the shape of human evolution: a geometric morphometrics ...pages.nycep.org/ed/download/pdf/nmg...

The Shape of Human Evolution: A GeometricMorphometrics PerspectiveKAREN L. BAAB, KIERAN P. MCNULTY, AND F. JAMES ROHLF

Study of morphological form is fundamental to the discipline of paleoanthro-pology. The size and shape of our ancestors’ anatomical features have longbeen the focus of research on hominin systematics, phylogeny, functional mor-phology, ontogeny, variation, and evolutionary change. Early physical anthropolo-gists relied on both qualitative descriptions of anatomical shape and linearmeasurements to assess variation among hominins. The seminal works of W. W.Howells1 and C. E. Oxnard2 helped to bring multivariate techniques to the fore-front of physical anthropology. Howells’ intention was the objective delineationof components of shape, which could then fuel further analyses and interpreta-tions, as well as clarification of the ways that growth influences interindividualand interpopulational differences in shape. He expressed concern that previouscomparisons of individual measurements did not capture the overall shape ofthe skull, which is ‘‘expressed by the relations between measurements.’’1:3 Simi-larly, Oxnard recognized that a multivariate approach to the study of complexshapes allows ‘‘for such perturbations (e.g., variation and covariation). . .that aredifficult to evaluate by eye and impossible to reveal by measurement and simpleanalysis alone.’’2:6 While multivariate methods offered clear advantages over uni-variate or bivariate representations of shape, the analysis of traditional morpho-metric measures such as linear distances, angles, and ratios, has limitations whenit comes to quantifying the complex geometry of some anatomical structures.

The advent of landmark-based geo-metric morphometric methods nar-rowed the gap between the subjectsof biometric analyses and the quanti-tative abstractions used to representthem (Box 1). In contrast to tradi-tional morphometric data, landmarkdata preserve both the dimensions ofthe object and the spatial relationshipsamong these dimensions3 (Box 2). Animportant advantage of this approach

is the capacity to address a greaternumber and, in some cases, differenttypes of research questions. Anotheruseful feature of geometric morpho-metrics (GM) is the ability to visualizeshape differences in the physical spaceof the organism, rather than interpret-ing extensive tables of numericalresults. This enhances an investigator’sability to interpret results within an ev-olutionary, functional, or ontogenetic

framework, and to present those resultsin a manner that is easily digested andevaluated by the scientific community.While landmark-based analyses are nota panacea for every paleoanthropologi-cal debate, they comprise a powerfulset of tools for quantifying and testingaspects of shape variation and covaria-tion.

Bookstein4 provides thorough doc-umentation of the theoretical andhistorical context of GM; reviews ofthe practical applications of GM arealso available.5 More recently, Slice6

reviewed the development and use ofGM within the broader subfield ofphysical anthropology, including thecontributions of anthropologists tothe development of GM. Therefore,the present review focuses primarilyon the contributions of GM to stud-ies of human evolution, particularlyin the areas of characterizing taxo-nomic variation, allometry, and de-velopment, including modularity andintegration. We begin by providingan overview of GM methods and theprocesses whereby raw data aremade ready for statistical analysis.We have framed this discussion ingeneral terms; mathematical detailscan be found in more technical treat-ments elsewhere in the literature.This is followed by a frank discus-sion of the strengths and weaknessesof GM, then a digest of a few impor-tant topics within paleoanthropologythat have benefited from GM analy-ses. We finally address possiblefuture directions for GM within thestudy of human evolution.

GEOMETRIC MORPHOMETRICSBACKGROUND

Data collection: Landmarks andSemilandmarks

The foundation of GM analysis isthe use of landmark data. A land-mark is a precisely defined point on

Karen Baab is an Assistant Professor in the Department of Anthropology and the Inter-departmental Doctoral Program in Anthropological Sciences at Stony Brook University.Her research focuses on the evolution of the skull in human and nonhuman primates andunderstanding the underlying forces responsible for inter- and intraspecific variation incranial form. Email: [email protected].

Kieran McNulty is an Associate Professor in the University of Minnesota’s EvolutionaryAnthropology Laboratory. His research interests in the evolution and diversification ofapes and humans are addressed using quantitative analyses to study hominoid cranialvariation and through field research in the early Miocene fossil sites of western Kenya.

F. James Rohlf is a John S. Toll Professor in the Department of Ecology and Evolution atStony Brook University and is interested in multivariate methods and applications in biol-ogy, especially in geometric morphometrics. He co-authored the text Biometry, articles onstatistical methodology, and a number of software packages.

Key words: shape analysis; paleoanthropology; systematics; allometry; integration; modularity

VVC 2012 Wiley Periodicals, Inc.DOI 10.1002/evan.21320Published online in Wiley Online Library (wileyonlinelibrary.com).

ARTICLE

Evolutionary Anthropology 21:151–165 (2012)

a specimen, the position of which isrecorded by a set of x-, y-, and (for 3-D data) z-coordinates. Whether ornot individual landmarks are homol-ogous can be debated, but they aregenerally chosen based on a criterionof homology of the underlying struc-tures (Box 2). Many features of inter-est to paleoanthropologists, however,cannot be sufficiently characterizedusing only homologous points. Thisis particularly true for anatomicalregions that have few or no easilyidentifiable discrete landmarks (forexample, neurocrania and boneshafts). Semilandmarks, a series ofordered points, were developed as ameans of quantifying such struc-tures: homologous curves, contours,or surfaces between landmarks (Box2).7 In these cases, the structure,rather than individual semiland-marks, is considered homologous.Because the initial spacing of semi-landmarks is arbitrary, sophisticatedalgorithms have been developed torespace (‘‘slide’’) semilandmarks tomaximize their correspondenceacross a sample. The advantage of

this approach has been demon-strated in structures that exhibitlocalized bending but, unfortunately,software to perform this sliding stepis not yet widely available for 3-Dsemilandmarks. A further complica-tion is that, as reviewed by Perez,8

there are two distinct ways to slidesemilandmarks. While minimizingbending energy results in smoother,less complex shape changes, the min-imization of Procrustes distancesmay be more useful for statisticalcomparisons and is more consistentwith minimizing Procrustes distan-ces for the overall superimposition.

Procrustes Superimposition

Raw coordinates from landmarkdata cannot themselves be meaning-fully compared across multiple speci-mens, as they encode informationnot just about shape, but also aboutlocation, orientation, and scale (Fig.1). Differences in location and orien-tation result from differences in thearbitrary starting position and align-ment of each specimen during data

collection. In the context of GM,scale equates to differences in iso-metric, but not allometric, size. Thenearly universal method used in GMto extract shape information fromraw coordinate data is called a gen-eralized Procrustes analysis (GPA)(Fig. 1). Briefly, this method firsttranslates specimen configurations toa common location by superimpos-ing their centroids (geometric cen-ters), then scales each configurationto unit centroid size (centroid size ¼1). The final step in a GPA involvesstandardizing the orientations by rig-idly rotating all configurations untilcorresponding landmarks across allspecimens are as close together aspossible.9,10 If the data include slid-ing semilandmarks, then an initialGPA is performed, followed by thesliding step, then a second GPA.

Once a GPA has been executed,superimposed specimen configura-tions can each be represented as asingle point in a high-dimensionalshape space. Each unique shape cor-responds to a specific position in this

Box 1. Glossary

Bending energy – a concept bor-rowed from mechanics; in the con-text of GM, it refers to the amountof energy required to bend a flat,infinite, and very thin metal plateupward or downward at points cor-responding to the locations of land-marks in a reference configuration.The signs and magnitudes of thedisplacements correspond to thedifferences in the x and y (andpossibly z) coordinates between thereference configuration and a tar-get configuration.Centroid size – the most com-

monly employed measure of size ingeometric morphometrics, this iscalculated as the square root of thesum of squared distances of eachlandmark in a landmark configura-tion to the configuration’s centroid.Geometric morphometrics – a

set of methods used to acquire,process, and analyze (using multi-variate statistics) landmarks orsemilandmarks defined by a set ofCartesian coordinates; these meth-

ods preserve the geometric rela-tions among the landmarksthroughout analysis, allowing forvisualization of shape, includingmean shapes and differencesamong groups or individuals.Landmarks - precisely defined

points in two or three dimensions,defined by some rule; they are usu-ally chosen to correspond to ho-mologous points that can be foundin all specimens.Landmark configuration – a

collection of landmarks recordedfrom a single biological specimen.Procrustes distance – the stand-

ard measure of the differencebetween two landmark configura-tions after Procrustes superimposi-tion; typically calculated as thesquare root of the sum of squareddistances between all correspond-ing landmark pairs.Procrustes superimposition –

the process by which two or morelandmark configurations are regis-tered so that differences due to ori-

entation, translation, and scale areremoved; the registration isachieved by translating specimensto the origin, scaling all configura-tions to unit centroid size and per-forming rigid rotations so that thesum of the squared distancesbetween corresponding pairs oflandmarks is minimized.Semilandmarks – a series of or-

dered points that are positionedalong curves or surfaces; often usedwhen there are an insufficient num-ber of homologous landmarks to fullycharacterize shape in that region.Shape – the geometric properties

of a landmark configuration thatare invariant to orientation, trans-lation and scaling.Shape space – the multidimen-

sional space in which each uniqueshape (a landmark configuration) isrepresented by a single point; mostanalyses take place in tangent space,the Euclidean space that is tangentto the mean configuration followingProcrustes superimposition.

