appropriate forthe different data types, concludingwith a discussion of multivariatemethods.

All Continuous Data

When all variables are continuous,the preferred method is independentcontrasts (Box 2). Contrasts are differ-ences in trait values between speciesor higher nodes. As such, they repre-

sent independent evolutionary changesince two species last shared a com-mon ancestor and thus deal with thenonindependence of species values.Independent contrasts can be used ex-plicitly to test hypotheses predictingcorrelated evolutionary change. Figure2 provides an example using contrastsin basal metabolic rate and contrasts inbody mass. This plot can therefore beinterpreted as evolutionary increases inbody mass are correlated with evolu-tionary increases in basal metabolicrate.

At first glance, treating differencesin trait values (Box 2) as a measure ofevolutionary change can be conceptu-

Box 2. Phylogenetically Independent Contrasts

Independent contrasts are calcu-lated as differences between pairs ofspecies, between a species value andan ancestral node, or between highernodes. Differences are calculated be-ginning at the tips of the tree. In thisexample, contrast a is calculated asthe difference between species i andii, while contrast b is calculated as thedifference between species iv and v.Contrasts then are calculated usinghigher nodes (that is, the “mixed”contrast c and internal contrast d),with values reconstructed as weightedaverages of the descendent taxa (in-dicated on the phylogeny). Contrastsare thus calculated up the tree, max-imizing the number of possible con-trasts while using each branch nomore than once.

With this phylogeny and data set,the unstandardized contrasts are:

contrasta

contrastb

contrastc

contrastd

X-variable 2 2 2 9

Y-variable 0 22 2 8

The direction of subtraction for cal-culating contrasts is arbitrary. Forplotting contrasts, however, someauthors have recommended forcingthe independent variable to be posi-tive.52 Thus, we forced the X-variablecontrasts to be positive in this exam-

ple, with the direction of subtractionretained for calculating the Y-variablecontrasts. For example, contrast d iscalculated as 16 2 7 5 9 for X. Main-taining the direction of subtractiongives 10 2 2 5 8 for Y. With fivespecies, there are four contrasts onthis fully resolved phylogeny. Meth-ods for standardizing these contrasts(that is, incorporating branch lengths)are explained in the text and else-where.10,12,52

These contrasts are independent ofone another and can be examinedusing standard statistical packages.Because the expected value of a con-

trast is 0, regressions and correla-tions must be forced through the or-igin.10,52 Before forcing the interceptto 0, however, we recommend thatthis be tested statistically, as inter-cepts that differ significantly from 0may indicate violations of the methodor a nonlinear underlying relation-ship.10 The statistical and evolution-ary assumptions of contrasts shouldalso be tested using established pro-cedures.10,52,53 Other assumptions ofthe method include correct topology,correct branch lengths, a Brownianmotion model of evolution, and negligi-ble intraspecific variation.14


ally difficult. It might seem more intu-itive to reconstruct the ancestralnodes of a phylogeny and then, foreach branch in the phylogeny, calcu-late change from deeper to shallowernodes or to species values. One prob-lem with this approach, however, isthat for a fully resolved phylogenywith n species, there are 2n-2branches, therefore giving more de-grees of freedom than there are spe-cies values. In other words, two non-independent observations would becalculated for each node. By compar-ison, contrasts give n-1 degrees offreedom with a fully resolved tree.Moreover, only one degree of freedomis lost in regression and correlationanalyses of contrasts because a con-trasts plot does not have an intercept(see Box 2). Thus, a contrasts analysisloses two degrees of freedom, one forcalculating contrasts and one for esti-mation of the slope, which is identicalto analysis of species values. (In re-gression of species values, for exam-ple, one degree of freedom is lost forthe slope estimate and one degree of

freedom for the intercept). However,additional degrees of freedom may belost in contrasts analysis when thephylogeny is incompletely resolved.This is true, for example, for “soft”polytomies47 that reflect ignorance ofthe true branching pattern.48,49

The method of independent con-trasts can also help control for con-founding variables shared throughcommon descent, although it cannotbe assumed to do so completely. Forexample, when the relationship be-tween group size and body mass isexamined with contrasts (Fig. 3), thestatistical results differ sharply fromthe strong and highly significant rela-tionship calculated from species val-ues (b 5 0.16, F1,94 5 2.94, P 50.09; see also Barton50). Visual inspec-tion of the contrasts reveals that atleast one data point, an outlier, mayexert excessive leverage on the slopeestimate and statistical results (Fig.3). We hypothesized earlier that diur-nality and terrestriality explain thestatistical association in Figure 1.When we control for the effects of

these variables by identifying and ex-cluding contrasts with evolutionarytransitions to diurnality and terrestri-ality, the body mass-group size rela-tionship weakens further (F1,77 5

1.42, P 5 0.24). Hence, this exampleshows that by examining evolutionary

change, contrasts analysis helps dealwith unmeasured confounding vari-ables, but that consideration of theseconfounding variables when they areknown and measurable further re-duces their effects.51

Another source of scatter arises fromhow the contrasts are standardized,

When there is only oneevolutionary transitionbetween ecologicalcategories, the truesample size is effectivelyone, reducing largenumbers of speciesvalues to a singledegree of freedom. Inhuman evolution, forexample, the correlationbetween less-woodedhabitats and bipedalismmay be entirelydependent on oneevolutionary transition atthe root of the hominidclade. This is why it isdifficult to makestatistical inferencesabout the adaptivesignificance ofbipedalism or, indeed,any unique hominidtrait, perhaps explainingwhy “just so” storiesabound.

