SERIAL HOMOLOGY AND THE EVOLUTION OF MAMMALIAN LIMB COVARIATION STRUCTURE

2691

q 2005 The Society for the Study of Evolution. All rights reserved.

Evolution, 59(12), 2005, pp. 2691–2704

SERIAL HOMOLOGY AND THE EVOLUTION OF MAMMALIAN LIMBCOVARIATION STRUCTURE

NATHAN M. YOUNG1,2 AND BENEDIKT HALLGRIMSSON1,3

1Department of Cell Biology and Anatomy, University of Calgary, Health Sciences Centre, 3330 Hospital Drive NW,Calgary, Alberta T2N 4N1, Canada

2E-mail: [email protected]: [email protected]

Abstract. The tetrapod forelimb and hindlimb are serially homologous structures that share a broad range of devel-opmental pathways responsible for their patterning and outgrowth. Covariation between limbs, which can introduceconstraints on the production of variation, is related to the duplication of these developmental factors. Despite thisconstraint, there is remarkable diversity in limb morphology, with a variety of functional relationships between andwithin forelimb and hindlimb elements. Here we assess a hierarchical model of limb covariation structure based onshared developmental factors. We also test whether selection for morphologically divergent forelimbs or hindlimbsis associated with reduced covariation between limbs. Our sample includes primates, murines, a carnivoran, and achiropteran that exhibit varying degrees of forelimb and hindlimb specialization, limb size divergence, and/or phy-logenetic relatedness. We analyze the pattern and significance of between-limb morphological covariation with lineardistance data collected using standard morphometric techniques and analyzed by matrix correlations, eigenanalysis,and partial correlations. Results support a common limb covariation structure across these taxa and reduced covariationbetween limbs in nonquadruped species. This result indicates that diversity in limb morphology has evolved withoutsignficant modifications to a common covariation structure but that the higher degree of functional limb divergencein bats and, to some extent, gibbons is associated with weaker integration between limbs. This result supports thehypothesis that limb divergence, particularly selection for increased functional specialization, involves the reductionof developmental factors common to both limbs, thereby reducing covariation.

Key words. Limb development, limb morphology, modularity, morphological integration, morphometrics.

Received April 27, 2005. Accepted September 15, 2005.

Hierarchically structured patterns of phenotypic covaria-tion are commonly exhibited by vertebrates and possibly allmutlicellular animals (Olson and Miller 1958; Van Valen1965). The magnitude of this phenotypic covariation variesbetween structures. Scaling with body size produces a base-line level of covariation. Above this, changes in shape withbody size are often of functional or developmental impor-tance. Thus, selection for size-appropriate shape producesallometric covariation, a predictable relationship betweensize and shape. Finally, covariation can exceed the level ex-pected on the basis of size alone or allometric relationshipsto size. Such high magnitudes of covariation might be se-lected for because of close functional relationships amongstructures. High covariation might also occur due to con-strained developmental relationships or, more trivially, phys-ical adjacency. Using Wagner’s (1996) terminology, selec-tion only for a relationship to size corresponds to dissociationor parcellation, whereas selection for allometric or higherlevel covariation would be integration. These terms refer toevolutionary and not developmental processes.

Integration is often thought of in terms of functional as-sociation. For example, optimal tooth function is dependenton the proper occlusion of the jaw. Consequently, one mightpredict that covariation between upper and lower jaw wouldbe higher than that predicted from body size alone. If so,these traits would be functionally integrated. However, theproximate cause of integration lies in the developmental fac-tors that produce phenotypic variation (Nemeschkal 1999).That is, functional association may drive selection for inte-gration, but the underlying target of this selection is devel-opment. To produce high levels of covariation, selection mustact on the underlying developmental architecture of traits by

selecting factors that are either common (e.g., response tohormonal control of size) or particular to individual structuresor sets of structures. Selection to coordinate the develop-mental factors underlying upper and lower jaw morphologywould therefore have the effect of higher observed pheno-typic covariation (integration), whereas selection to disso-ciate these factors would lead to lower phenotypic covariation(parcellation).

Serially homologous structures, such as vertebrae, teeth,ribs, or limbs, represent a special case of the relationshipbetween covariation and developmental factors. Serial ho-mologues occur when the underlying developmental programfor a modular structure is duplicated and expressed in a newlocation and often at a new time (Hall 1995). The duplicateddevelopmental programs can then diverge with or withoutphenotypic divergence (Hall 1995). Because the develop-mental architecture is the same in serial homologues at thetime of duplication, presumably they are at first highly in-tegrated. Immediately following duplication, departure fromperfect covariation would likely only be due to environmentaleffects or to developmental factors that differ between thesites or times of expression (such as the level of some sys-temic determinant of growth). Covariation between serial ho-mologues would then remain high unless there was selectionto reduce it (i.e., parcellation). Selection for parcellation islikely driven by functional differentiation of the homologues(Wagner and Altenberg 1996).

The tetrapod forelimb and hindimb are serially homolo-gous and their development is particularly well characterized.Therefore, they serve as a valuable model for understandingthe evolution of covariation structure and its relationship toshared developmental factors. We present a brief outline of

2692 N. M. YOUNG AND B. HALLGRIMSSON

FIG. 1. (a) Schematic outline of some genes involved in specifyinglimb identity and outgrowth. Hox genes specify positional infor-mation and induce localized expression of genes in the lateral platemesoderm that contribute to limb identity: Tbx5 is expressed in theforelimb and Pitx1 and Tbx4 in the hindlimb. In both limbs, Fgf10is expressed in the early limb field and induces Fgf8 expression inthe ectoderm. Fgf8 expression in turn induces Shh, which then main-tains Fgf8 expression. Differences in either Tbx4/5 target genes orthe regulation of target genes common to both Tbx4/5 likely con-tribute to differences in morphology between limbs (Weatherbeeand Carroll 1999). Figure adapted from Ruvinsky and Gibson-Brown (2000). (b) In tetrapods the limbs consist of three segments(proximal to distal: stylopod, zeugopod, and autopod). Proximo-distal patterning of the limbs is thought to be influenced either bythe amount of time cells spend in the progress zone of the growinglimb-bud (Tickle and Wolpert 2002) or their spatial organizationin limb-bud mesenchyme prior to outgrowth (Dudley et al. 2002;

←

Sun et al. 2002). Regardless of mechanism, the 59 Hox paralogues9–13 are known to be involved early on in the patterning of specificlimb segments (Davis et al. 1995). In this diagram primary ex-pression pattern is shown in black, and lesser expression is rep-resented by gray shading. There are small differences between limbsin this expression pattern (e.g., Hox 9 paralogs are not active in thehindlimb stylopod; Wellik and Capecchi 2003). Figure adapted fromWellik and Capecchi (2003): c, carpals; mc, metacarpals; t, tarsals;mt, metatarsals; d, digits.

limb development and a model of limb covariation structurebased on developmental factors shared between limbs.