152 Baab et al. ARTICLE

space, and the cloud of points inshape space reflects the differentshapes of the specimens in the sam-ple: the more two shapes differ, thefurther apart they are in shapespace.4 The new coordinates of thesuperimposed specimens are free ofdifferences due to location, orienta-tion, and scale; however, the shapespace occupied by these superim-posed landmark configurations is

non-Euclidean, violating a funda-mental assumption of standard para-metric statistical methods. Hence, touse such methods, the landmark con-figurations must be projected into aspace where Euclidean geometryapplies. This space is typically con-structed tangential to the GPA spaceat the point of the mean shape, and iseponymously called tangent space(see Box 3 for more details regarding

this projection).11,12 An analogousprojection that will be familiar tomost readers is the mapping of thecurved geography of the earth onto aflat 2-D surface.

Coordinates subjected to superim-position and projection into tangentspace can now be analyzed with theusual multivariate statistical tools.These transformed coordinates aretypically called shape variables (ortangent space coordinates). Thin-platesplines can also be used to visualizethe tangent space (Box 4).

Procrustes Distance

The usual measure of the differ-ence in shape between two superim-posed landmark configurations iscalled a Procrustes distance. Thisdistance is the square root of thesum of all the squared distancesbetween corresponding landmarks inthe two superimposed objects. Pro-crustes distance is the quantity mini-mized during GPA superimposition.It can also be interpreted as the dis-tance between the two points repre-senting the individual configurationsin a multidimensional shape space(technically Kendall’s shape space)(Box 3). Thus, Procrustes distance isa measure of differences in shape: alarger distance implies a greatermagnitude of shape difference, whilea distance of zero indicates that thetwo shapes are identical.

The use of the term ‘‘Procrustesdistance,’’ however, is somewhatimprecise in the literature. Asdescribed in Box 3, there are threeshape spaces commonly associatedwith GM analyses: Kendall’s shapespace, named after the mathemati-cian David Kendall, who outlinedmuch of the theoretical underpin-ning of shape analysis,13 is the spaceof all possible pairwise superimposi-tions; GPA space is the result ofsuperimposing more than two speci-mens on the sample mean; and tan-gent space is the Euclidean spaceinto which configurations are typi-cally projected for analysis. The term‘‘Procrustes distance’’ is only properlyapplied to the distance between con-figurations in Kendall’s shapespace.12,14 However, most shapeanalyses occur in either GPA or tan-

Figure 1. Procrustes superimposition. A. Three landmarks (1 ¼ lambda, 2 ¼ bregma, 3 ¼ pros-thion) are identified on two human skulls. B. For 2-D data, the landmark positions arerecorded using two Cartesian coordinates (x,y). Coordinates of the centroid (geometriccenter) of each landmark configuration are calculated simply as the arithmetic mean of itsx- and y-coordinates. C. Translation. By subtracting the centroid coordinates from the re-spective coordinates of each landmark in the configuration, differences in the location ofeach specimen are removed. This effectively moves the entire configuration so that its cent-roid is positioned at the origin of the coordinate system. D. Scaling. The centroid size foreach specimen is calculated by first finding the distance of each landmark to its configura-tion’s centroid, squaring these distances and summing them, and then taking the squareroot of the entire sum. Differences in scale are removed by dividing each coordinate of aconfiguration by its centroid size, thereby resizing each specimen to unit centroid size. Whileisometric size differences are now eliminated from the data, the original centroid sizes canbe retained as a covariate to study size-correlated shape differences. E. Rotation. Differen-ces in orientation are removed by rotating configurations around their centroids to minimizedifferences between each configuration and a reference (by minimizing the sum of squareddistances across all corresponding landmarks). In an ordinary Procrustes analysis (N ¼ 2specimens; illustrated here), there is a direct solution whereby one specimen (Skull 1) is opti-mally rotated to fit the reference (Skull 2). In a generalized Procrustes analysis (N > 2 speci-mens), a mean configuration is first computed and all specimens are superimposed to thismean using an interative process. Coordinate data resulting from a Procrustes superimposi-tion are now considered shape data, free of differences in location, scale, and orientation.[Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

ARTICLE THE SHAPE OF HUMAN EVOLUTION 153

Box 2. Landmarks and Geometry

Descriptive morphological analy-sis allows for the exhaustive char-acterization of a specimen’s anat-omy, which is an important com-ponent of any morphologicalstudy. However, qualitativedescriptions do not provide objec-tive criteria by which specimenscan be compared to known rangesof variation and allow only coarsecharacterizations of variation andcovariation among multiple taxa.For these reasons, many research-ers turn to quantitative morpho-metric analyses that use rigorousepistemological criteria imposedby statistical analysis.

Univariate analyses provide en-

tree to the statistical toolkit, butcapture only individual dimensions

of the objects being studied. Multi-

variate analyses of linear measure-ments capture more of the objects’

shapes, but do not retain the geo-

metric relationships between meas-

urements. Consider, for example,the simple interpoint measure-

ments illustrated here (Fig. 2).

Dimensions of basion-bregma andinion-glabella are easily obtained

using calipers, and provide quanti-

tative output describing two fea-tures of the specimen. The resulting

distances, however, have lost their

geometric relationship to each

other (Table 1). The quantities ‘‘9.7’’and ‘‘13.1’’ differ only in their magni-

tude and are uninformative about

the angle between these chords, thepoint at which they intersect, and the

distances between their endpoints.The strength of landmark-based

geometric morphometric analysesis that the original geometries ofthe specimens under study are pre-served in the coordinate data.Rather than measuring the dis-tance between pairs of points, geo-metric morphometric analyses usethe landmarks themselves meas-ured within a 2-D (x, y) or 3-D (x,y, z) coordinate system.

Going back to the same exam-ple, we could instead analyze thex-, y-coordinate data for the end-

points of the two linear measure-ments. Unlike the linear outputs,the coordinate data retain infor-mation on exactly how each ofthese landmarks relates to theothers. Whereas the full geometryof the configuration is encoded inthis set of four 2-D landmarks, sixinterlandmark distances would benecessary to capture this same in-formation. Moreover, the discrep-ancy between the number of land-marks and the possible interland-mark distances increases as thenumber of landmarks increases.By retaining more of the biologicalinformation from the organism(that is, the geometric relation-ships among landmarks), more

complex and subtle morphologicalquestions can be addressed. More-over, the preservation of geometricinformation within the data meansthat important morphologicalissues such as shape differences,vectors of variation, and axes ofcovariation can be easily visual-ized. And, of course, landmarkcoordinate data can be used to cal-culate all of the traditional contin-uous variables that were them-selves defined by the landmarks:inter-point distances, angles, areas,volumes, and so forth.

The traditional ‘‘classes’’ of land-marks can also be seen in Figure2. Bregma is a good example of aType I landmark, where multiple

Figure 2. Example of two simple interpoint measurements, basion to bregma andinion to glabella. [Color figure can be viewed in the online issue, which is availableat wileyonlinelibrary.com.]

TABLE 1. Comparison of Measurement Data Derived from Linearand Coordinate Data

Type of data Measurement Data

Linear basion - bregma 9.7inion - glabella 13.1

Coordinate (x, y) basion 12, 2.4bregma 10, 11.3

inion 16.5, 4.1glabella 3.8, 8.0


gent space, and analogous measuresin these spaces are usually labeledProcrustes distances as well. Thisimprecision in terminology is justi-fied on the grounds that the distancebetween two configurations in any ofthe three shape spaces will be verysimilar, provided that overall shapevariation is relatively small, as is thecase in most biological analyses.15

APPLICATION OF GM METHODS

While the ‘‘morphometric revolu-tion’’3 began more than 20 years ago,geometric morphometrics is still rel-atively new compared to traditionalapproaches, and research topics thatare well suited for these methodsmay not always be clear to new prac-titioners. Broadly speaking, GMmethods operate in the same realmsas do other morphometricapproaches, and can be used in bothexploratory and hypothesis-testingframeworks. For example, a studymay investigate shape differencesbetween two extinct hominin species(exploratory), then go on to evaluatethe hypothesis that a particular fossilshould be assigned to one of thesetwo species (hypothesis testing). Theaims of most GM analyses fall intothree main categories: characterizingand quantifying the main directionsof shape variation or covariation in asample; testing whether two or moregroups differ significantly in some as-pect of shape; or establishing the na-ture of relationships between shapeand one or more additional variables.

In paleoanthropology, GM hasbeen most frequently applied toquestions regarding systematics,comparative anatomy, ontogeneticdevelopment, ecomorphology, andmorphological integration. Theoreti-cally, landmark-based morphomet-rics could also play a role in studiesof biomechanics or phylogenetics,but historically they have had mini-mal impact in these fields.

Landmark data are particularlyuseful for recovering complex orsubtle shape differences, which oftencharacterize members of the same orclosely related species or subsequentontogenetic stages of development.Landmark data also provide opportu-nities for shape visualization that arenot available using traditional mor-phometrics. However, there will beinstances in which the effort requiredto collect, process, and analyze alarge amount of landmark data out-weighs the benefits of this approach.If the research question can be easilyanswered by collecting a small num-ber of caliper-based measurements,then this tack will be both faster andcomputationally simpler. In fact,while subtle shape differences may bemore easily identified using GMamong very similar specimens, theymay likewise be overwhelmed whencomparing objects that differ greatlyin other respects. Those subtle differ-ences will still be encoded in the data,but it may take more sophisticatedanalyses to elucidate them.