Figure 2. Association between basal metabolic rate and body mass in primates. Contrastsin basal metabolic rate are positively correlated with contrasts in mass (r2 5 0.92, t 5 14.2,P , 0.0001). The slope of the line and the deviations from it (residuals) can be interpreted inthe conventional way. For example, Kleiber’s Law112 states that basal metabolic rateincreases to the 0.75 power of mass, and the slope in this figure matches this predictedvalue perfectly (confidence interval: 0.64–0.86). Large residuals indicate evolutionarychanges in basal metabolic rate that are either larger (positive residuals) or smaller (neg-ative residuals) than predicted by changes in mass, and these deviations may be associ-ated with specific ecological factors.113 Basal metabolic rate data are those listed asmeeting reliability criteria in Ross.113


which raises issues regarding the evo-lutionary model that implicitly under-lies most phylogenetic comparativemethods. Computer programs typi-cally standardize contrasts by divid-ing each contrast by the sum of itsbranch lengths. These branches arefurther adjusted by increasing thelengths of branches deeper in thetree.12 Dividing by branch length ef-fectively changes the placement of thecontrasts relative to the origin. Forexample, dividing X and Y contrastsby a larger value, representing longerbranches, places the data point in abivariate plot closer to the origin, giv-ing it less statistical leverage on theoverall relationship. The underlyingassumption is that on longer branchesmore evolution is likely to take place,leading to greater change in X and Y.These contrasts, therefore, would leadto problems of heteroscedasticity (dif-ferent variances) if they were not stan-dardized. Lengthening branches todeeper nodes also places these con-trasts closer to the origin, effectivelygiving them less leverage because theline is forced through the origin,which may be appropriate if recon-struction of ancestral character statesis less certain for these deepernodes.12 It should be noted, however,

that such “reconstructions” are reallyweighted averages of descendent taxa,which are necessary to maintain theindependence of the contrasts.

Hence, the main reasons to stan-dardize independent contrasts involvethe statistical problem of heterosce-dasticity and reduced certainty of an-cestral states. The usual means ofstandardization is based on a modelof evolution known as Brownian mo-tion.12,45 This model assumes that foreach branch on the tree evolutionarychange is independent of previouschange and drawn from a normal dis-tribution with a mean of zero, suchthat positive and negative changes areequally likely. The variance of this dis-tribution is proportional to the lengthof the branch on which change tookplace, allowing standardization byBrownian motion to control for greaterchange on longer branches.

We can empirically test the assump-tions to determine whether contrastsare properly standardized under dif-ferent transformations of the data andbranch lengths.52,53 This is similar totesting the assumptions of parametricstatistical tests such as the normalityassumption, in that appropriate trans-formation of the data and branchlengths can often be used to meet the

assumptions.35,36 Common transfor-mations include taking logarithms ofthe data or branch lengths and seem-ingly more radical transformations ofbranch lengths, such as the assump-tion of “speciational” change (branchlengths set equal throughout thetree44), or transformation of branchesas a function of the number of speciesbelow each node.54 In the contrastsplot in Figure 3, for example, wefound that log-transformed data and aspeciational model of evolution bestmet the assumptions of contrasts. Toillustrate the effect of using anotherassumption, we repeated the analysiswith the raw data and a “gradual” evo-lutionary model (branch lengths setproportional to time since diver-gence55). These assumptions result ingreater scatter of some points (Fig. 4),but the conclusion that no relation-ship exists is maintained.

Combination of Continuousand Discrete Data

Comparative analysis commonly in-volves a combination of continuousand discrete data. A good example is acomparative study of home-range sizein carnivores and ungulates by Gar-land et al.44 that tested the hypothesisthat species of carnivores, as preda-tors, require larger ranging areas thando closely related nonpredatory mam-mals. These authors found a highlysignificant difference when using spe-cies values and controlling for bodymass by analysis of covariance(F1,46 5 23.97, P , 0.001), but thedifference in home range size was notsignificant when phylogeny was incor-porated into the analysis (P 5 0.15 to0.29, range based on simulation testsusing different assumptions). This ex-ample therefore illustrates the funda-mental difficulty in analyzing discretedata: When there is only one evolu-tionary transition between ecologicalcategories, the true sample size is ef-fectively one, reducing large numbersof species values to a single degree offreedom. In human evolution, for ex-ample, the correlation between less-wooded habitats and bipedalism maybe entirely dependent on one evolu-tionary transition at the root of thehominid clade. This is why it is diffi-cult to make statistical inferences

Figure 3. Association between body mass and group size using independent contrasts.When the data from Figure 1 are examined using independent contrasts, a nonsignificantpositive slope is found (see text for details). This plot uses contrasts calculated assumingequal branch lengths (a “speciational” model), with the data log-transformed. The arrowpoints to the outlier discussed in the text.


about the adaptive significance of bi-pedalism or, indeed, any unique hom-inid trait, perhaps explaining why“just so” stories abound. There areways to examine continuous traits sta-tistically over a single transition in adiscrete character, but extremelylarge differences may be needed to ob-tain significant results.44

In many cases involving continuousand discrete data, however, more thanone transition exists between classesof discrete data. Each of these transi-tions potentially provides an indepen-dent data point, and the average effectcan be tested statistically. One com-monly used approach in this situationis a variant on independent contrastsknown as BRUNCH.53 This methodidentifies the discrete trait as the in-dependent variable. It then calculatescontrasts with the direction of sub-traction set such that the discrete vari-able is positive, retaining the directionof subtraction for contrasts in the con-tinuous variable (Box 3). The predic-tion to test is whether contrasts in thecontinuous dependent variable areconsistently positive or negative over

evolutionary increases in the discreteindependent variable.