Limb Development

In tetrapods, limbs are divided into three segments: a sty-lopod (humerus, femur), zeugopod (radius/ulna, tibia/fibula),and autopod (carpals, tarsals, metacarpals, metatarsals, anddigits). Comparative anatomy, as well as the fossil record,indicates that the autopod is a more recent addition to thelimb skeleton, appearing at the same time in both limbs(Coates 1994; Shubin et al. 1997; Capdevila and Belmonte2000; Coates et al. 2002). The evolution and morphologicalorganization of the limbs is mirrored in their development.

Forelimbs and hindlimbs differ in how their identity isspecified, but both use many of the same basic developmentalpathways to regulate outgrowth and axis specification (Logan2003). Several genes are known to be involved in specifyinglimb identity (Fig. 1a): Ptx1 and Tbx4 are expressed in lateralplate mesoderm corresponding to the hindlimb-bud, and Tbx5is expressed in the region associated with the forelimb-bud(Logan et al. 1998; Logan and Tabin 1999; Ahn et al. 2002;Logan 2002, 2003; Agarwal et al. 2003; Marcil et al. 2003;Rallis et al. 2003). Despite differences in limb identity mech-anism, outgrowth is induced and regulated in much the sameway in both limbs. A complex series of gene interactions,including numerous feedback loops, promotes and maintainslimb growth (Fig. 1a; Dudley and Tabin 2000).

Proximo-distal patterning of the stylopod, zeugopod, andautopod is also similar in both limbs (Fig. 1b). Two alter-native models have been proposed for how limbs are pat-terned proximo-distally that differ in whether the mechanismis related to timing (Wolpert 2002; Tickle and Wolpert 2002)or spatial organization (Dudley et al. 2002; Sun et al. 2002).Regardless of the exact mechanism, as one moves more dis-tally, individual limb segments have been shown to be pat-terned by sequential members of 59 paralogous Hox 9–13(Davis et al. 1995; Wellik and Capecchi 2003; Fig. 1b). Thesesystems are virtually identical in both limbs, but there aresmall differences in expression pattern (Wellik and Capecchi2003). It is not clear whether these differences have any directeffect on limb morphology, although there is some evidenceHox genes expressed in these elements may affect the pro-liferation of chondrocytes (e.g., in forming normal growthplates) and undifferentiated mesenchymal cells (e.g., affect-ing condensation size; Goff and Tabin 1997; Boulet and Ca-pecchi 2004). Disruptions to proximo-distal patterning, eitherby knockouts or by physical manipulation of the limb-bud,can lead to loss, truncation, or malformation of segments(Wolpert 2002; Zelzer and Olsen 2003). Developmental ab-

2693LIMB COVARIATION STRUCTURE

FIG. 2. Hypothesized limb modules and hierarchical covariancestructure. In this model, size acts as on overall integrating factor.Hindlimb and forelimb are predicted to covary, as well as elementswithin a limb and homologous elements between limbs (stylopod,zeugopod, autopod). Individual elements should also covary highlywith themselves. Figure adapted from Hallgrımsson et al. (2002).

normalities also tend to be segmentally restricted in theirexpression (e.g., hemimelias, autopodal segment duplica-tions; Grzeschik 2002; Wilkie et al. 2002). Together thiswould suggest that genes associated with limb segment de-velopment have spatially restricted effects.

Factors that contribute to morphological differences be-tween limbs are not as well understood, although there havebeen attempts to characterize overall differences in gene ex-pression (Margulies et al. 2001). The limb identity genesTbx4, Tbx5, and Pitx1 or others further upstream may con-tribute to differences by either activating downstream genesuniquely expressed in either limb or by differential regulationof genes common to the development of both limbs (Weath-erbee and Carroll 1999). For example, small differences inHox hindlimb/forelimb proximo-distal patterning may be in-fluenced by genes that help establish limb identity.

Limb Covariation Model and Hypotheses

Hallgrımsson et al. (2002) proposed a model of limb co-variation structure based on developmental factors sharedbetween limbs. In this model, covariation is hierarchicallystructured between overall body size, between limbs, withinlimbs, between homologous elements, and within elements(Fig. 2). This model is consistent with morphometric data

from both fetal mice and rhesus macaques. In particular, Hall-grımsson and colleagues demonstrated significant covariationbetween homologous limb elements and that, when the limbgirdles are excluded, covaration between homologous ele-ments was higher than covariation within limbs. Results fromavian datasets are also consistent with this model (Van Valen1965; Wright 1968; Marcus 1990; Magwene 2001). However,in the avian datasets there is evidence that covariation ishigher within limbs than it is between homologous elements.For example, Van Valen (1965) found in hens that covariationbetween the forelimbs and hindlimbs was weaker than within-limb covariation. Magwene’s (2001) reanalysis of Wright’s(1968) fowl dataset also indicates that integration is strongerwithin limbs than between stylopod and zeugopod. Despitethese differences, results from these studies are consistentwith developmental factors playing a role in structuring limbcovariation.

If limb covariation is structured by shared developmentalfactors, selection on them should affect both limbs in a par-allel manner. For example, selection on the components ofproximo-distal patterning or outgrowth in one limb wouldlikely affect the other limb in a similar manner. This co-variation can be a constraint if selectively advantageouschanges in one limb produced selectively disadvantageouschanges in the other limb. This must not be the case in nature,because there is an an enormous diversity of forelimb andhindlimb size, shape, and function. This diversity occurs notonly in the specialization of forelimb relative to the hindlimbbut of particular elements within limbs (e.g., the bat’s highlyelongated autopod compared to both hindlimb and other fore-limb elements). How has limb diversity evolved in the faceof constraints from developmentally induced covariation?