Another disadvantage of GM anal-ysis is its steep learning curve. Someanalyses, such as principal compo-

nents analysis, can be performed rel-atively easily with freely availableand user-friendly software such asMorphologika, MorphoJ, or the Tps-series of programs, but more sophis-ticated analyses require moreadvanced geometric, algebraic, andstatistical knowledge. There is also afair amount of jargon associatedwith GM, which, in some cases,obfuscates what would otherwise beclear. For example, the axes associ-ated with a two-block partial leastsquares analysis, an approach usedin integration or modularity studies,are commonly referred to in non-GMcontexts as ‘‘factors’’ or ‘‘dimen-sions.’’ However, the term ‘‘singularwarps’’ was coined for the situationwhere the two blocks of variablesbeing analyzed are coordinate data.17

An additional strength of GM isthe ability to mathematically sepa-rate shape variation from isometricsize variation. Information about theoriginal centroid sizes of landmarkconfigurations is sequestered duringthe superimposition process, and canthen be used to examine the relation-ship between size and shape. Isomet-ric size differences are removed dur-ing superimposition, but allometricshape variation is unaffected. There-fore, studies that are explicitly inter-ested in the relationship between sizeand shape may benefit from the useof GM methods.

The ability to collect data in theregions between homologous land-marks (that is, through the use ofsemilandmarks) is an important con-tribution of the GM toolkit, andopens many new avenues of investi-

discrete tissues (the frontal andtwo parietal bones) intersect at asingle point; the case for homologyis strongest for Type I landmarks.Basion, on the other hand, is aType II landmark; its homology issupported only by the geometry ofthe surrounding anatomy, theregion immediately surroundingthe foramen magnum. Glabellacan be considered a Type III land-mark in that its position, the mostanterior midline point on the fron-

tal bone when a skull is in theFrankfurt Horizontal position, isdefined in part by distant anatomi-cal structures (poria and orbitale).

Semilandmarks are illustrated inFigure 2 by the smaller spheresarrayed along the median planebetween glabella and bregma.Unlike landmarks, which are indi-vidually presumed to be homolo-gous across all specimens in a sam-ple, homology in semilandmarks ispresumed at the level of the struc-

ture or surface (here, the medianplane of the frontal bone). Thismakes semilandmarks similar toType III landmarks in that each isdefined in part by the position ofthe semilandmarks on either sideof it rather than by local anatomy.Thus, a semilandmark is not free tovary in any direction because it isbound in a series of other semi-landmarks. This has implicationsfor the overall degrees of freedomone has in statistical analysis.


gation. However, the use of semi-landmarks often results in a largenumber of variables, in some casesexceeding the number of individualspecimens, which is problematic forstandard statistical tests. A common‘‘work around’’ is to subject the land-mark data to a PCA, then use PCscores along a smaller number of PCaxes as the variables for analysis.While this does reduce the numberof variables being analyzed, neitherbiology nor statistics offers a clearrule-of-thumb for deciding howmany PCs to analyze, and research-ers use different criteria in makingthis decision.

Researchers embarking on aresearch project using GM data haveseveral data collection techniquesavailable to them. 2-D landmark datacan be collected from photographsor x-ray images using freely availablesoftware such as tpsDig. However,many paleoanthropological subjectsare ill-suited for 2-D analyses, sincethey vary in three dimensions and 2-Drepresentations of 3-D objects canobscure anatomical relationships. Forexample, 2-D analysis of a gorilla cra-nium in frontal view would treat thenasal aperture as very close to the ma-lar root because the length of the ros-trum is obscured in that perspective.3-D landmark data can be recordeddirectly from specimens using theportable Microscribe digitizer, amulti-joint mechanical arm with astylus at one end. Alternatively, land-mark data can be recorded from ‘‘vir-tual surfaces’’ using specialized soft-ware such as Landmark Editor orAVIZO. These surfaces might be ren-dered from CT or MRI data, or gener-ated using laser or white-light surfacescanners. In all cases, the goal is togenerate a landmark configuration foreach specimen that follows a commonorder and number of landmarks forthe sample.

Systematics

Affinities of individual fossils

Since hominin taxa are generallydefined by a combination of discreteand continuous characters, many ofwhich relate to the shape of anatomi-cal structures, morphometric data

are frequently analyzed to addresstaxonomic questions. There is a longhistory of assigning individual fossilsto taxa based on phenetic affinitiesestablished by traditional morpho-metric comparisons. The landmark-based assessments have shared simi-lar success in this arena, as a fewkey examples will attest.

The cranium of the Late Mioceneputative hominin Sahelanthropus(TM 266) has been the subject of bothin silico reconstruction and GM anal-ysis.18,19 The initial publication of thecranial reconstruction18 includedsome basic landmark-based quantita-tive analyses, which concluded thatTM 266 belongs within the homininlineage and that it may have usedbipedal postures. A more extensive

study by the same team19 presentedlinear measurements as well as multi-variate ordinations and clusters basedon landmark data to support theseinitial conclusions. More recently inthe hominin fossil record, the LatePleistocene Hofmyer skull fromSouth Africa, dated to 36 ka, wasdemonstrated to more closely resem-ble other contemporaneous humansfrom Europe than younger but geo-

graphically closer Khoe-San crania.This was done using a combination ofPCA, canonical variates analysis, andUPGMA clustering.20 The affinities ofmany other hominin specimens,including Kenyanthropus,24 Indone-sian H. erectus,21 and early AfricanHomo,22 have been analyzed usingsimilar tools.

GM is well suited for incorporatingbiological information about differ-ent morphogenetic factors such asontogeny, size, and sex, when testingfossil affinities. These more sophisti-cated studies are becoming commonas the methods mature within paleo-anthropology. For example, the rela-tionship between adult size andshape (static allometry) has been animportant theme in GM analyses ofthe recently recovered fossil‘‘hobbits’’ from Flores. The mostextensive study to date was carriedout by Baab and McNulty,23 whoused a series of phenetic, allometric,and asymmetry analyses to testhypotheses about the affinities of theLB1 cranium. Basic multivariateordinations and clustering suggest astrong affinity between LB1 and cra-nia of Pleistocene hominin taxa,including H. erectus and H. habilis.When scale was taken into consider-ation, the LB1 cranium was shownto conform to the pattern of mor-phology expected for a Pleistocenehominin, but not a modern human,of the same diminutive size. Thesame study also assessed asymmetryin LB1 by computing Procrustes dis-tances between specimen configura-tions and their mirror images, reject-ing the hypothesis that LB1’s asym-metry is outside of the range ofnormal asymmetry.23

McNulty, Frost, and Strait24 tooka unique approach to assessing thetaxonomic affinities of the Taungchild by applying developmentaltrajectories from different extanttaxa (apes and humans) to thejuvenile specimen to estimate itsadult morphology. Their resultssuggested that with regard to cra-nial shape, the estimated adultTaung specimen was most similarto the Sterkfontein Australopithe-cus africanus, and specifically toSts 71 rather than Sts 5. They alsoreconciled some earlier contentious

The aims of most GManalyses fall into threemain categories:characterizing andquantifying the maindirections of shapevariation or covariationin a sample; testingwhether two or moregroups differ significantlyin some aspect ofshape; or establishingthe nature ofrelationships betweenshape and one or moreadditional variables.


results from both linear andlandmark studies of African apeontogeny, showing that significantvariation in some stages of devel-opment is not necessarily coinci-dent with substantial differences inadult morphology.

Testing the single-species

hypothesis in paleoanthropology

The degree and pattern of variationwithin single species can also beused as a benchmark for testing thenull hypothesis that a sample of fos-

sils represents a single species. If var-iation in the fossil sample is exces-sive relative to the comparator spe-cies, this can be interpreted assupport for the alternative hypothe-sis, that the sample includes mem-bers of more than one species; like-

Box 3. Spaces and Distances

The relationships among shapescomprising three landmarks in (A)Kendall’s shape space, (B) GPAspace (‘‘Slice’s shape space’’), and(C) tangent space, are depicted inFigure 3. Landmark configurationslose degrees of freedom as a resultof holding constant translation,rotation, and scaling during Pro-crustes alignment. Thus, any con-figuration of three landmarks canbe represented as a single point ina 2-D space. Kendall’s shape spacecan be visualized as the surface ofa sphere and GPA space as the sur-face of a hemisphere; for configu-rations with more than three land-marks, these are, respectively,higher-dimensional spaces on the‘‘surfaces’’ of a hypersphere andhyperhemisphere. Similarly, forconfigurations of three landmarks,Euclidean tangent space is 2-Dspace (that is, a plane), butbecomes a higher-dimensionalspace for analyses with more thanthree landmarks.

The large black dot at the ‘‘northpole’’ represents the mean configu-ration from a GPA alignment. Thisshape is also used as the point oftangency for constructing the tan-gent space and, for convenience, isshown here as the reference forKendall’s shape space. The threewhite dots all represent the posi-tions of a second shape in the dif-ferent shape spaces. The blacklines connecting these three pointsrepresent the projections of thispoint from Kendall’s shape spaceto the GPA shape space to Euclid-ean tangent space. The projectionto tangent space shown here is anorthogonal (perpendicular) projec-tion, which best preserves the dis-tances among specimens in Ken-dall’s shape space.