For example, we proposed earlierthat transitions to diurnality and ter-restriality result in increased bodymass and group size, leading to a spu-rious relationship between these twocontinuous variables. With a three-part discrete scoring of nocturnal spe-cies (5 1), diurnal-arboreal species(5 2), and diurnal-terrestrial species(5 3), we used the CAIC computerprogram53 to examine transitions inbody mass and group size over evolu-tionary shifts to diurnality and terres-triality. These discrete values cantherefore be considered a rankedscore relative to our expectations ofgroup size. We identified a total of 17contrasts with reconstructed changesin the discrete variable. The directionof subtraction for both variables is setsuch that the discrete variable is pos-itive (for example, subtracting a noc-turnal clade’s value from a diurnal-arboreal clade’s value). The expectedmean of contrasts in the dependent(continuous) variable is zero, but wefind a mean increase in body mass of0.10 and a mean increase in group

size of 0.11 (using log-transformedvalues). These values indicate thatevolutionary transitions to diurnalityand terrestriality are associated withevolutionary increases in body massand group size. We need to test, how-ever, whether these means differ sig-nificantly from expectations under thenull hypothesis of no consistent pat-tern of change (that is, a mean of 0).

The statistical test typically is con-ducted in one of two ways.53 First, anonparametric test, the sign test, canbe used to determine if observed in-creases are more common than ex-pected by chance. In this case, the nullhypothesis is an equal number of gainsand losses distributed binomially.56

The null hypothesis can be rejected:15 of 17 contrasts in body mass arepositive (P , 0.02), and 13 of 17 con-trasts in group size are positive (P ,0.05). Second, the observed meanscan be tested versus the null hypothe-sis of 0 using a t-test. Again, the nullhypothesis can be rejected (groupsize: t 5 3.12, P 5 0.007; femalebody mass: t 5 3.40, P 5 0.004). Inchoosing among these tests, the non-parametric test has the advantage that

Box 3. Combinations of Discrete and Continuous Data: The BRUNCH Algorithm

The CAIC computer program canbe used to examine combinations ofcontinuous and discrete data usingthe BRUNCH algorithm.53 In the fol-lowing example, there are two recon-structed transitions, or contrasts, inthe discrete variable, labeled a and b.Contrasts in this variable are forcedto be positive; thus, for contrast a, thetrait value for species vi (5 0) is sub-tracted from species vii (5 1), givingan unstandardized contrast valueof 11.

Contrasts in the continuous vari-able are calculated only overbranches with transitions in the dis-crete variable. The direction of sub-traction is retained for the continuous(dependent) variable, giving an un-standardized contrast of 5.8 for thevii 2 vi contrast. A similar procedureis followed for the other discrete tran-sition, at b, which involves a highernode.

The hypothesis to test in this case

is whether transitions from 0 to 1 re-sult in consistent positive or negativechanges in the dependent variable,as indicated by their contrasts. Thetext describes two statistical tests,one based on the nonparametric signtest and the other based on a t-test, todetermine whether the mean contrastdiffers significantly from zero. There

are too few contrasts to obtain a sig-nificant result with a sign test in thiscase, although both contrasts arepositive (at a, after standardizationassuming equal branch lengths,DY 5 2.9, at b, DY 5 3.23). A t-test,however, gives a significant result(mean of a and b 5 3.065, t 518.84, P 5 0.03).


fewer assumptions are made. How-ever, at least six gains are required toshow significance.56 By comparison,the t-test can work with smaller sam-ples and may have higher statisticalpower, although a low varianceamong contrasts can lead to signifi-cant results with surprisingly small P-values (for an example, see Box 3).

Discrete Variables

Ridley16 provided the first methodfor explicitly incorporating phylogenyin the study of discrete traits. Hismethod has been used to addressquestions in primate biology such asthe association between breeding sea-sonality and single-male groups.59

Other methods, however, have beenused more commonly since Ridley’spioneering research.

Maddison’s13 concentrated changestest is probably the most commonlyused method for testing statistical as-sociations between two discrete vari-ables. It is described thoroughly else-where10,13 and is implemented in thecomputer program MacClade.60 Givena phylogeny and the distribution oftwo traits, one identified as indepen-

dent and the other dependent, themethod calculates the probability ofgetting a certain number of gains inthe dependent trait on branches witha particular character state (“distin-guished branches”) in the indepen-dent trait (Fig. 5). This probability,which serves as a P-value for statisti-cally testing the association of the twocharacters, can be solved analyticallyfor small numbers of species, as inFigure 5. For larger phylogenies andmore complicated hypotheses of traitevolution, a simulation procedure iseasily implemented in MacClade.60

The concentrated changes test can po-tentially identify causality; that is, thetemporal order of trait changes. How-ever, this requires that the two traitsare not reconstructed as changing si-multaneously. It also requires accu-rate estimation of ancestral characterstates.61

To illustrate how the concentratedchanges test is used, we return to thepreceding example, focusing on thetwo discrete variables of activity pe-riod and substrate use. No nocturnalprimate species are classified as ter-restrial,29 explaining why we com-bined these two discrete variables into

one variable with three, rather thanfour, character states (nocturnal, diur-nal-arboreal, and diurnal-terrestrial;see Fig. 1). If each species is treated asindependent, as in the “old” compar-ative approach, activity period andterrestriality are significantly associ-ated (Chi-square 5 8.20, degrees offreedom 5 1, P 5 0.004; 188 species,data updated from Nunn and vanSchaik29). But this test ignores thefact that activity period is recon-

structed as having changed only fourtimes in the evolutionary history ofprimates. Thus, we used the concen-trated changes method to test whetherterrestrial substrate use is signifi-cantly concentrated on branches ofthe tree characterized by diurnality.