A prediction from this model is that limb specializationfavors the reduction of covariation between limbs or ho-mologous elements (i.e., stylopod, zeugopod, autopod). Re-duced covariation would permit independent selection (i.e.,reduced developmental constraints) on forelimb and hindlimbmorphology and could help explain the evolution of limbdiversity. In addition, between-limb covariation should de-crease as a function of limb specialization (Hallgrımsson etal. 2002). This hypothesis also would indicate that divergencein limb form or function is associated with a reduction in therelative importance of developmental factors associated withboth limbs and the increase in relative importance of devel-opmental factors that only affect either the forelimb or hind-limb. Alternatively, limb covariation patterns could remainconstant. For example, there is little evidence for change incovariance structure associated with phylogenetic distance(Marroig and Cheverud 2001) and differences between theresults of Van Valen (1965), Magwene (2001), and Hall-grımsson et al. (2002) could be explained as methodological.Nearly constant covariation structure across these taxa wouldsuggest that selection on phenotypic means is not necessarilyconstrained by covariation between limbs. Developmentalfactors should therefore be relatively constant as well. Herewe assess Hallgrımsson et al.’s (2002) model of limb co-variance structure and test the prediction that between-limbcovariation decreases as forelimbs and hindlimbs divergefrom each other in size and function.


FIG. 3. Locations of landmarks on representative macaque limbskeletal elements: from left, humerus, femur, radius, tibia, meta-carpal (top right), metatarsal (bottom right).

MATERIALS AND METHODS

Sample

Six mammalian species representing a range of functionallocomotor types, limb divergence, and phylogenetic relat-edness were included in this study: Mus musculus (commonhouse mouse; randombred CV1 strain; n 5 84), Lophuromysflavopunctatus (brush-furred mouse; n 5 72), Mustela vison(American mink; n 5 51), Macaca mulatta (rhesus macaque;n 5 71), Hylobates lar (white-handed gibbon; n 5 63), andCarollia brevicauda (silky short-tailed bat; n 5 42).

Murines are represented by two species. Lophuromys de-rives from two wild-caught East African (Tanzania and Ugan-da) populations, whose skeletonized remains are housed atthe Field Museum of Natural History (FMNH). All specimensare sexed and adult, but exact ages are unknown. The M.musculus sample is a laboratory population that has beenoutbred to maintain genetic variation on par with naturalpopulations (Leamy 1974). This sample, which has been thefocus of numerous research papers (e.g., Leamy 1974, 1977),is composed of males and females of known age of death(100 days). Mus is important in comparison to Lophuromysbecause it is not only similar in size and closely related phy-logenetically, but control for age reduces the effect of sizeon variance. This is a very useful characteristic because micehave indeterminate growth (Riska et al. 1984; Lammers etal. 1998), which can lead to overestimates of covariance dueto ontogenetic sample heterogeneity. Both murine species areprimarily quadrupedal.

The primate sample is comprised of two species. The gib-bon is a small-bodied ape characterized by forelimb-domi-nated suspensory locomotion and long forelimbs relative tohindlimbs. The sample is made up of a single wild-caughtpopulation collected from a single locality in Thailand in the1920s by the Asian Primate Expedition and is now housedin the Museum of Comparative Zoology (Harvard Univer-sity). All gibbon specimens are adults of known sex. Themacaque is a terrestrial quadrupedal Old World monkey. Thesample used here comes from the Cayo Santiago collectionof the Laboratory of Primate Morphology and Genetics (Uni-versity of Puerto Rico). This population has been extensivelyanalyzed in the literature (Cheverud 1982, 1989; Hallgrıms-son et al. 2002; Willmore et al. 2005). Although provisioned,these macaques otherwise live under natural conditions. Allmacaque specimens are of known age at death. To insure thatspecimens were fully grown, only those aged eight years pluswere used.

Bat and mink samples are comprised of specimens housedat the FMNH. The bat sample was collected at a single geo-graphic locality in Oaxaca, Mexico. The mink sample wasoriginally collected from a game management reserve in Min-nesota. Both samples are adults of known sex.

Data

Data are derived from right and left femur, humerus, tibia,radius, metacarpal III, and metatarsal III. To simplify anal-ysis, a single representative bone was used for the zeugopod(radius/tibia) and autopod (metacarpal/metatarsal). Elementswere placed on a flatbed scanner (Epson Perfection 1650,

Epson America, Long Beach, CA) and scanned in 24-bit colorat either 600 or 1200 dpi (TIFF format), depending on thescale of the species. This method has similar characteristicsto camera-based systems, but with the added benefits of easeof setup and portability and reduced parallax associated withlenses. Although not completely eliminated, parallax errorwas minimized by the two-dimensional nature of most of thestructures scanned (Schubert 2000), as well as by the use ofhighly standardized positions for each element.

Two-dimensional landmark data were collected from thesescanned images. Landmarks were primarily chosen to coin-cide with epiphyseal boundaries or repeatable morphologicalfeatures (Fig. 3). The added difficulty of locating homologouslandmarks on phylogenetically distant taxa of various sizesnecessitated the use of reduced numbers of landmarks forsome species. Mus and mink datasets consisted of only max-imum length measurements for individual elements. As such,Mus and mink were included in only a subset of the analysesdescribed below. Landmarks were digitized from scannedimages using the software SigmaScan Pro (Systat Corp.,Richmond, CA). Bilateral linear measures between all pos-sible combinations of within-element landmarks were com-puted and averaged across sides. Raw distances were z-trans-formed within sex and/or geographic locality when necessaryto minimize the effect of sexual dimorphism or populationsubstructuring on covariance estimation.

As an alternative method to account for the effect of sexualdimorphism and general size, Burnaby’s (1966) method ofsize correction was used as implemented in NTSYS-pc (Rohlf2002). This method is essentially a multivariate residualsanalysis. In morphometric datasets, the first principal com-ponent is often highly correlated with size. Burnaby’s methodprojects data onto a plane orthogonal to the first principalcomponent of variation to correct for this size factor. However,a drawback of this method is that missing data cannot be


TABLE 1. Standardized lengths of limb segments. The average sumof the lengths of both limbs of each species was standardized toone with segments representing a portion of this length. MC, meta-carpal; MT, metatarsal.