If we were to section the figure onthe left through the plane defined bythe configurations’ radii within GPAspace (forming the angle q), wewould see the simplified depiction tothe right. As before, (A) representsKendall’s shape space, (B) is GPAspace, and (C) is tangent space. Pro-crustes distance (q) is properlydefined as the angular distancebetween two specimens in Kendall’sshape space, the great-circle distancebetween two points on the (hyper)surface of Kendall’s (hyper) sphere.Because specimens that lie in Ken-dall’s shape space are scaled to acentroid size of 1, the great-circledistance between two points is equalto the angle (q, in radians) depictedhere. Note that for these two configu-rations, the ‘‘south pole’’ of Kendall’sshape space is coincident with the‘‘center’’ of GPA space (gray dot).

The situation is slightly differentfor GPA-aligned specimens. Unlikespecimens in Kendall’s shapespace, specimens aligned by GPAare optimally superimposed on themean configuration. Thus, the onlytrue Procrustes distances in GPAspace are between a specimen andthe mean. Distances between any

other two specimens do not repre-sent optimal alignment of thosetwo; one can imagine that differen-ces between two specimens couldbe reduced if they were alignedwith only each other rather thanwith the sample mean. As in Ken-dall’s shape space, when centroidsizes are scaled to 1 during GPA,the great-circle distance in GPAshape space is also equal to theangle (in radians) between the twopoints.

An alternate distance used bymany is the value D, seen in thesecond diagram, which representsthe straight-line (chord) distancebetween two points in shape space.While this is not a ‘‘true’’ Procrustesdistance as such, it very closelyapproximates the great-circle dis-tance, particularly when distancesbetween specimens are small (as isnearly always the case in biologicalsamples). Dryden and Mardia use-fully distinguish these two metricsas Procrustes angular distance (q)and Procrustes chord distance (D).Of course, when the specimens areprojected into tangent space, the‘‘shape distance’’ between them is asimple Euclidean distance (d).

Figure 3. The relationships among shapes comprising three landmarks in (A) Kendall’sshape space, (B) GPA space (‘‘Slice’s shape space’’), and (C) tangent space.


wise, a distinct pattern of variationmay constitute important evidence oftaxonomic diversity. This approachwas applied to the H. erectus sensu

lato samples from Africa, Asia, andEurasia, using various extant papio-nin and hominoid species, as well asthe extinct Theropithecus dartii.25

Although some of these species weremore sexually dimorphic than H.erectus was likely to be, only the neu-rocranium was analyzed, which

Box 4. Thin-Plate Splines

One of the most compelling con-tributions from GM is the TPS rep-

resentation of shape differences

between two specimens (Fig. 4). As

Bookstein16 noted, much of themorphometric work of the twentieth

century has been implicitly trying to

produce mathematically groundedmethods with the explanatory power

of D’Arcy Thompson’s transforma-

tion grids. The TPS does this by pro-

viding an intuitive visualization that

allows one to represent shape differ-

ences as a deformation of one shape

into another, rather than as vectors

or lists of numerical output. Unlike

other methods for visualizing differ-

ences between sets of landmarks,

TPSs provide continuous functions

that interpolate shape differences in

the regions between landmarks,

much as a regression equation is a

continuous function that can be

used to interpolate the value of the y

within the range of values of x. This

makes it possible to visualize shape

differences as deformations rather

than separate displacements at each

landmark. While this is a powerful

visual tool, the shape changes in the

interpolated regions cannot be inter-

preted literally because they are

determined by the landmarks them-

selves.As compelling as TPS grids are for

displaying 2-D data, they are diffi-cult to employ for 3-D visualization.

Workers have tried three methodsfor depicting 3-D splines (as parallel

stacks of 2-D grids, as an individual

2-D grid sectioned from a region ofinterest, or as an animation that

moves a 2-D grid through a third

axis, showing concomitant gridchanges along its course), but none

of these approaches has yielded the

same impact and explanatory power

of 2-D TPS grids.

Figure 4. Two methods for depicting the same shape differences between two landmarkconfigurations. Data were derived from lateral radiographs of modern human skulls. Theimages represent differences along a principal component of the sample shape variation.For clarity, mandibular landmarks are shown in blue. The upper figure illustrates differencesusing vectors to connect the corresponding landmarks. The lower figure uses a TPS interpo-lation. Options to include both configurations or a single configuration plus vectors, andchoices about which landmarks to connect can greatly affect the ease with which figuresare interpreted. [Color figure can be viewed in the online issue, which is available atwileyonlinelibrary.com.]


somewhat mitigated this effect. Theresults were mixed: the fossil samplewas more variable than some singlespecies, but was less variable thanmany other species. Interestingly, theneurocranial shape of OH 9, an Afri-can specimen often assigned to theotherwise Asian H. erectus sensustricto, more closely resembled otherAfrican specimens assigned to H.ergaster. Given the more extensivetemporal and geographic range of theH. erectus sample, as well as the lackof a clear distinction in shapebetween H. erectus s.s. and H. ergaster,the null hypothesis of a single specieswas not rejected in this case.

Whereas the previous exampleused the magnitude of intraspecificvariation as a yardstick to test taxo-nomic hypotheses, other studies haveused intertaxon variation for similarpurposes. To test the null hypothesisthat Neanderthals were a subspeciesof H. sapiens rather than a separatespecies, Harvati, Frost, andMcNulty26 compared the Mahalano-bis’ D2 distances in the Neanderthalsample and several modern humanpopulations to the distances amongmodern human populations and amongspecies and subspecies of other catar-rhine primates. They concluded thatNeanderthals were best interpreted as adistinct species based on the observa-tion that the distances between Nean-derthals and modern humans exceedednearly all of the intraspecific compari-sons, as well as several of the interspe-cific comparisons.

Exploring evolutionary change in

biological structure

Beyond establishing the speciesaffinities of individual fossils andclarifying the taxonomic status ofvarious fossil samples, workers havealso explored the evolutionary impli-cations of interspecific shape varia-tion in the dentition,27–29 exocra-nium,30 and endocranium.31 Forexample, Lieberman, McBratney,and Krovitz30 used a combination oflinear- and landmark-based analysesof the exocranium to examine thedevelopmental processes that pro-duce a uniquely globular neurocra-nium and small, retracted face in H.

sapiens relative to archaic Homo. Bru-ner, Manzi, and Arsuaga31 also identi-fied two distinct allometric trajecto-ries in endocranial shape, one thatincludes all extinct Homo species andone that is unique to H. sapiens, dem-onstrating that the large brains ofNeanderthals are the end-point of anarchaic allometric pattern, whereasmodern humans achieved a similarbrain size with a different suite ofaccompanying shape changes.

Identifying the underlying causesof intraspecific variation in recenthumans also contributes to ourunderstanding of hominin evolution.Cranial shape variation within mod-ern humans has been used toaddress hypotheses about the dias-pora of modern humans out ofAfrica,32 and to examine the influ-ence of factors such as populationreplacement and gene flow on thecranial morphology of prehistoricand recent human populations in theAmericas.33 Studies using GM meth-ods have also explored variation incranial robusticity among modernhuman populations to clarify both itsappearance during ontogeny,34 andits relationship to craniofacial shapeand mastication.35 For example,Baab and coworkers35 examinedcovariation between discrete traitsthat reflect cranial robusticity and 3-D landmarks capturing overall cra-niofacial shape. They found a weakrelationship between cranial shapeand robusticity, but no relationshipbetween robusticity and size. Boththis study and an earlier caliper-based study36 found that the mostrobust skulls were also long, withbroader upper faces and prognathicmaxillae.36 The earlier study, how-ever, interpreted this combination ofshape features as a link between cra-nial robusticity and an increase inskull size.36 Using a GM approach,the capacity to separate clearly theeffects of shape versus size demon-strated that long, narrow skulls withprojecting faces were robust, but notnecessarily large.

The Relationship Between Sizeand Shape

Ontogeny and heterochrony

Some of the earliest quantitativestudies in comparative anatomy were

aimed at understanding developmen-tal changes in size and shape, as wellas the relationship between them(ontogenetic allometry). Within GM,allometry is generally investigated bylinear regression of either superim-posed coordinates or individual PCson a size variable; the process iscomparable to regression of linearmeasurements on a size variablesuch as the geometric mean. Bergeand Penin’s37 analysis of ontogeneticshape change in African apes usedthis approach, confirming the tradi-tional view that allometric variationis a large component of the shapedifferences between chimps andgorillas, but also describing how spe-cies-specific allometric and nonallo-metric shape variation contribute totaxonomic differences in cranialshape.

A more recent development is theanalysis in size-shape space. Ratherthan analyzing only shape and thenregressing it against size, thisapproach includes the natural log ofcentroid size as an additional vari-able alongside the superimposedcoordinates in a PCA.38 Because sizehas a larger variance than do theindividual coordinates, which havebeen scaled to a configuration size of1, the first PC axis will primarilyreflect absolute size differences inthe sample (as well as allometricshape differences that are commonto the entire sample).38 Concentrat-ing the common allometric shapevariation into a single componentoffers a clear advantage over a stand-ard PCA in shape space, where thisvariation may be distributed acrossseveral axes.