To implement the concentratedchanges test, we first mapped the twocharacters, activity period and sub-

Figure 4. Improperly standardized contrasts. Using the same data as in Figures 1 and 3,contrasts were calculated assuming that branch lengths were proportional to time55 andusing raw (unlogged) data. The scales of the X and Y-axes therefore differ from those inFigure 3. These changes resulted in a different spatial distribution of the data points, withmore outliers, but the general conclusion remains: There is no relationship between bodymass and group size once phylogeny is taken into account. This example highlights theneed to test the assumptions of independent contrasts.52,53

We agree that moreprogress is possible ifhypotheses are testedwith variation at allpossible levels, includingvariation amongspecies, populations,groups, and individuals.In general, however,intraspecific variationtends to obscurecomparative trendsrather than to createspurious ones. By thislogic, intraspecificvariation may explainwhy some results arenonsignificant, but it isnot clearly a legitimatecriticism when a well-supported pattern isfound.


strate use, onto a phylogeny. Mac-Clade requires a fully bifurcating treeto implement this test, yet the phylog-eny most commonly used to conductcomparative studies of primates hasseveral unresolved nodes.53 Thesepolytomies were therefore randomlyresolved using MacClade, although wecreated ten different random resolu-tions to examine the effect of differenttree topologies on the results. To ap-ply these tests for each tree, we set thedistinguished branches as diurnal(character state 5 1), because we wereinterested in testing whether terrestri-ality is significantly associated withthis independent character state. Weran 1,000 simulations, with nocturnalas the ancestral character state, andsimulated 7 gains of the dependentvariable (that is, the number of gainsreconstructed in MacClade). We arenot concerned with losses of terrestri-ality, so the losses dialog box was notaltered.

From these simulations, we calcu-lated the probability that seven gainsoccur on the diurnal branches. Withthe different phylogenies, the range ofresults was remarkably narrow butnot significant (P 5 0.22 to 0.26).Thus, in comparison to nonphyloge-netic analysis, we found that diurnal-ity and terrestriality are not statisti-

cally associated. For nonsignificantstatistical results, it is useful to con-sider how many gains of the indepen-dent variable are required to obtainsignificance, which is effectively aform of power analysis. In this case,the answer turns out to be about 14gains, which we determined by run-ning the simulations with progres-sively more gains in the dependentvariable.

A recent computer simulation studyhas shown that the concentratedchanges test has acceptable Type I er-ror rates,62 but the method has othershortcomings. For example, it re-quires a bifurcating tree and does notincorporate branch length informa-tion (see Sillen-Tullberg63 and Werde-lin and Tullberg64). Although theseproblems are minor relative to thebenefits, including ease of implemen-tation, several other methodologicaloptions are available for discretetraits. For example, Read and Nee65

provide an alternative method thatavoids many of the assumptions in-volved in the analysis of discrete com-parative data, including the model ofcharacter evolution. This method ex-amines pair-wise comparisons in taxathat differ in the independent variablesuch that comparisons are genuinelyindependent of one another. Their ap-

proach makes the fewest possible as-sumptions about evolutionary change.At the other extreme is a method devel-oped by Pagel,66 which explicitly mod-els trait evolution using a Markovmodel. Statistical significance is deter-mined using maximum likelihoodmethods. Pagel’s method also makesuse of branch lengths and, in theory,can identify causality even when twotraits are reconstructed as changing si-multaneously. A related version foranalysis of continuous characters15,67 isavailable.

Multivariate Analyses

Contrasts can be examined easilyusing multivariate statistical meth-

ods, including principal componentsanalysis.68 The CAIC computer pro-gram53 allows a user to select multiplevariables for calculating contrasts.Even in multivariate analyses, how-ever, the regression line is constrainedto pass through the origin.52,68 An im-portant statistical issue in multivari-ate analyses is a possible reduction insample sizes, as only species withinformation on all variables can beincluded in the analysis.53 Thus, vari-ables should be chosen wisely to max-imize the number of contrasts.

Figure 5. Maddison’s concentrated changes test. This test13 begins by identifying traits asindependent (X) and dependent (Y), and the character states of interest for each trait (inthis case, 1 for both traits). With this information, one calculates the probability of aparticular number of gains or losses in the “distinguished branches” of the tree, those withthe character state of interest in the independent variable. In this simple example, we areinterested in the probability of one gain in character state 1 for the dependent variable onbranches reconstructed as having character state 1 in the independent variable; that is,branches a, b, and c. To meet this condition, character state 1 in the dependent variablecould therefore evolve on any of these three branches. Because this tree has eight totalbranches, excluding the root, the probability is 3/8, or P 5 0.375.

Computer simulation hasshown that incorrectlyspecifying the topologyor branch lengths leadsto higher Type I errorrates. These simulationshave also shown,however, that failure toincorporate phylogeny,and thereby assuming astar phylogeny,produces an even lessdesirable outcome inthat Type I error ratesare usually increased.


For combined discrete and contin-uous data, several multivariate ap-proaches are possible. First, one cantreat an independent discrete variableas continuous and enter it along withthe other variables. In multiple regres-sion analysis of the example given ear-lier, activity period and substrate useaccount for significant variance ingroup size when treated as continuousvariables (b 5 0.33, F1,92 5 4.82,P 5 0.03 and b 5 0.23, F 5 8.81,P 5 0.004, respectively), but femalemass is not significant (b 5 2 0.006,F 5 0.003, P 5 0.96). These resultstherefore confirm that variables otherthan body mass account for variationin group size. Second, correlationsamong continuous characters can beinvestigated by examining only thosecontrasts with corresponding changesin discrete variables. Such a testwould identify whether alternative ex-planations can explain significant re-sults in a BRUNCH analysis. Thus, fo-cusing only on contrasts in the three-character activity period-substratecodes from the earlier example, bodymass and group size are not statisti-cally significant (F1,16 5 2.61, P 5

0.13), suggesting that activity periodand substrate use are responsible forthe comparative patterns. Finally,Grafen’s54 “phylogenetic regression”can be used to examine discrete andcontinuous independent variables in amultivariate context.