Species

Stylopod

Humerus Femur

Zeugopod

Radius Tibia

Autopod

MC MT

Bat 0.193 0.117 0.273 0.116 0.277 0.024Gibbon 0.243 0.210 0.266 0.177 0.061 0.043Macaque 0.202 0.247 0.204 0.225 0.052 0.071Mink 0.219 0.203 0.148 0.249 0.072 0.109Lophuromys 0.180 0.242 0.172 0.262 0.050 0.093Mus 0.183 0.234 0.170 0.266 0.045 0.102

easily accounted for, precluding its use in datasets that in-clude a significant number of missing landmarks or elements(e.g., mink).

Two combinations of measurements were used to estimatecovariance matrices. The first consists of all within-elementz-transformed linear distance measurements (complete da-taset, CD). This dataset has the benefit of not biasing theanalysis with a priori assessments of which measures arerelevant. However, this dataset does include a large degreeof redundancy in information. The second dataset consists ofonly the length of each element either reported as a rawmeasure (ELD-r), a z-score (ELD-z), or as a Burnaby-trans-formed variable (ELD-b). This simplified dataset can be com-pared to prior studies of limb covariation that used similarmeasures (e.g., Magwene 2001; Hallgrımsson et al. 2002).However, there is also significant loss of information, par-ticularly pertaining to epiphyseal width measures that yieldadditional information on limb shape.

Analyses

The degree of between-species limb divergence was com-puted by standardizing the average raw length of both limbsto one in each species. Covariance matrix repeatability (t),the proportion of total variance due to individual differencesrather than measurement error, was calculated using a formof autocorrelation (Marroig and Cheverud 2001). Each da-taset was resampled 1000 times and the covariance matrixrecalculated. The mean matrix correlation between the orig-inal covariance matrix and the resampled covariance matricesis the estimate of covariance matrix repeatability.

Additional comparisons of species covariance matriceswere made using several complementary methods. Matrixcorrelations were computed between species for the overallcovariance matrix, between limbs, between elements, andbetween homologous elements (i.e., stylopod, zeugopod, au-topod). Significance of the matrix correlation was computedusing a Mantel’s test (1000 replicates) as implemented inPoptools (Hood 2003). The maximum correlation (Rmax) ap-proaches one when sample sizes are large, but with smallersample sizes Rmax can be estimated using matrix repeatability:Rmax 5 (tatb)1/2. Observed matrix correlations were adjustedvia the formula Radj 5 Robs/Rmax (Marroig and Cheverud2001).

Average within- and between-element correlations werecalculated to compare the relative strength of covariationbetween different subsets of traits. Correlations are not nor-mally distributed, so both raw correlations and Fisher-trans-formed correlations (Simpson et al. 1960) were averaged andcompared. As a prediction of our model, between-limb cor-relations should differ as a function of limb divergence (i.e.,they will be lower in species with divergent limbs).

As a measure of overall integration, Wagner’s (1984, 1990)index of integration was calculated by computing the varianceof the eigenvalues (VE) from each species covariance matrix(both from the CD and ELD). Subsets of the data (e.g., be-tween homologous elements) were also compared using thismethod. Higher VE indicates that most variance can be ex-plained by a single or only a few eigenvalues, which cor-responds to higher integration between the traits in question.

Lower VE indicates variance is more evenly distributedacross principal components, corresponding to lower inte-gration between traits. Significance of the difference betweenspecies VEs was calculated by resampling species data andrecomputing VE (Manly 1991). The P-value corresponds tothe number of times a given species VE exceeds the otherspecies VE (i.e., the difference between VEs . 0) dividedby the number of replicates (1000). All calculations weremade using the program R (R Development Core Team 2004).We predict that VE will be significantly lower in taxa whoselimbs are structurally or functionally divergent.

To further compare the pattern of integration, the elementlength dataset (ELD) was analyzed using partial correlations.Partial correlations are a measure of the strength of the re-lationship of two variables conditioned on other variables(i.e., the correlation of two variables independent of infor-mation from other variables in the correlation matrix). Partialcorrelations from three iterations of each species ELD wereanalyzed: raw measurements (ELD-r), z-transformed data(ELD-z), and Burnaby-transformed data (ELD-b). A partialcorrelation matrix was computed from these datasets. Theconditional independence of limb elements can be assessedusing partial correlations and an information theoretic mea-sure known as the edge exclusion deviance (EED):

2EED 5 2N ln(1 2 r ),ij·{K} (1)

where N is the sample size and rij·{K} is the partial correlationof variables i and j with all other elements held constant(Magwene 2001). In this case, an EED value of less than3.84 (corresponding to P 5 0.05, df 5 1 from the x2 distri-bution) indicates the two measures compared are conditonallyindependent. Diagrams were constructed in which elementsthat were not conditionally independent share an edge, asdescribed in Magwene (2001). We predict that within-limband between-homologous element measures will not be con-ditonally independent (i.e., they will share an edge), but thatbetween-limb measures will be conditionally independent ordissociated (i.e., no or weaker edge present) in taxa withstructurally divergent limbs.

RESULTS

Limb Divergence

Quantitative comparisons of standardized limb lengths arepresented in Tables 1 and 2 and a graphical illustration isshown in Figure 4. Bats have the longest relative forelimbs,


TABLE 2. Relative size between limb segments within the species.Numbers reflect the size of the forelimb element or module dividedby the hindlimb element or module. For example, a bat’s forelimbis on average 2.891 times the length of its hindlimb. H, humerus;F, femur; R, radius; T, tibia; MC, metacarpal; MT, metatarsal.

Species

Relative proportions

Forelimb-hindlimb H-F R-T MC-MT

Bat 2.891 1.647 2.361 11.464Gibbon 1.325 1.156 1.500 1.431Macaque 0.842 0.817 0.904 0.730Mink 0.781 1.079 0.593 0.659Lophuromys 0.674 0.742 0.658 0.540Mus 0.662 0.781 0.640 0.446

FIG. 4. A visual representation of relative limb proportions from Tables 1 and 2. For each species the average total limb length (forelimb1 hindlimb) was standardized to one to control for differences in body size and enable the comparison of limb proportions across taxa.In this figure individual elements were aligned proximally within the appropriate box. Within each species, hindlimb elements appearon the left side of the box and forelimb elements on the right. Bats have metacarpals that are roughly 10 times the length of theirmetatarsals and four times the length of any other species’ autopodal elements in this analysis.

followed by gibbons. Murines have the longest relative hind-limbs. The homologous elements of macaques are most sim-ilar in overall size (i.e., closest to one) of all the speciescompared.