Mitteroecker and colleagues’38

analysis of ontogenetic allometryamong great ape and human craniain size-shape space showed thathumans have the most distinct cra-nial shape at birth, but that theorangutan cranium also differsslightly from that of the African apeseven at this early stage. In additionto different initial shapes, both thehuman and orangutan trajectoriesalso diverge from that of the Africanapes, and each other, early in ontog-eny, further distinguishing these twotaxa. In contrast, gorillas and chim-panzees appeared to follow very sim-


ilar trajectories in this multi-taxonanalysis. However, when the analysiswas limited to the African apes, itwas clear that more subtle differen-ces in the trajectories of chimpan-zees and gorillas were masked in thelarger ordination, and that, in agree-ment with Berge and Penin,37 thesetaxa differ by more than just allomet-ric scaling.

Researchers have taken advantageof juvenile fossils to extend thesecomparisons to extinct hominin spe-cies. For example, using the Taungchild as well as adult A. africanusfossils, Cobb and O’Higgins39 foundthat the primary direction of ontoge-netic shape change in the face of A.africanus was more similar to that inchimpanzees and gorillas than thatin modern humans (based on a com-parison of the first PC in species-spe-cific PCAs). McNulty et al.24 obtaineda similar result using the full dimen-sionality of shape space. They fur-ther demonstrated that despite dif-ferences between late-stage develop-mental patterns among African apes,any model of development applied tothe Taung child predicts an adultform more like that of Sts 71 thanSts 5. Differences in ontogenetic de-velopment have been quantified evenamong the more closely relatedNeanderthals and modern humans.Based on a PCA in size-shape space,Bastir, O’Higgins, and Rosas40 dem-onstrated that the mandibles ofNeanderthals <1 year of age areindistinguishable from those ofyoung modern humans, but that thespecies’ ontogenies diverge after thistime. This postnatal divergence inthe ontogenetic trajectories results inthe distinct adult morphologies ofthese two species.

In addition to the relationshipbetween size and shape, studies ofheterochrony are concerned with theassociation or dissociation of thesefactors with age. To identify the typeof heterochronic process (sensuGould41) responsible for dissocia-tions during ontogeny, it is necessaryto also analyze information about de-velopmental stage and possibly chro-nological age, as well as phylogeneticinformation.42,43 Heterochronic anal-yses using GM have typically fol-lowed traditional approaches, usingbivariate plots comparing PC scores,

log centroid size, and a time dimen-sion to detect dissociations amongshape, size, and age.44,45

An example of this approach inhuman paleontology is the diagnosisof rate hypermorphosis in bothgrowth and development of the skullin Neanderthals compared to mod-ern humans using GM methods.44 Itseems likely that species-specificmorphologies were present at birth,but that differences in skull morphol-ogy were further enhanced by diver-gent ontogenetic trajectories and afaster postnatal rate of size andshape change in Neanderthals.45 ThePonce de Leon and Zollikofer44 studynicely demonstrates the full visualimpact that is possible using 3-D GMmethods by illustrating shapechanges over ontogeny in modernhumans and Neanderthals usingcolor-coded vector fields superim-posed on the average shape for bothspecies (Fig. 3, p. 535, in that publi-cation).

However, the use of bivariate com-parisons of PC scores, size, and time,is somewhat controversial. Thedebate centers on whether similargroup distributions on a limitednumber of PC axes (for example, PCs1 and 2) signify that those groupsundergo similar ontogenetic shapechange, or whether a common allo-metric or ontogenetic trajectory isvalid only if it can be demonstratedfor the entirety of shape space (thatis, along all PC axes). Researcherswho advocate the use of only a lim-ited number of PCs argue that PCsare as valid as linear measurementsor ratios for describing biologicalshape; covariation in traits capturedby PCs are likely to be the result ofdevelopmental processes; and PCscan highlight testable hypothesesregarding morphogenesis.45 Criticsof this approach point out that PCsare simply statistical constructs anddo not necessarily have easy biologi-cal interpretations.12,46,47 They alsoargue that similar slopes on only afew PCs does not mean that trajecto-ries are necessarily parallel in fullshape space (that is, if all PCs areinspected).38,39,46 Moreover, individ-ual PC axes may include shape varia-tion not directly related to ontogeny,including interspecific shape differ-ences.38

If these criticisms are correct andthe signal from the first few PCs isnot a reliable way to compare inter-specific allometric or ontogeneticpatterns, then what is the alterna-tive? Among the possibilities, onestands out because it avoids usingordination methods like PCA alto-gether and instead uses direct com-parison of ontogenetic or allometrictrajectories within the entire shapespace.38,39 These trajectories are alist of beta (slope) coefficients foreach coordinate from a multivariateregression of the coordinates oncentroid size35 or dental stages.24 Adisadvantage of this approach is thatthese trajectories are multivariate andcannot be visualized on a 2-D or 3-Dplot. Nevertheless, one can measurethe angle between these multivariatetrajectories just as one measures theangle between two regression slopesin a bivariate analysis. Comparisonsbetween groups can then proceedwith reference to the angular differen-ces.24,35 Taken to its logical extreme,the consequence of this approach isthat if the ontogenetic trajectories oftwo species diverge on even one PCaxis, no matter how little variationthat PC accounts for, we would haveto reject the hypothesis of global het-erochrony.

In fact, Mitteroecker, Gunz, and

Bookstein46 argue just this, based on

the observation that for classic heter-ochronic descriptors to be valid, the

underlying ontogenetic trajectories

between species must be identical,thus allowing only disassociations

between shape, size, and time rather

than changes in shape trajectories.

They demonstrated that the trajecto-ries of Pan troglodytes and P. panis-cus are not identical in full shape

space, and thus rejected a purely het-erochronic explanation for observed

differences in craniofacial shape.

Even when the cranium was dividedinto the neurocranium, upper face,

and lower face, heterochrony for

each of these regions was rejected.46

These results appear to contradictthe findings of Lieberman and co-workers45 who also investigated therole of heterochrony in Pan at thelevel of the entire cranium. Lieber-man and coworkers’ results were

consistent with earlier studies based


on linear dimensions that identifiedheterochrony in Pan. They specifi-cally identified postformation, theearly underdevelopment of shape, asthe likely explanation for particularshape differences (those on PC 1)between the two chimpanzee species.They also concluded that while post-formation explains some importantdifferences, particularly in the vaultand base, other evolutionary proc-esses must be invoked to explain dif-ferences in facial morphology. How-ever, the apparent conflict betweenthe two results is due to the fact thatLieberman and associates45 applied aless strict criterion for heterochronythan did Mitteroecker, Gunz, andBookstein46 and accepted an apparentpattern of heterochrony on PC 1 asbiologically meaningful even if thetrajectories did not overlap on all PCs.

Ultimately, resolution of this dis-agreement is not simple. On one hand,the argument that ontogenetic trajec-tories should be identical before invok-ing heterochronic explanations is rea-sonable. On the other hand, it may berelatively easy to find a significant dif-ference between two multi-dimen-sional vectors, given the copiousamounts of data that can now be col-lected and analyzed in GM analyses.Unfortunately, there is no clear rulefor how many variables must differand by how much before two trajecto-ries are ‘‘significantly’’ different (in abiological rather than a statisticalsense). While heterochrony providesan elegant theoretical framework forexplaining evolutionary change inmorphology, it seems increasinglyunlikely that global heterochrony willbe validated in multivariate analysesof shape. Rather than focusing solelyon significant p-values, therefore, itmay be more fruitful to identify theactual similarities and differencesamong shape trajectories, assess thetiming of those differences, and tracktheir ultimate impact on adult mor-phology. These avenues of investiga-tion have the potential to identify newhypotheses related to the developmen-tal and evolutionary pathwaysinvolved in lineage diversification.

Modularity and Integration

The idea that biological processessuch as heterochrony act differen-

tially across a structure is intimatelytied to the concept of modularity.Modularity predicts that develop-mental, functional, or other biologi-cal processes produce natural parti-tions among sets of characters,called modules. For example, pio-neering work by Moss48 emphasizedthe importance of epigenetic effectsfrom the surrounding soft tissuesand spaces (functional matrices) dur-ing development of the distinct cra-nial components. A key assumptionof current modularity studies is thattraits exhibit stronger covariationwithin than among modules.49 Theweaker among-module connectivitymay allow for the semi-independentaction of evolutionary and develop-mental processes (such as differen-tial heterochrony) on individualmodules. Conceptually, modularity isrelated to morphological integration,which is based on the idea that indi-vidual morphological features do notevolve in isolation; rather, individualphenotypic features evolve in a coor-dinated fashion.

Analytical methods related to inte-gration and modularity have severalgoals, including quantification of themagnitude of integration (for exam-ple, among modules or taxa), identi-fication of the underlying processleading to integration, verification ofa priori defined modules, and com-paring and visualizing patterns ofintegration or modularity.50,51 Wewill focus on the latter two points.