Approaches like analysis of covari-ance are available for three or morevariables, for example by using com-puter simulation methods developedby Garland and colleagues.44 Theseprograms can be implemented in thecomputer package PDAP, althoughvariants on the basic method thatavoid simulations are also possible.44

Simulation-generated null distribu-tions also provide a means to incorpo-rate phylogeny in novel statisticaltests of comparative hypotheses.69

At present, however, it is not possi-ble to analyze associations amongmultiple discrete traits in a phyloge-netic context. One approach might beto examine subsets of the phylogenywhere some potentially confoundingvariable is absent, but this would tendto reduce statistical power.

COMMONMISUNDERSTANDINGS OFCOMPARATIVE METHODS

Benton70 identified four types ofcritics of large-scale paleontologicalstudies. Not surprisingly, the sametypes of criticisms often are leveled atcomparative biologists who examinebroad evolutionary patterns. Ben-ton’s70 categories of critics, appropri-

ately altered for comparative studies,include the proofreader, who discov-ers errors in the database used by acomparative study and therefore be-lieves there are serious flaws in theconclusions; the trades unionist, whoaims to protect his or her field of re-search and cannot bear to have an“outsider” use data secondhand; theLuddite, who cannot stand new meth-

ods and the idea of taking vast data-sets and reducing them to simplegraphs; and the Utopian, who sug-gests that we have inadequate infor-mation to conduct comparative stud-ies, rendering the whole processpointless, although eventually such in-formation will become available.

Although there is some validity tothese caricatures, and some of thecriticisms should be taken seriously,Benton70 has excellent counter-argu-ments to each of these critics that alsoapply to comparative biology. Data-base errors noted by proofreaders, forexample, are a serious matter, butthey rarely alter conclusions. Follow-ing correction, in fact, the strength ofpatterns often improves, such thatregular “sloppiness in big data sets ac-tually strengthens the case for . . . pat-terns”70 (p. 256). Similarly, some da-tabases are too large for any oneperson to compile from first-handdata (the trades unionist), and we willnever have sufficient data to cover allspecies equally (the Utopian), espe-cially given current rates of extinc-tion.

A final issue relating to the tradeunionist should be considered. Somebiologists, particularly those with ac-tive field research, often claim that thecomparative approach ignores in-traspecific variation, and that thissomehow limits the conclusions of acomparative study when intraspecificvariation is unknown. We agree thatmore progress is possible if hypothe-ses are tested with variation at all pos-sible levels,71,72 including variationamong species, populations, groups,and individuals. In general, however,intraspecific variation tends to ob-scure comparative trends rather thanto create spurious ones.11 By thislogic, intraspecific variation may ex-plain why some results are nonsignif-icant, but it is not clearly a legitimatecriticism when a well-supported pat-tern is found.

The development of phylogeneticcomparative methods has given someof these critics new ammunition tofire at the comparative approach, in-cluding some criticisms by biologicalanthropologists.20,21,73 We considersome of these issues in what follows(see also Purvis and Webster26). Ourgoal is to clarify misconceptions while

. . . there is often somereluctance amongbiologicalanthropologists to relyon ancestral characterstate reconstruction.Incorrectly specifyingancestral states canobviously result inerroneous conclusionswhen examining thesequence ofevolutionary events, buterror in reconstructingancestral states seemsto be less of a problemfor contrasts. Thisdifference arisesbecause contrastsinvolve speciesdifferences, not theactual reconstructednodes.


providing further guidelines for im-plementation of these methods, espe-cially those based on independentcontrasts.

Phylogenetic Uncertainty: TreeTopology and Branch Lengths

Proofreaders find errors in phyloge-netic relationships, using these errorsto weaken the conclusions of a partic-ular study, while Utopians argue thatour knowledge of phylogeny, includ-ing both topology and branch lengths,is imperfect. Computer simulationhas shown that incorrectly specifyingthe topology or branch lengths leadsto higher Type I error rates. Thesesimulations have also shown, how-ever, that failure to incorporate phy-logeny, and thereby assuming a starphylogeny, produces an even less de-sirable outcome in that Type I errorrates are usually increased.32–37 Branchlengths may be particularly prone toerror, but it is important to rememberthat branch lengths mainly addressthe statistical issue of heteroscedastic-

ity. With appropriate transformationof data and branch lengths35,36,52 andanalysis of outliers,30 spurious resultsare less likely.

Sensitivity tests can be used to ex-amine the effects of different branchlength assumptions or topologies. Amore radical approach uses computersimulation to generate a large numberof random trees.74,75 If the results re-main consistent on a large proportionof these trees, then greater confidencecan be placed in the conclusions, al-though results should be interpretedwith caution.41,76

Another solution is to perform pair-wise comparisons that use informa-tion only from extant taxa (Fig. 6),thereby avoiding ancestral state re-construction.65,77–79 The problem withpair-wise comparisons is that manypotential comparisons are not used,thereby reducing statistical power. InFigure 6, for example, only four pair-wise comparisons are available,whereas independent contrasts wouldextract seven values for analysis. Themethod of pair-wise comparisons is

preferred for particular questions,however, such as when branch lengthinformation is critical to the hypothe-sis at hand.80

As a related issue, there is oftensome reluctance among biological an-thropologists to rely on ancestralcharacter state reconstruction. Incor-rectly specifying ancestral states canobviously result in erroneous conclu-sions when examining the sequence ofevolutionary events,39 but error in re-constructing ancestral states seems tobe less of a problem for contrasts.81

This difference arises because con-trasts involve species differences, notthe actual reconstructed nodes. Thus,errors in some ancestral states willmost likely affect the magnitudes ofspecies differences but not their sign,and only internal contrasts will be af-fected. This issue has been examinedempirically using a known viral phy-logeny, which was experimentallygenerated in the laboratory so that an-cestral states were known.82 The re-sults showed that reconstructed val-ues failed to match known values at

Figure 6. Pair-wise comparisons. When the phylogeny is insufficiently resolved, or when less confidence can be placed in ancestral statereconstructions, pair-wise comparisons are sometimes used.77 The method is illustrated here with the example of the correlation betweenmale and female number.46,78 With the key requirements that internal nodes are not reconstructed and branches are not used more thanonce, four pair-wise comparisons can be extracted from this phylogeny. It is often easiest to calculate pair-wise comparisons by hand, ascomputer programs will identify “mixed” contrasts (a species contrasted with a higher node; for example, Macaca fascicularis contrastedwith the reconstructed value for M. mulatta and M. fuscata).


internal nodes by wide margins formost traits, but contrasts analysisgenerally identified the evolutionarycorrelations among these traits.