Covariance Matrix Comparisons

Matrix repeatability in all taxa and for all datasets washigh (0.808–0.937; Table 3), indicating that individual sam-pling has a negligible effect on covariance matrix estimation.The lowest repeatability was associated with the mink (t 50.808) and is likely due to missing data for metacarpals andmetatarsals. Overall covariance matrix correlations and ad-justed matrix correlations from both the CD and ELD arepresented in Table 3. Matrix correlations between specieswithin elements, between homologous elements, within


TABLE 3. Between-species covariance matrix similarity (Rm) from both the complete dataset (CD) and element length dataset (ELD;see text). Raw correlations are shown below the diagonal, matrix repeatability (t) is in bold along the diagonal, and adjusted correlationsabove the diagonal. A Mantel’s test (1000 replicates) for all correlations was significant at P 5 0.001.

CD Bat Gibbon Macaque Lophuromys

Bat 0.849 0.761 0.813 0.761Gibbon 0.671 0.916 0.850 0.784Macaque 0.719 0.781 0.922 0.709Lophuromys 0.668 0.715 0.648 0.907

ELD Bat Gibbon Macaque Mink Lophuromys Mus

Bat 0.929 0.721 0.488 0.995 0.816 0.439Gibbon 0.672 0.936 0.854 0.620 0.571 0.555Macaque 0.449 0.790 0.914 0.301 0.403 0.616Mink 0.862 0.539 0.259 0.808 0.776 0.353Lophuromys 0.757 0.532 0.371 0.671 0.926 0.847Mus 0.403 0.511 0.561 0.302 0.776 0.906

TABLE 4. Average Fisher’s z-transformed correlations from the complete dataset (CD). Values along the diagonal are average correlationsof within-element measurements. Values below the diagonal are average correlations of between-element measurements. There is novalue for the Lophuromys tibia correlation. MC, metacarpal; MT, metatarsal.

Humerus Femur Radius Tibia MC MT

BatHumerus 0.826Femur 0.476 0.661Radius 0.531 0.469 0.855Tibia 0.372 0.453 0.502 0.796MC 0.289 0.256 0.459 0.291 0.823MT 0.179 0.165 0.131 0.122 0.081 0.601

GibbonHumerus 0.945Femur 0.537 0.958Radius 0.462 0.466 0.958Tibia 0.391 0.441 0.442 0.832MC 0.207 0.291 0.335 0.239 0.896MT 0.127 0.211 0.201 0.156 0.402 0.585

MacaqueHumerus 0.808Femur 0.446 0.754Radius 0.478 0.458 0.794Tibia 0.410 0.485 0.487 0.825MC 0.319 0.339 0.400 0.387 0.578MT 0.339 0.347 0.386 0.387 0.393 0.606

LophuromysHumerus 0.991Femur 0.821 1.157Radius 0.669 0.576 0.844Tibia 1.020 1.169 0.957 *MC 0.374 0.403 0.263 0.567 0.851MT 0.261 0.319 0.191 0.382 0.350 0.727

limbs, and overall covariance matrices computed from theCD were all highly significant (P , 0.001). Matrix corre-lations between ELD covariance matrices were also signifi-cant, although in some cases much lower than those from theCD. These results indicate overall structural similarities incovariance across a broad phylogenetic and functional sampleof mammalian limb types.

Average correlations and Fisher’s z for both the CD andELDs are presented in Tables 4 and 5. Both the CD and ELDresults indicate similar patterns of correlation among pri-mates, murines, the bat, and the mink. In the CD results thehighest correlations are within elements, followed by between

homologous elements, and between stylopod and zeugopodelements. High within-element correlations (Table 4) supportlimb element modularity; that is, within-element traits covarymore with themselves than with other elements. Correlationsof autopodal measures to other limb elements are among thelowest in all of the species.

ELD-z average correlations are similar to those from theCD but are generally higher (Table 5), most likely becausewidth measures have lower correlations both with other widthmeasures and with length measures. Several comparisons areof note: bats versus gibbons, Mus versus all other taxa, be-tween primates, and between quadrupeds (macaque, Lophu-


TABLE 5. Average correlations (Ravg) and average Fisher’s z-transformed correlations from the element length dataset (ELD) and thecomplete dataset (CD). Nohomologous, correlations between all nonhomologous elements; homologous, correlations between all limbhomologous elements; overall, average of all correlations.

ELD

Element set Bat Gibbon Macaque Mink Lophuromys Mus

CD

Element set Bat Gibbon Macaque Lophuromys

Ravg

Forelimb 0.700 0.593 0.659 0.806 0.747 0.146 Forelimb 0.376 0.376 0.402 0.388Hindlimb 0.544 0.489 0.742 0.583 0.638 0.461 Hindlimb 0.281 0.369 0.392 0.514Humerus-radius 0.837 0.763 0.773 0.821 0.913 0.411 Humerus-radius 0.430 0.391 0.413 0.412Femur-tibia 0.768 0.707 0.845 0.910 0.931 0.623 Femur-tibia 0.346 0.375 0.389 0.752Stylopod 0.831 0.804 0.795 0.893 0.886 0.597 Stylopod 0.407 0.490 0.405 0.607Zeugopod 0.810 0.767 0.802 0.908 0.905 0.537 Zeugopod 0.415 0.400 0.434 0.343Autopod 0.343 0.818 0.845 0.478 0.465 0.369 Autopod 0.196 0.372 0.387 0.420Nonhomologous 0.618 0.542 0.702 0.749 0.697 0.316 Nonhomologous 0.240 0.333 0.385 0.352Homologous 0.705 0.788 0.804 0.775 0.792 0.479 Homologous 0.371 0.444 0.415 0.553Overall 0.613 0.583 0.721 0.723 0.692 0.347 Overall 0.302 0.352 0.382 0.427