Verification of a priori modules

Several approaches are available totest whether empirical data are con-gruent with hypothesized modules.One approach involves comparingthe correlation matrix from the em-pirical measurements to a connectiv-ity matrix of expected correlationsbased on the hypothesized modules(derived from genetic, developmen-tal, or functional considerations).51,52

In this context, the connectivity ma-trix is composed of a ‘‘1’’ or a ‘‘0’’ inthe cell corresponding to each pairof traits, depending on whether ornot the traits are expected to be inthe same module. The matrix corre-lation between the original, empiri-

cally derived correlation matrix andthe connectivity matrix is used toassess whether the observed patternof trait correlations corresponds tothe hypothesized modules. Thisapproach has been applied broadlyacross mammals53 and within prima-tes,54–57 including hominoids,58 usinglinear measurements. An alternativeapproach is to calculate the correla-tion (or covariation) between thetraits assigned to each hypothesizedmodule.51,59,60 This value can thenbe compared to an empirical distri-bution of correlation values gener-ated through a permutation proce-dure that randomly assigns traits,without replacement, to modules. Ifthe hypothesized modules are indeedtrue biological modules, then the cor-relation between the hypothesizedmodules should be relatively low,reflecting their (semi-) independencefrom one another.51,59,60

A potential challenge to both ofthese methods is the fact that a spa-tially structured pattern of covari-ance among landmarks could mas-querade as evidence for modules.For example, the strength of covaria-tion between any two landmarkscould be negatively correlated withtheir interlandmark distances. This isa reasonable expectation because inmany cases ‘‘internal integration ofmodules relies on tissue-bound inter-actions among their parts.’’ 51:412

However, due to the highly unevendistribution of landmarks on mostbiological structures, spatially dis-junct clusters of landmarks wouldbehave as distinct modules regard-less of any underlying biologicalmodularity. In most studies of modu-larity, each a priori module is definedas a set of traits from a restrictedmorphological region (for example,the bones surrounding the nasal cav-ity) rather than landmarks from spa-tially disparate regions (for example,the bones surrounding the nasal cav-ity and the foramen magnum). Thispresents a distinct challenge becauseit means that low levels of integra-tion among a-priori-defined modulesis not necessarily support for theunderlying theoretical model onwhich these partitions were based.This pattern of spatial autocorrela-tion may explain why many studies


find support for multiple alternativemodels of modularity.61,62

One way to address this problem isto modify the second test describedabove to require that the landmarksassigned to each module during thepermutation process be spatially con-tiguous (that is, neighboring land-marks).51,58,59 This more closelyresembles the reality that hypothe-sized modules are composed of land-marks from a restricted spatialregion and therefore provide a moreconservative test of modularity. How-ever, it remains unclear whethereven this solution goes far enough,as suggested by the two examplespresented by Klingenberg51 to dem-onstrate this method. This permuta-tion test rejected the anterior andposterior compartments of the flywing as distinct modules, but sup-ported the presence of ascendingramus and alveolar modules in themouse mandible.51 However, theproposed modules of the wing arenot nearly as spatially disjunct as arethe modules proposed for the mousemandible. Furthermore, there is noother combination of the mousemandible landmarks that results intwo modules as spatially isolated asthe hypothesized modules. It istherefore difficult to know whetherthese results should be interpreted assupporting the developmental modu-larity of the mouse mandible but notthe fly wing, or whether this simplyreflects a pattern of spatial autocor-relation among landmarks in bothstructures.

The increasing popularity of mod-ularity studies in anthropologymakes it likely that these approacheswill soon be extended to hominins ina geometric morphometric frame-work. We suggest that it may be ad-visable to establish that a simple spa-tial model of covariation is insuffi-cient to explain the observedcovariation patterns before testingwhether theoretically derived a priorimodules are supported by empiricaldata. The means and criteria fordoing so, however, have not yet beenestablished. Of course, even if theobserved pattern of covariation isconsistent with a simple spatialmodel, this does not rule out thepresence of developmental or func-

tional modularity. The difficulty indistinguishing between these twointerpretations, however, does high-light the need for more sensitive testsof hypothesized modules.

Comparing and visualizing

patterns of integration or

modularity

The GM toolkit offers a distinctadvantage over linear morphometricsin its ability to visualize coordinatedshape change (that is, integration)across a structure or among struc-tures. For example, two-block partialleast squares analysis (2-B PLS), alsocalled singular warps analysis, is fre-quently used to visualize covariationbetween different structures or ana-tomical regions. 2-B PLS calculatesthe direction of maximum covaria-tion shared between two blocks ofvariables, such as the face and theneurocranium, and each successivepair of axes accounts for progres-sively less of the shared covariance(much as successive PC axes accountfor progressively less of the total var-iance).17,52,53 Each specimen can beplotted along the corresponding axes,one axis for each block of variables,and the coordinated shape variationcaptured by these axes can be visual-ized.

A 2-B PLS analysis of 3-D craniallandmarks subdivided into facial,neurocranial, and basicranial regionsfound that the main patterns of inte-gration among these cranial regionsare shared across taxa and through-out ontogeny in African apes andhumans.54,55 In fact, a large propor-tion of the shape differences amongthese taxa is due to differential trun-cation or extension of shared devel-opmental pathways, with a smallerproportion of the intertaxic shapedifferences due to more modular(local) changes. These results con-firmed an earlier analysis of integra-tion in African apes and humansbased on linear measurements.54 Arecent investigation further con-firmed that Pongo also shares the pri-mary patterns of integration withAfrican apes and humans, despite itsdistinct cranial shape.56 These com-parisons are important for under-

standing the evolution of develop-mental pathways and may explainwhy evolution appears to occur morefrequently in certain directions thanothers. Furthermore, this work hasbearing on the use of living taxa asanalogs for extinct species; althoughsimilar, patterns of integration in liv-ing hominoids are not identical toone another, and are unlikely to beidentical in extinct species.54

In regard to integration in fossilhominins, Bookstein and col-leagues17 extended the two-blockPLS to a three-block model, usingone of several possible algorithms, toexamine integration among the cra-nial vault, base, and face simultane-ously rather than on a pair-wise ba-sis. Careful sample design allowedcovariation among cranial regions tobe investigated both over ontogenyin H. sapiens and through evolutionin Pleistocene Homo. Overall, thepatterns of developmental and evolu-tionary integration were similar, withthe largest divergence occurring inthe cranial base: the anterior cranialbase underwent a rotation duringevolution that is not mirrored by on-togeny. Using the same three-blockapproach, Gunz and Harvati57 foundthat modern humans and Neander-thals have similar patterns of inte-gration among the temporal bones,midsagittal parietal, and midsagittaloccipital profiles. In both taxa, anoccipital bun occurred along with aflattened midsaggital parietal profileand with temporal bones positionedmore anterosuperiorly. In this con-text, the Neanderthal pattern ofextreme ‘‘bunning’’ could be viewedas an extrapolation of the humanpattern of cranial integration. Whatremains to be clarified, in this andother similar studies, is what under-lying forces result in these patternsof covariation.

FUTURE DIRECTIONS ANDCHALLENGES

Having highlighted the most com-mon and, arguably, successful appli-cations of GM approaches to paleo-anthropological questions, we turn toseveral areas that are only beginningto be explored and represent both


great promise and challenge fornovel applications of GM analyses:fossil reconstruction, functional mor-phology, quantitative genetic models,and phylogeny reconstruction. Someworkers have already begun explor-ing these areas, but additional workremains in all cases.

Fossil Reconstruction

The combination of visual and sta-tistical tools represented by the GMtoolkit has enormous potential foraiding in the reconstruction of dam-aged and warped fossil specimens.While fossil reconstruction usingthese methods is already well estab-lished in some research teams, thecomplex algorithms and expensivesoftware used for extensive recon-structive ‘‘surgery’’ have made thisapplication the domain of very fewpractitioners. More widely used arethe less technically sophisticatedmethods for estimating the positionof missing landmarks based on theexisting ones. The most straightfor-ward case is in a symmetrical speci-men when a bilateral landmark ismissing on only one side. The land-mark can be ‘‘mirrored’’ from thepreserved to the missing side in aprocess called reflected relabeling,which exploits the inherent symme-try of biological organisms.23,58

Other options exist for estimatingmidline landmarks or bilateral land-marks missing on both sides, includ-ing using the average landmark posi-tion in a morphologically similarcomparative sample or interpolatingthe position of a missing landmarkbased on multiple regression or athin-plate spine function.58

More elaborate and detailed recon-structions of fossil crania includerepositioning displaced or brokenmorphology, unwarping areas thathave suffered plastic deformation,and estimating the morphology ofmissing surfaces. These reconstruc-tions allow for more robust compari-sons across a fragmented fossil re-cord and also facilitate researchusing methods such as finite elementanalysis. Several studies that incor-porate complex reconstructions havenow been published,18,58,59 and Zol-likofer and Ponce de Leon60 have

published a book describing methodsfor virtual reconstructions. We referinterested readers to these sourcesfor details of these methods. Never-theless, the future potential of thisapplication of GM is in making vir-tual reconstruction more accessibleto the paleoanthropology communityin terms of data acquisition (avail-ability of digital fossil representa-tions) and software (priced towardmodest anthropology budgets).

Functional Morphology

More functionally oriented applica-tions of GM have either comparedshape differences to a priori predic-tions based on theoretical functionalmodels72 or done a 2-B PLS analysisof shape variables and functionalvariables.73 Although the linear andangular measurements that are themainstay of comparative functionalmorphology fail to account for thecomplex 3-D geometry of biologicalstructures, they have been chosen tomaximize the (functional) signal-to-noise ratio. In contrast, landmarksprovide a more realistic representa-tion of 3-D shape, but it is difficult toseparate the functional signal fromthe other signals also encoded in thelandmark data, such as, phylogenetichistory. Choosing a landmark config-uration that reflects the most func-tionally relevant aspects of shape, aswell as statistical approaches thatcan partition out the different sour-ces of variation, may be useful inovercoming this obstacle. Further-more, coordinate data may be partic-ularly useful in detecting morpholog-ical changes that are relativelysubtle, such as those between groupssubject to different experimentalconditions. As an example, animalsraised on different diets may exhibitslight but consistent osteologicalchanges more easily captured by 3-Dlandmark data than by traditionalmeasures.