Phylogenetic Uncertainty: TheUnderlying Evolutionary Model

To standardize contrasts, themethod of independent contrasts re-lies on an underlying model of traitevolution. In most cases, this Brown-ian motion model is likely to be anoversimplification. As noted, however,altering this model typically has littleeffect on the conclusions.

Recent work by Price51 and Harveyand Rambaut83 has examined a radi-cally different evolutionary modelthat may have implications for themethod of independent contrasts.Whereas the contrasts method as-sumes that traits evolve in a correlatedfashion down a phylogeny, this new“niche model” assumes that the traitsare correlated in niche space, withopenings of new niches and invasionby similar species leading to phyloge-netic topology (Fig. 7). This new modeltherefore focuses on the correlation oftraits in niche space, not on the corre-lation of evolutionary change. As mightbe expected, then, use of species valuesgives expected Type I error rates in sim-ulation of the niche model, whereascontrasts gives higher than expected er-ror rates.83

The niche model makes some sur-prising assumptions in that it playsdown the importance of phylogenetichistory, assumes that species valuesare constant through time, and ig-nores correlated evolutionary change.Important questions remain, but sev-eral lines of evidence suggest thateven this model will not lead to anabandonment of contrasts-based ap-proaches. First, the correlation be-tween species and contrasts valuesshould differ if the niche model is cor-rect, with lower correlations arisingfrom contrasts. When correlationsfrom species values and contrasts arecompared, however, they are remark-ably similar.24,51 Second, a simulationstudy that used diagnostic statisticssuch as those discussed earlier notonly detected violations of the Brown-ian motion model,83 but found thatincreased Type I error rates arise

through occasional outliers with highstatistical leverage (P. Harvey and A.Rambaut, personal communications).These empirical results therefore sug-gest that diagnostic tests and carefulexclusion of outliers may improve thestatistical properties of contrasts whenthe underlying evolutionary model isunknown. Finally, if we are explicitlyinterested in correlated evolution,which is how adaptive hypotheses areoften framed, then independent con-trasts is the method to use, as contrastsrepresent evolutionary change.

One benefit arising from research oncontrasts methodology is that biologists

have developed a variety of underlyingevolutionary models such as the nichemodel. At present, however, new evolu-tionary models are unlikely to lead toabandonment of independent con-trasts. Accepting that the niche modelreflects valid concerns83 does not pre-clude the use of independent con-trasts.84–86 Methods based on maxi-mum likelihood may provide a usefulapproach to comparative data gener-ated under the niche model.83,87

Statistical Power Is Too Low

Many researchers seem to believethat phylogenetic comparative meth-ods, including independent contrasts,reduce the degrees of freedom,thereby eliminating data points foranalysis.20,21 Moreover, we have heardresearchers say, “I ran the analysis us-ing species values and contrasts, butgot the same answer for both. I amtherefore going to use the species val-ues.” The reasoning seems to involvethe sentiment that phylogenetic com-parative methods result in fewer de-grees of freedom.

As noted earlier, however, a con-trasts analysis with a fully resolvedphylogeny has the same degrees offreedom as does analysis of speciesvalues.52 While some phylogeneticcomparative methods, most notablymethods dealing with discrete data,have fewer degrees of freedom, wethink that the reduction in degrees offreedom in such cases accurately rep-resents the statistical realities of theseevolutionary analyses.13,16,65 Moreconfidence should therefore be placedin the phylogenetic results.

Some biological anthropologistshave noted that phylogenetic compar-ative methods ignore stabilizing selec-tion.20 It is true that most methodsfocus on evolutionary change to testhypotheses. In part, this is becausecorrelated change is more convincingthan correlated stasis, and it is un-clear how to demonstrate “indepen-dence” in the case of stabilizing selec-tion. Some more recent methods,however, have been developed to in-corporate the effects of stabilizing se-lection.87–89

Other researchers have noted thatthey are not attempting to understandthe evolutionary basis of some trait,but rather to describe the patternsamong species. Examples of this frommorphological studies are particularlycommon, including reconstruction ofan extinct taxon’s body size usingmorphological variation in extanttaxa.90 Any statistical results, how-ever, will be affected by the noninde-pendence of species data points. Forexample, Garland et al.’s44 analysis ofcarnivore and ungulate home ranges,which might be used to infer the be-havior of a fossil taxon, was essen-tially a descriptive study. However,

One benefit arising fromresearch on contrastsmethodology is thatbiologists havedeveloped a variety ofunderlying evolutionarymodels such as theniche model. At present,however, newevolutionary models areunlikely to lead toabandonment ofindependent contrasts.Accepting that theniche model reflectsvalid concerns does notpreclude the use ofindependent contrasts.


as shown earlier, the statistical re-sults differed greatly when usingnonphylogenetic statistical tests ver-sus controlling for phylogeny. Like-wise, it might seem that the analysisof group size and body mass in Fig-ure 1 could be used to reconstructthe behavior of extinct primates: Alarge-bodied species is more likely tohave lived in a large group. A morevalid approach, however, would re-construct group size based on know-able features of the fossil taxon withstatistical linkage to group size, suchas activity period and substrate use,possibly with body mass as a covari-ate in the analysis.29

We suspect that most, if not all,cases where investigators claim to ex-amine trait associations at a descrip-tive level, an underlying evolutionaryquestion is implicit in the analysis.Moreover, these analyses are likely tobe plagued by spurious statistical re-sults due to sampling of a small num-ber of hierarchically structured taxa,including multiple exemplars of closelyrelated and similar species. Only phy-logeny-based methods can be assuredof providing independent data pointsfor any sort of statistical analysis. Ef-forts to avoid these methods are statis-tically unjustified.