Fisher’s z averageForelimb 0.925 0.725 0.823 1.116 1.049 0.155 Forelimb 0.560 0.578 0.555 0.612Hindlimb 0.646 0.560 0.980 0.812 0.913 0.518 Hindlimb 0.432 0.550 0.570 0.817Humerus-radius 1.210 1.002 1.028 1.160 1.547 0.436 Humerus-radius 0.531 0.468 0.487 0.633Femur-tibia 1.015 0.881 1.237 1.530 1.663 0.729 Femur-tibia 0.453 0.436 0.495 1.169Stylopod 1.193 1.109 1.085 1.438 1.402 0.689 Stylopod 0.599 0.754 0.614 0.972Zeugopod 1.128 1.014 1.105 1.519 1.497 0.600 Zeugopod 0.649 0.681 0.669 0.790Autopod 0.358 1.151 1.238 0.521 0.503 0.388 Autopod 0.385 0.565 0.489 0.562Nonhomologous 0.769 0.640 0.898 1.030 0.973 0.356 Nonhomologous 0.318 0.453 0.499 0.487Homologous 0.972 1.069 1.114 1.159 1.237 0.528 Homologous 0.564 0.709 0.625 0.899Overall 0.772 0.716 0.939 1.009 0.974 0.388 Overall 0.410 0.474 0.497 0.617

FIG. 5. Boxplot of the variance of eigenvalues (VE) resamplingdistribution from the complete dataset. Boxes represent the 95%confidence interval and whiskers the resampling range. ObservedVE values: bat 5 18.24, gibbon 5 20.60, macaque 5 21.22, andLophuromys 5 28.18.

romys, and mink). Bats and gibbons differ from the othertaxa by having weaker overall average correlations. However,the pattern of correlations between these two species differs.For example, in bats the metacarpal-metatarsal correlation isclose to zero, whereas in gibbons it is close to one. The Musresults are remarkable for the low average correlations acrossall categories when compared to other taxa, including theclosely related taxon Lophuromys. This anomalous result islikely due to the fact that the Mus sample is composed ofindividuals of the same age. As a consequence, variance in

the sample is reduced, an attribute that tends to reduce es-timates of population covariance. The gibbon is very similarto the macaque, with primary differences in lower correla-tions within limbs, between nonhomologous elements, andin overall correlation. The macaque is discriminated furtherfrom the gibbon and bat in the ELD than it is in the CDresults. Quadrupedal taxa are similar in having relatively highoverall average correlations. These quadrupeds also havehigher within-hindlimb correlations compared to forelimb,while the opposite is true of the bat and gibbon.

Variance of the Eigenvalues

Variance of the eigenvalues (VE) as calculated from theCD indicates bats are the least integrated (VE 5 18.24), withgibbons (20.60), macaques (21.22), and Lophuromys (28.18)successively more integrated. The largest difference in thisanalysis was that of bat and primates compared to Lophu-romys. Resampling of each species VE indicates that the dif-ferences between bats, gibbons, and macaques are not sig-nificant, but that the difference between primates and Lo-phuromys is significant at the P , 0.05 level (Fig. 5). Therange of the resampled bat VE was large, likely due to smallersample size and lower CD covariance matrix repeatability.This affected the associated P-value of the bat-Lophuromyscomparison (P 5 0.101). These results indicate that Lophu-romys is more integrated than primates and likely more in-tegrated than bats. It cannot be said that primates or bats aresignificantly more or less integrated compared to each other.The VE from CD subsets revealed no other significant dif-ferences between species except for the comparison of meta-carpals and metatarsals (bat 5 5.38, gibbon 5 7.72, macaque5 6.71, Lophuromys 5 7.47; Fig. 6). In this case, bats exhibit


FIG. 6. Boxplot of the variance of eigenvalues (VE) resamplingdistribution from the complete dataset metacarpal and metatarsalsubset. Boxes represent the 95% confidence interval and whiskersthe resampling range. Observed VE values: bat 5 5.38, gibbon 57.72, macaque 5 6.71, Lophuromys 5 7.47.

FIG. 7. Boxplot of the variance of eigenvalues (VE) resamplingdistributions from the ELD-z. Boxes represent the 95% confidenceinterval and whiskers the resampling range. Observed VE values:bat 5 2.45, gibbon 5 2.24, macaque 5 3.17, mink 5 3.32, Lo-phuromys 5 2.89, Mus 5 1.02.

lower integration compared to other species (P 5 0.004–0.081).

Results from the VE analysis of the ELD-z are congruentwith the ELD-z average correlation results. Figure 7 showsthat quadrupedal taxa with the exception of Mus (macaque5 3.17, mink 5 3.32, and Lophuromys 5 2.89) are the mostintegrated, whereas gibbons (2.24) and bats (2.45) are lessso. Mus (1.02) is the least integrated. Differences betweengibbon and macaque are significant (P 5 0.024), but differ-ences are not significant between the two rodent species.Gibbon VE exceeded the observed mink VE in only onereplicate. There is only weak evidence that bat VE is sig-nificantly less than macaques (P 5 0.096) and no supportthat it is significantly less than Lophuromys (P 5 0.206).However, these results could be affected by small samplesizes. As in the comparison of average correlations, the anom-alous Mus result would appear to be a function of low var-iance in the original sample, thus complicating its comparisonto taxa from natural populations where age and size are notcontrolled.

Partial Correlations

Partial correlation matrices from the ELD-b of bat, gibbon,macaque, Lophuromys, and Mus are presented in Table 6.These results are consistent with those from the ELD-r andELD-z. Comparison of species’ first principal componentsvia vector correlation indicates highly correlated size allom-etries (average rv 5 0.966) although these were lower in batscompared to other taxa (average rv 5 0.792; Table 7). Com-parison of partial correlation matrices indicates commonal-ities across all taxa that are generally consistent with ourmodel, but also demonstrates differences in the pattern ofconnections between limb elements that may be associatedwith function (Fig. 8). In all taxa, there is evidence for sig-nificant edges within limbs and across most homologous el-ements, although there is variation in the strength of these

connections. The connection of forelimb autopod and zeu-gopod occurs only in bats and primates. Hindlimb autopodand zeugopod are linked in Mus and Lophuromys. Only inprimates is there an edge between forelimb and hindlimbautopod elements. Humerus-femur and radius-tibia partialcorrelations are strong in all taxa with the exception of thebat. Radius and tibia are conditionally independent in bats,as are their metacarpals and metatarsals. Together these re-sults suggest bats have the weakest relationship between fore-limb and hindlimb elements. In all other species edges areconsistently detected between stylopod and zeugopod, withvariable relationships between autopodal elements and be-tween autopod and zeugopod.