An innovative application of GMwas the evaluation of the effect ofincluding the periodontal ligament ina finite element model of the humanmandible by measuring shapechange associated with deformationalongside the traditional analysis ofstrain data.61,62 This study repre-

sented an application of methods forcombining geometric morphometricsand functional simulations firstdeveloped by O’Higgins and co-workers.61 In addition to changesassociated with including the peri-odontal ligament (versus no liga-ment), they also documented differ-ent patterns of shape change in mod-els where varying material propertieswere assigned to the ligament. It isalso possible to use coordinate datato track changes in posture by col-lecting landmarks (at joint positions,for example) on the same individualat consecutive time slices. This or-dered sequence of landmark configu-rations (a trajectory) contains infor-mation about changes in positionover the course of a movement. Bypartitioning this trajectory into shape,size, and orientation components, itbecomes possible to quantitativelydescribe and compare differentmotions or different individuals per-forming the same motion.63

Quantitative Genetics

One emerging field of interest isthe study of how quantitative geneticmodels can explain morphologicalvariation. Quantitative genetics pro-vides insights into the heredity ofcontinuous traits and the underlyingevolutionary processes, such as selec-tion or genetic drift, that generateand maintain variation.64 In quanti-tative genetics, parameters such asheritability are estimated from largepedigreed samples or breedingexperiments. The existence of mod-ern human cranial data sources withknown or estimated pedigrees hasallowed anthropologists to study theheredity of craniofacial morphology.One of these sources, the FELS Lon-gitudinal Study, includes data frommore than a thousand modernhumans, including extended familieswith known relationships and DNAsequences for many individuals. Astudy conducted by Sherwood andMcNulty65 used landmarks and semi-landmarks to estimate heritability incraniofacial shape and correlationsbetween components of shape varia-tion and genetic variance. The resultswere highly suggestive, demonstrat-ing that specific regions of the ge-


nome may be linked to particularvariations in cranial shape, includingvariations in cranial flexion, midfa-cial prognathism, chin development,and other features that figure promi-nently in hypotheses about humanevolution. A larger study to test theselinkages and to look for additionalcorrelations is currently under way.Further research along these lineswill be possible as research on thehuman, chimpanzee, and Neander-thal genomes leads to additionalinsights into the genotype-to-pheno-type map for hominins.

Phylogeny Estimation

Reconstructing phylogeny withshape data is of great interest withinthe paleoanthropology community,but has proven challenging. Therehave been some limited attempts touse landmark-derived shape data toestimate phylogenetic relationshipsbased on converting shape informa-tion into discrete characters,66,67 usingphylogenetic methods developed spe-cifically for continuous data,68 or tree-building algorithms that cluster basedon distance measures.69 The long-standing debate over the theoreticaland empirical issues surrounding theconversion of continuous traits to dis-crete characters notwithstanding, therecent method advocated by Gonzalez-Jose et al.67 has been strongly criticizedon methodological grounds70 andshould not be applied.

Lockwood, Kimbel, and Lynch69

recovered the ‘‘correct’’ phylogeneticrelationships (that is, those based ongenetic data) among modern humansand apes by applying neighbor-join-ing and ordinary least squares algo-rithms to Procrustes distances from3-D temporal bone landmarks. Theyattributed their positive results toboth the repeatability and higher re-solution of landmark data comparedto qualitative and traditional mor-phometric data, and to the fact thatthe temporal bone’s ‘‘functional com-plexity should minimize the possibil-ity that a single behavioral shift inunrelated taxa could lead to homo-plastic similarity across a suite offeatures.’’69:4356 However, this studywas limited to the large-bodied apes,and it is unclear whether these

results could be replicated with alarger primate sample. Furthermore,subsequent studies have found thatthe parietal, sphenoid, and frontalbones are just as strongly correlatedas is the temporal bone with neutralgenetic distances among modernhuman populations.71 Overall cranialvault shape has also been shown tocorrelate with neutral genetic distan-ces among human populations.72

Together, these results indicatethat information regarding geneticrelationships may be encoded in cra-nial shape, but there is not yet a reli-able way to separate the phylogeneticsignal from the homoplastic informa-tion. For example, patterns of allom-etry can manifest in distinct lineagesas convergent morphology. Simplemethods to account for this, such asby regressing shape variables againstlog centroid size, may be inappropri-ate in many circumstances. Otherforces besides size changes can leadto homoplasies (for example, func-tional convergence), and it is alsounclear how to account for these.These difficulties are not unique toGM or even traditional quantitativevariables used in phylogeny recon-struction. However, when adopting aquantitative approach it becomesnecessary to account for such factorsin a rigorous and repeatable fashion.A final obstacle to using landmarkdata in phylogeny reconstruction isthat there is no single ‘‘best’’ solutionfor extracting the phylogenetic infor-mation. Rohlf68 suggested the use ofphylogenetic methods designed forcontinuous data, particularly themaximum likelihood methods of Fel-senstein,73 but this has not beenused in practice.

CONCLUSIONS

The GM toolkit evolved through ablending of shape theory from the fieldof mathematics, thin-plate spline anal-ogy from engineering, and multivari-ate analysis championed by biostatisti-cians. This synthesis resulted in a bio-logically and statistically powerful toolfor studying form that has substan-tially affected the study of human evo-lution. We have highlighted some ofthe contributions to date. However,the full power of GM will not be real-

ized until further integration takesplace between GM and analyticalapproaches from functional morphol-

ogy, quantitative genetics, phyloge-

netic comparative methods, and phy-logeny estimation. Important strides

forward are being made in these areas,

both from within biological anthropol-ogy and from closely allied disciplines

like evolutionary biology. We see

great potential for GM to contribute

further to paleoanthropological

research, not only in the areas dis-

cussed here, but also in new applica-

tions and modes of analysis.

ACKNOWLEDGMENTS

We thank John Fleagle for his ini-tial suggestion that we write thisreview, and for his continuedpatience. We also thank the reviewersfor their insightful and helpful com-ments on this manuscript.

REFERENCES

1 Howells WW. 1973. Cranial variation in man.Papers of the Peabody Museum of Archaeologyand Ethnology 67. Cambridge: Harvard Univer-sity Press.

2 Oxnard CE. 1973. Form and pattern in humanevolution. Chicago: University of Chicago Press.

3 Rohlf FJ, Marcus LF. 1993. A revolution inmorphometrics. Trends Ecol Evol 8:129–132.

4 Bookstein FL. 1991. Morphometric tools forlandmark data: geometry and biology. Cam-bridge: Cambridge University Press.

5 Adams DC, Rohlf FJ, Slice DE. 2004. Geomet-ric morphometrics: ten years of progress fol-lowing the ‘‘revolution.’’ Ital J Zool 71:5–16.

6 Slice DE. 2007. Geometric morphometrics.Annu Rev Anthropol 36:261–281.

7 Bookstein FL. 1997. Landmark methods forforms without landmarks: localizing group dif-ferences in outline shape. Med Image Anal1:225–243.

8 Perez SI, Valeria B, Paula NG. 2006. Differen-ces between sliding semi-landmark methods ingeometric morphometrics, with an applicationto human craniofacial and dental variation. JAnat 208:769–784.

9 Gower JC. 1975. Generalized Procrustes anal-ysis. Psychometrika 40:33–51.

10 Rohlf FJ, Slice D. 1990. Extensions of theProcrustes method for the optimal superimposi-tion of landmarks. Syst Zool 39:40–59.

11 Kent JT. 1994. The complex Bingham distri-bution and shape analysis. J Roy Stat Soc B56:285–299.

12 Rohlf FJ. 1999. Shape statistics: Procrustessuperimpositions and tangent spaces. J Classif16:197–223.

13 Kendall DG. 1989. A survey of the statisticaltheory of shape. Stat Sci 4:87–99.

14 Slice DE. 2001. Landmark coordinatesaligned by Procrustes analysis do not lie inKendall’s shape space. Syst Zool 50:141–149.


15 Marcus LF, Hingst-Zaher E, Zaher H. 2000.Application of landmark morphometrics toskulls representing the orders of living mam-mals. Hystrix 11:27–47.

16 Bookstein FL. 1996. Biometrics, biomathe-matics and the morphometric synthesis. BullMath Biol 58:313–365.

17 Bookstein FL, Gunz P, Mitteroecker P, et al.2003. Cranial integration in Homo: singularwarps analysis of the midsagittal plane in on-togeny and evolution. J Hum Evol 44:167–187.

18 Zollikofer CPE, Ponce de Leon MS, LiebermanDE, et al. 2005. Virtual cranial reconstruction ofSahelanthropus tchadensis. Nature 434:755–759.

19 Guy F, Lieberman DE, Pilbeam D, et al.2005. Morphological affinities of the Sahelan-thropus tchadensis (Late Miocene hominid fromChad) cranium. Proc Natl Acad Sci USA102:18836–18841.

20 Grine FE, Bailey RM, Harvati K, et al. 2007.Late Pleistocene human skull from Hofmeyr,South Africa, and modern human origins. Sci-ence 315:226–229.

21 Delson E, Harvati K, Reddy D, et al. 2001.The Sambungmacan 3 Homo erectus calvaria: acomparative morphometric and morphologicalanalysis. Anat Rec 262:380–397.

22 Baab KL. 2008. A re-evaluation of the taxo-nomic affinities of the early Homo craniumKNM-ER 42700. J Hum Evol 55:741–746.