Traits Vary in How StronglyThey Correlate WithPhylogeny

Recent interest has emerged in diag-nostic tests that examine whether phy-logeny “needs” to be incorporated in acomparative study.91 The basic ap-proach is to determine whether the con-tinuous traits in question are signifi-cantly correlated with phylogeny.92–96 Ifso, then a phylogenetic comparativemethod should be used; otherwise, ithas been proposed, the investigator cantreat species values as if they were inde-pendent.94,96

Although we are skeptical that anytrait is truly uncorrelated with phylog-eny, traits with large amounts of in-traspecific variation, such as groupsize, may be diagnosed as having lowphylogenetic correlations.94 Two im-portant issues, however, have yet to befully addressed regarding these tests.First, the statistical effects of usingcontrasts analysis when species values

are independent have not been fullyinvestigated, although at least onestudy suggested that contrasts givehigher Type I error rates in this situ-ation.93 Second, the diagnostics relyon acceptance of the null hypothesisthat there is no correlation with phy-logeny, rather than rejection of a hy-pothesis. Other tests of statistical as-sumptions have this characteristic,but the consequences of incorrectlyaccepting the null hypothesis in com-parative tests may be more severe (forexample, a spurious relationship, as inFig. 1). Thus, we recommend that re-

sults from contrasts be given greatestconfidence, although it is often usefulto compare the results to those ob-tained from species values.

This discussion also brings up theissue of intraspecific variation andmeasurement error more generally,which has recently become an issuewith independent contrasts24 and maybe a particular problem with behav-ioral data. In effect, intraspecific vari-ation adds a “burst” of evolution ontothe terminal tips across the tree,

which may therefore violate the as-sumptions of independent contrasts(C. Janson, personal communication).Moreover, contrasts from tips of thetree may be more strongly affected bysampling and measurement errorthan are deeper contrasts.24,26,30 Onesolution is to exclude these sister-taxacontrasts on the tips of the tree, butthis is directly opposite to suggestionsby advocates of pair-wise compari-sons (Fig. 6). Further research isneeded to address this issue, but thesimplest solution may involve appro-priate transformation of branchlengths24 (for example, by lengtheningterminal branches).

Contrasts Are Inappropriatefor Allometric Studies

It is not always appreciated that in-ference about scaling relationships issimply a specific case of the generalproblem of how two variables evolvetogether. Interspecific allometry, asdistinct from growth allometry, is, orshould be, the study of the quantita-tive change in Y with change in X. Aswith the detection of correlated evolu-tion, determination of the preciseform of an allometric relationshipmust exclude phylogeny-based con-founding variables.

We think that three general reasonsexplain why many biologists incor-rectly argue against using contrastsfor allometric questions. First, it is notimmediately clear to some investiga-tors how slope estimates from con-trasts, which represent evolutionarychange, relate to allometry, which isusually thought of as the relationshipamong species values at the tips of thetree. In fact, statistical measures ofassociation calculated from contrastsand species values are equivalent, asbased on analytical10,73,97 and empiri-cal investigation.24,51 Thus, contrastsare fully appropriate for estimating al-lometric slopes, as discussed in detailby Harvey and Pagel.10 Also, differentmethods of slope estimation, includ-ing least squares, major axis, and re-duced major axis, can be used withcontrasts.10,30,52,98

Second, it is sometimes argued thatthe allometric coefficient (the inter-cept, or elevation, in a species plot)cannot be determined using contrasts,

Some biologicalanthropologists havenoted that phylogeneticcomparative methodsignore stabilizingselection. It is true thatmost methods focus onevolutionary change totest hypotheses. In part,this is becauseevolutionary change ismore clearlyindependent, whereas itis unclear how todemonstrate“independence” in thecase of stabilizingselection, or stasis.


as a regression of contrasts is con-strained to pass through the origin.While this is technically true,67 it ispossible to use the reconstructed val-ues of the root node to position theregression line and calculate the inter-cept.40 Confidence intervals can beplaced on ancestral estimates, al-though some recent studies have sug-gested that such intervals can bewide.40,81,91,99 In any case, the phylog-eny-free regression line and its inter-cept can be forced onto the raw datafor detailed study of factors that causedeviations from this line.

Finally, it has been argued that thecontrasts method is inappropriate forstudies of allometry due to the con-founding effect of grade shifts.73 Agrade shift occurs when some vari-able, shared through common de-scent, produces a shift in the relation-ship between the main variables withno change in their slopes (Fig. 8).Thus, the allometric exponent is thesame in the two groups, but the allo-metric coefficient differs. A commonexample involves brain size in mam-mals. For example, Figure 9 showsthat anthropoid primates have largerneocortices relative to the rest of thebrain than do prosimians, and thatprimates in general have larger rela-

tive neocortices than do other mam-mals, such as insectivores.84

Contrary to the argument, however,the contrasts method tends to do bet-ter than analysis of species values inthis situation.26,30,100 This is becausemultiple data points in a species anal-ysis are treated incorrectly as inde-pendent but, with the method of inde-pendent contrasts, only a singlecontrast is calculated for each gradeshift, and this single data point willproduce less bias (Fig. 8). Moreover,the method of independent contrastscan be used to provide a rigorous di-agnostic for grade shifts. Followingthe logic in Figure 8, this is done bydemonstrating that the slopes for thetaxa do not differ, and next by show-ing that the contrast between them issignificantly greater than expected.44

Thus, grade shifts cause no problemsfor calculating allometric slopes withthe contrasts method, and the generalcontrasts approach actually allowsformal analysis of such grade shifts.