DISCUSSION

In Hallgrımsson et al.’s (2002) model, limb covariation ishypothesized to be hierarchically structured as the result ofshared developmental factors and is apportioned among size,between limbs, within limbs, between homologous elements,and within elements. Results from this comparative analysisof mammals are consistent with this model, as are previouslyreported findings from samples of fetal mice, rhesus ma-caques (Hallgrımsson et al. 2002), and birds (Van Valen1965; Magwene 2001). In addition, our results indicate thereis a relationship between covariation structure and the degreeof functional divergence in limbs. This result supports Hall-grımsson et al.’s prediction that increased functional diver-gence is correlated with a reduction in between-limb co-variation. Results reported by Van Valen (1965) and Mag-wene (2001) were also consistent with this interpretation.Another prediction of this result is that divergence in mor-phology involves a reduction in shared developmental factorsbetween limbs relative to factors that act individually on theforelimb or hindlimb.


TABLE 6. Species partial correlation matrices computed from the Burnaby-transformed element length dataset (ELD-b). Partial corre-lations significantly greater than zero (P , 0.05) are highlighted in bold. MC, metacarpal; MT, metatarsal.

Humerus Femur Radius Tibia MC MT

BatHumerus 1Femur 0.421 1Radius 0.454 20.083 1Tibia 0.070 0.446 0.113 1MC 0.054 0.107 0.640 0.239 1MT 0.070 0.018 20.022 0.071 20.032 1

GibbonHumerus 1Femur 0.530 1Radius 0.450 0.120 1Tibia 0.142 0.273 0.446 1MC 20.221 20.131 0.454 0.088 1MT 0.056 0.239 20.188 20.209 0.744 1

MacaqueHumerus 1Femur 0.412 1Radius 0.444 0.157 1Tibia 0.154 0.492 0.311 1MC 20.215 20.102 0.321 0.062 1MT 0.102 20.073 20.013 0.151 0.501 1

LophuromysHumerus 1Femur 0.290 1Radius 0.495 0.135 1Tibia 20.053 0.575 0.479 1MC 0.194 0.078 20.164 0.043 1MT 0.165 20.053 20.102 0.262 0.187 1

MusHumerus 1Femur 0.365 1Radius 0.265 0.327 1Tibia 0.282 0.430 0.236 1MC 20.098 0.004 20.004 0.053 1MT 0.103 20.118 0.016 0.384 0.185 1

TABLE 7. Species pairwise vector correlations (Rv) between thefirst principal component (PC1) as calculated from the elementlength dataset.

PC1 Bat Gibbon Macaque Mink Lophuromys Mus

Bat 1Gibbon 0.874 1Macaque 0.818 0.965 1Mink 0.783 0.940 0.986 1Lophuromys 0.756 0.922 0.980 0.971 1Mus 0.731 0.936 0.982 0.992 0.981 1

Support for Developmental Factors StructuringLimb Covariation

Covariance matrices derived from the CD are similarlystructured and well correlated across all species. Althoughoverall matrix correlations of ELD covariance matrices arelower than those from the CD, they are still significantlysimilar. Partial correlations also support a common limb co-variance structure among these taxa. Across all species, av-erage correlations within elements are higher than betweenelements, supporting modularity of individual limb segments.The next highest correlations are between stylopod and zeu-

gopod elements, that is, humerus-femur and radius-tibia com-parisons. These values typically exceed within-limb corre-lations, contra results of Van Valen (1965) and Magwene(2001). Within-limb partial correlations are also as stronglysupported as those between homologous elements, which dif-fers from the pattern reported by Magwene (2001). Edges aredetected between homologous elements of the zeugopod andstylopod. However, only in primates is there evidence ofsignificant covariation between forelimb and hindlimb au-topod. Correlations between homologous elements also havehigher correlations compared to between-limb nonhomolo-gous elements (e.g., femur-radius, humerus-metatarsal).

With the exception of the autopod, these results are con-sistent with what is known of limb developmental genetics.That is, conserved genetic pathways associated with the out-growth and patterning of limbs are reflected in similaritiesin covariance structure. This overall similarity is seen despitelong periods of independent evolution (e.g., a Lophuromysand Mus ancestor was estimated at 13–21 million years ago[Springer et al. 2003], while gibbon and macaque lineagessplit 29–34 million years ago; Steiper et al. 2004), and mod-ifications from a primitive body plan and proportions thatwere most likely similar to the murines (Fischer et al. 2002).


FIG. 8. Diagrams illustrating signifcant edges (P , 0.05) betweenhomologous limb elements and within limbs. Numbers refer to thecorresponding partial correlation (see Table 6). MC, metacarpal;MT, metatarsal; R, radius; T, tibia; H, humerus; F, femur.

This result may not be surprising given the conservation ofmany developmental pathways from flies to mammals (Cap-devila and Belmonte 2000).

There is some evidence that covariance structure is mostsimilar in closely related taxa. ELD matrix correlations arehighest between phylogenetic pairs (primates, murines). Theadjusted matrix correlation between bat and mink is inflateddue to low matrix repeatability in the mink (a function ofsmall sample size for the autopod measures). Although Lo-phuromys and Mus differ in the magnitude of average cor-relations and in VE, the pattern of correlations, matrix cor-relations, and partial correlations indicate they are more sim-ilar to each other than to any of the other species. The sameis true of gibbons and macaques. Gibbons have significantlychanged limb function and proportions relative to macaques,yet both primates have covariance matrices that are moresimilar to each other than to any other species analyzed here.

A result not explicitly predicted by this model is the var-iation in autopod integration. Murines, mink, and bat all havelow correlations between the forelimb and hindlimb autopod.

In primates there is significant covariation between the au-topod, as was found by Hallgrımsson et al. (2002) using datafrom the same macaque population. Within limbs, either theforelimb or hindlimb zeugopod and autopod (i.e., radius/metacarpal or tibia/metatarsal) are integrated in all speciesas measured by partial correlations. This link is in the fore-limb of primates and bat but in the hindlimb of murines. Thiswould suggest that covariation between the forelimb andhindlimb autopod has undergone significant changes in somelineages.

In general, autopodal elements are more variable in mor-phology than are proximal limb segments (Shubin et al. 1997;Capdevila and Belmonte 2000) and may be under greaterselection due to their interaction with the substrate. Hall-grımsson et al. (2002) demonstrated in macaques that phe-notypic and environmental variances increase and heritabilitydecreases as one moves down the limb. These results arepredicted by the fact that development proceeds proximo-distally, thus variation will tend to accumulate in distal struc-tures. The results reported here also indicate that there issubstantial variation in developmental factors associated withautopod patterning not present in more proximal elements.Indeed, patterning of the autopod involves substantial re-deployment of many Hox genes, which may involve changesin downstream targets. It is telling that the lowest autopodcorrelations occur in bats, whose autopods have undergonethe most radical changes for flight.