23 Baab KL, McNulty KP. 2009. Size, shape,and asymmetry in fossil hominins: the status ofthe LB1 cranium based on 3D morphometricanalyses. J Hum Evol 57:608–622.

24 McNulty KP, Frost SR, Strait DS. 2006.Examining affinities of the Taung child by devel-opmental simulation. J Hum Evol 51:274–296.

25 Baab KL. 2007. Cranial shape variation inHomo erectus. PhD dissertation, City Universityof New York.

26 Harvati K, Frost SR, McNulty KP. 2004. Nean-derthal taxonomy reconsidered: implications of3D primate models of intra-and interspecific dif-ferences. Proc Natl Acad Sci USA 101:1147–1152.

27 Gomez-Robles A, Martinon-Torres M, Ber-mudez de Castro JM, et al. 2007. A geometricmorphometric analysis of hominin upper firstmolar shape. J Hum Evol 53:272–285.

28 Gomez-Robles A, Martinon-Torres M, Ber-mudez de Castro JM, et al. 2008. Geometricmorphometric analysis of the crown morphol-ogy of the lower first premolar of hominins,with special attention to Pleistocene Homo. JHum Evol 55:627–638.

29 Martinon-Torres M, Bastir M, Bermudez deCastro JM, et al. 2006. Hominin lower secondpremolar morphology: evolutionary inferencesthrough geometric morphometric analysis. JHum Evol 50:523–533.

30 Lieberman DE, McBratney BM, Krovitz G.2002. The evolution and development of cranialform in Homo sapiens. Proc Natl Acad Sci USA99:1134–1139.

31 Bruner E, Manzi G, Arsuaga JL. 2003.Encephalization and allometric trajectories inthe genus Homo: evidence from the Neandertaland modern lineages. Proc Natl Acad Sci USA100:15335–15340.

32 Gunz P, Bookstein FL, Mitteroecker P, et al.2009. Early modern human diversity suggestssubdivided population structure and a complexout-of-Africa scenario. Proc Natl Acad Sci USA106:6094–6098.

33 Perez SI, Bernal V, Gonzalez PN. 2009. Evo-lutionary relationships among prehistorichuman populations: an evaluation of related-ness patterns based on facial morphometric

data using molecular data. Hum Biol 79:25–50.

34 Gonzalez PN, Perez SI, Bernal V. 2010. On-togeny of robusticity of craniofacial traits inmodern humans: a study of South Americanpopulations. Am J Phys Anthropol 142:367–379.

35 Baab KL, Freidline SE, Wang SL, et al 2010.Relationship of cranial robusticity to cranialform, geography and climate in Homo sapiens.Am J Phys Anthropol 141:97–115.

36 Lahr MM, Wright RVS. 1996. The questionof robusticity and the relationship between cra-nial size and shape in Homo sapiens. J HumEvol 31:157–191.

37 Berge C, Penin X. 2004. Ontogenetic allome-try, heterochrony, and interspecific differencesin the skull of African apes, using tridimen-sional Procrustes analysis. Am J Phys Anthropol124:124–138.

38 Mitteroecker P, Gunz P, Bernhard M, et al.2004. Comparison of cranial ontogenetic trajec-tories among great apes and humans. J HumEvol 46:679–698.

39 Cobb SN, O’Higgins P. 2004. Hominins donot share a common postnatal facial ontogeneticshape trajectory. J Exp Zool B 302:302–321.

40 Bastir M, O’Higgins P, Rosas A. 2007. Facialontogeny in Neanderthals and modern humans.Proc R Soc B 274:1125–1132.

41 Gould SJ. 1977. Ontogeny and phylogeny.Cambridge: Harvard University Press.

42 Godfrey L, Sutherland MR. 1996. Paradox ofperamorphic paedomorphosis: heterochronyand human evolution. Am J Phys Anthropol99:17–42.

43 Klingenberg CP. 1998. Heterochrony and al-lometry: the analysis of evolutionary change inontogeny. Biol Rev Camb Philos Soc 73:79–123.

44 Ponce de Leon MS, Zollikofer CPE. 2001. Ne-anderthal cranial ontogeny and its implicationsfor late hominid diversity. Nature 412:534–538.

45 Lieberman DE, Carlo J, Ponce de Leon M,et al. 2007. A geometric morphometric analysisof heterochrony in the cranium of chimpanzeesand bonobos. J Hum Evol 52:647–662.

46 Mitteroecker P, Gunz P, Bookstein FL. 2005.Heterochrony and geometric morphometrics: acomparison of cranial growth in Pan paniscusversus Pan troglodytes. Evol Dev 7:244–258.

47 Mitteroecker P, Gunz P, Weber GW, et al.2004. Regional dissociated heterochrony inmultivariate analysis. Ann Anat 186:463–470.

48 Moss ML. 1972. Twenty years of functionalcranial analysis. Am J Orthodont 61:479–485.

49 Winther RG. 2001. Varieties of modules:kinds, levels, origins, and behaviors. J Exp Zool291:116–129.

50 Chernoff B, Magwene PM. 1999. Afterword:morphological integration: forty years later. In:Olson EC, Miller RL, editors. Morphologicalintegration. Chicago: University of ChicagoPress. p 319–353.

51 Mitteroecker P, Bookstein F. 2007. The con-ceptual and statistical relationship betweenmodularity and morphological integration. SystBiol 56:818–836.

52 Bastir M, Rosas A. 2005. Hierarchical natureof morphological integration and modularity inthe human posterior face. Am J Phys Anthropol128:26–34.

53 Rohlf FJ, Corti M. 2000. Use of two-blockpartial least-aquares to study covariation inshape. Syst Biol 49:740–753.

54 Ackermann RR. 2002. Patterns of covaria-tion in the hominoid craniofacial skeleton:implications for paleoanthropological models. JHum Evol 43:167–187.

55 Mitteroecker P, Bookstein FL. 2008. The ev-olutionary role of modularity and integration inthe hominoid cranium. Evolution 62:943–958.

56 Singh N, Harvati K, Hublin J-J, et al. 2012.Morphological evolution through integration: aquantitative study of cranial integration inHomo, Pan, Gorilla and Pongo. J Hum Evol62:155–164.

57 Gunz P, Harvati K. 2007. The Neanderthal‘‘chignon’’: variation, integration, and homol-ogy. J Hum Evol 52:262–274.

58 Gunz P, Mitteroecker P, Neubauer S, et al.2009. Principles for the virtual reconstructionof hominin crania. J Hum Evol 57:48–62.

59 Grine FE, Gunz P, Betti-Nash L, et al. 2010.Reconstruction of the Late Pleistocene humanskull from Hofmeyr, South Africa. J Hum Evol59:1–15.

60 Zollikofer CPE, Ponce de Leon MS. 2005.Virtual reconstruction: a primer in computer-assisted paleontology and biomedicine. NewYork: Wiley.

61 O’Higgins P, Cobb SN, Fitton LC, et al.2011. Combining geometric morphometrics andfunctional simulation: an emerging toolkit forvirtual functional analyses. J Anat 218:3–15.

62 Groning F, Fagan MJ, O’Higgins P. 2011.The effects of the periodontal ligament on man-dibular stiffness: a study combining finite ele-ment analysis and geometric morphometrics. JBiomech 44:1304–1312.

63 Adams DC, Cerney MM. 2007. Quantifyingbiomechanical motion using Procrustes motionanalysis. J Biomech 40:437–444.

64 Lande R. 1979. Quantitative genetic-analysisof multivariate evolution, applied to brain -body size allometry. Evolution 33:402–416.

65 Sherwood RJ, McNulty KP. 2011. Dissectingthe genetic architecture of craniofacial shape.In: Lestrel PE, editor. Biological shape analysis.Singapore: World Scientific. p 145–171.

66 Bookstein FL. 2000. Creases as local featuresof deformation grids. Med Image Anal 4:93–110.

67 Gonzalez-Jose R, Escapa I, Neves WA, et al.2008. Cladistic analysis of continuous modular-ized traits provides phylogenetic signals inHomo evolution. Nature 453:775–778.

68 Rohlf FJ. 1998. On applications of geometricmorphometrics to studies of ontogeny and phy-logeny. Syst Biol 47:147–158.

69 Lockwood CA, Kimbel WH, Lynch JM. 2004.Morphometrics and hominoid phylogeny: sup-port for a chimpanzee-human clade and differ-entiation among great ape subspecies. ProcNatl Acad Sci USA 101:4356–4360.

70 Adams DC, Cardini A, Monteiro LR, et al.2011. Morphometrics and phylogenetics: princi-pal components of shape from cranial modulesare neither appropriate nor effective cladisticcharacters. J Hum Evol 60:240–243

71 von Cramon-Taubadel N. 2009. Congruenceof individual cranial bone morphology and neu-tral molecular affinity patterns in modernhumans. Am J Phys Anthropol 140:205–215.

72 Harvati K, Weaver TD. 2006. Human cranialanatomy and the differential preservation ofpopulation history and climate signatures. AnatRec 288A:1225–1233.

73 Felsenstein J. 1981. Evolutionary trees fromDNA sequences: a maximum likelihoodapproach. J Mol Evol 17:368–376.

74 Dryden IL, Mardia KV. 1998. Statisticalshape analysis. New York: John Wiley andSons.

VVC 2011 Wiley Periodicals, Inc.


the shape of human evolution: a geometric morphometrics ...pages.nycep.org/ed/download/pdf/nmg...

Documents