An alternative to using independentcontrasts in allometry uses the speciesvalues but adjusts the degrees of free-dom.21 This “degrees-of-freedom ap-proach” has been used in biologicalanthropology,101–104 but we think itsuse should be reconsidered for severalreasons. First, computer simulation

has shown that this approach is con-servative,34 which has been construedto mean that the method is accept-able. By comparison, the method ofindependent contrasts gives expectedType I error rates; that is, it behavesstatistically as expected. The contrastsmethod should therefore be preferredover other methods.34 Second, non-independence is not simply about thetotal degrees of freedom, but ratherhow those degrees of freedom are par-titioned among the available speciesdata points.97 The degrees-of-freedommethod reduces the degrees of free-dom, but it does not partition the datainto truly independent components.Finally, when applying the method toallometric questions, a large numberof data points from speciose cladesmay bias the allometric estimate. Thisoccurs, for example, if there are manyclosely related species giving datapoints on extreme edges of the X- orY-axes (that is, high leverage points).Despite these concerns, nested analy-sis of variance methods may have heu-ristic value for assessing the degree ofphylogenetic correlation, althoughmore direct approaches are availablethat avoid problems of unequal sam-ple sizes in nested classes56 (for exam-ple, using Moran’s I92 or simulationmethods96).

Figure 7. An alternative evolutionary model. The “niche” model assumes that two or more traits (X1 and X2) are correlated in niche space.The niche is originally filled by one species, labeled 1. Then, as subsequent niches open randomly in niche space, the species closest in thisbivariate space undergoes a speciation event to fill the new niche. Thus, niche 1 is filled by species 2, niche 3 by species 2 (because species5 and 6 have not yet arisen), and so on. In this model, species maintain “trunk” lineages that form the material for new lineages in adjacentniches later in time.


CONCLUSIONS AND FUTUREDIRECTIONS

The comparative method has playeda pivotal role in generating and testingadaptive hypotheses. Because the com-parative approach is nonexperimental,comparative methods control for con-founding variables statistically ratherthan directly.25,26 This review showsthat phylogenetic comparative meth-ods have distinct advantages overprevious approaches to comparativeanalysis. We do not recommend, how-ever, that investigators simply apply aphylogenetic comparative methodwithout first testing its assump-tions.52,53,105 In addition, differencesbetween results calculated from phy-logenetic and nonphylogenetic analy-ses can often be informative. For ex-ample, if correlations are lower inanalysis of independent contraststhan species values, this may indicatethe existence of confounding vari-ables.51 Thus, phylogenetic analysis

should often go hand-in-hand withanalysis of species data points, al-

though greater confidence should gen-erally be placed in the phylogeneticresults.

Many areas for future research onphylogenetic comparative methodsremain. Because primates are such awell-studied group of organisms, pri-mate researchers, with their largecomparative datasets, have much tooffer toward improvements in thesemethods. For example, we investi-gated the scaling of home range sizewith group metabolic needs in pri-mates30 and discovered that the appli-cation of different line-fitting modelsto contrasts data was not so clear-cut.10 We therefore outlined steps forconducting such analyses. Computersimulation of particular unresolved is-sues, such as the effect of using con-trasts with traits that are uncorrelatedwith phylogeny, are particularlysuited to primatologists, as there arenumerous cases available for empiri-cally testing the simulation results(see similar work on carnivores by

Figure 8. Grade shifts and contrasts. In a plot of species values, a grade shift tends to bias the allometric exponent (the slope). In thisexample, the allometric exponent is biased upward, although biases downward are also possible.30 In a contrasts plot, however, thecontrast corresponding to the difference between these grades shows up as a single outlier, indicated by the arrow. While this outlier, if notexcluded, will still exert positive bias, the resulting bias is less than the multiple degrees of freedom in a species analysis. This figure illustrates,in the case of allometry, how phylogenetic relations can result in biased analysis of species values. (Figure taken, with permission, from Nunnand Barton,30 copyright 2000 by The University of Chicago.).

Although we areskeptical that any trait istruly uncorrelated withphylogeny, traits withlarge amounts ofintraspecific variation,such as group size, maybe diagnosed as havinglow phylogeneticcorrelations. Twoimportant issues,however, have yet to befully addressedregarding these tests.


Gittleman et al.94). Thus, traits withextensive intraspecific variation inprimates, such as group size, can beexamined to evaluate conditions un-der which a phylogenetic comparativemethod should be used.

Finally, it is possible to alter the ba-sic phylogenetic approach to addresstotally new questions.5,15,17–19,69,106,107

For example, Deaner and Nunn80 useda method based on independent con-trasts to test whether brain size is sub-ject to evolutionary lag relative tobody size, but found no support forthis hypothesis as an explanation forresiduals in brain-body size plots.Thus, phylogenetic approaches tocomparative biology have the poten-tial to offer important insights intobiological anthropology. We hope thatthis review results in greater explora-tion of comparative patterns in a phy-logenetic context.

ACKNOWLEDGMENTS

We thank Dan Blumstein, JohnGittleman, Charles Janson, BillJungers, Terry Ord, Andy Purvis,

Karen Strier, Carel van Schaik, andseveral anonymous reviewers forhelpful discussion. During the writingof this paper, CLN was supported byan NSF Post-Doctoral Research Fel-lowship in Biological Informatics. Ad-ditional support was provided fortravel by the NSF, the Duke UniversityGraduate School, the Duke chapter ofSigma Xi (Sally-Hughes SchraderTravel Grant), and the Evolutionary An-thropology Research Group at the Uni-versity of Durham.

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© 2001 Wiley-Liss, Inc.

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