Divergence in Limbs is Correlated with Function

There is additional evidence for variation in covariancestructure associated with limb divergence and/or function.Both bat and gibbon have the lowest overall average limbcorrelations, the lowest VE (from both the CD and ELD,although not consistently significant), and higher within-fore-limb correlations compared to hindlimb. Both of these speciesalso have relatively long forelimbs (Table 2). However, it isnot necessarily relative size that is correlated with lower limbcovariation. Indeed, murines have hindlimbs that are almostas divergent in size as gibbon forelimbs. Instead, the degreeof coordinated limb function or specialization may play arole. That is, species that are primarily quadrupedal are moreintegrated than species that use the forelimb or hindlimb formuch different functions. This is not to say that the forelimband hindlimb of quadrupeds are not under different selectivepressures (e.g., support vs. propulsion). However, the degreeto which selection acts on differences in these quadrupedsmay not be as high as it is in bats or gibbons. We predictthat animals that use hindlimbs for a largely exclusive func-tion (e.g., bounding in kangaroos, bipedalism in humans)would exhibit similarly reduced covariation between limbs.Another difference between these taxa and quadrupeds is inwithin-limb covariation. Both bat and gibbon have higherwithin-forelimb covariation than in the hindlimb, whereasthe opposite is true of quadrupeds.

The bat diverges the most from the other species in co-variance structure. Bat forelimb and hindlimb differ both intheir primary function (flying, hanging) and relative length.Although neither the comparison of VE nor matrix correla-tions from the CD distinguished bats from primates, com-


parison of average Fisher-transformed correlations, elementsubset VE, and partial correlations from the ELD indicatedifferences in between-limb covariance structure. Averagecorrelations between metacarpal and metatarsal traits in batsare low in both the CD and ELD compared to other taxa.This is apparent in the VE of the CD metacarpal-metatarsalsubset as well. By itself, this is not too remarkable becauseboth murine species and the mink have low autopodal cor-relations. However, partial correlations between bat zeugo-podal elements are not significantly different than zero. Thisresult is somewhat surprising given the strong average cor-relations of bat zeugopod elements. There are significant par-tial correlations within the bat forelimb but none between theradius and tibia or between the metacarpal and metatarsal.Furthermore, the comparison of first principal component al-lometric vectors suggests bats have a pattern of limb allom-etry different from the other taxa. Together these results sug-gest bats have a distinctive pattern of limb covariation. Giventhe similarity of all other taxa, the most parsimonious ex-planation for this result is that bat forelimb and hindlimbdevelopment has become dissociated from a more integratedpattern.

If phenotypic covariance is linked to developmental factorscommon to both limbs, we can predict from these results thatthere are differences in developmental factors between theradius and tibia and metacarpal and metatarsal of bats com-pared to other mammals. Although it is not possible to testthis hypothesis here, there is emerging evidence to supportthis idea. For example, Chen et al. (2005) reported that, rel-ative to mice, the expression boundary of Hoxd13 is shiftedanteriorly in the bat metacarpals and phalanges, but the hind-limb expression boundary is identical to that in the mouse.Sears et al. (2005) reported that the initial size of limb con-dendations is similar in bat and mouse, but both the hyper-trophic zone and the Bmp2 expression area is expanded inthe forelimb digital growth plates of bats. These findingsindicate differences in the expression of common develop-mental factors between bat autopods and support the hy-pothesis that reduction in covariation is associated with re-duction in developmental processes common to both limbs.

Evolvability and Developmental Constraint

The observation that limb covariation structure is similarwithin and across limbs in the taxa sampled here impliesthere are constraints on the production of variation. That is,selection on one limb will have effects on both, unless mech-anisms evolved that reduce covariation. At the same time,these taxa represent a range of limb diversity that is the resultof selection on morphology, suggesting that limb morphologyis highly evolvable using a standard developmental toolkit.What mechanisms exist to break down covariation betweenintegrated traits? One possibility is the differential regulationof common developmental pathways (Raff 1996; Carroll etal. 2001). For example, Shapiro et al. (2004) speculated thatdevelopmental control genes could have tissue-specific cis-regulatory elements that would enable major morphologicalchanges in specific body regions without disrupting othertissues. A better grasp of the evolution of regulatory elementswill likely play an important role in understanding how co-

variance structure and morphological diversity are related(Rudel and Sommer 2003; Fondon and Garner 2004; Gompelet al. 2005).

These results also show that covariation structure can bemodified in different ways to produce similar types of limbdivergence. For example, comparison of bats to gibbons sug-gests elongated and specialized forelimbs can be producedwith or without constraints imposed by covariation structure.The bat exhibits weak covariation between zeugopodal andespecially autopodal elements, whereas these elements arestrongly integrated in the gibbon. This indicates that selectionin bats for elongated forelimbs has involved a reduction incommon developmental factors between limbs. As discussedabove, there is emerging evidence to support this conclusion.In contrast, elongation of the gibbon forelimb would appearto involve the modification of developmental processes thataffect both limbs. Indeed, although the gibbon has a com-paratively long forelimb, it also has absolutely long hindlimbelements (e.g., the metacarpals and metatarsals are both long).Compared to the macaque, homologous elements of gibbonsare reversed in relative length, that is, the gibbon humerusis the same relative length as the macaque femur (see Tables1, 2; Fig. 4). The gibbon also has relatively symmetrical handand foot morphology, while the bat wing exhibits substantialvariability in length along its anterior-posterior axis and nonein the foot.

This finding indicates that constraints imposed by a com-mon mammalian covariation structure are weak enough toallow differences on the order of those between gibbon andmacaque, perhaps by reducing developmental factors affect-ing covariation between nonhomologous elements. However,differences in forelimb and hindlimb morphology seen in batsrequire the breakdown of previously integrated patterns (e.g.,between radius and tibia, metacarpal and metatarsal). Al-though there is still covariation between bat limbs, it is lessthan would be expected given what we know of limb de-velopment. The addition of other taxa with highly divergentlimb morphologies (e.g., seals, humans, kangaroos, glidingpossum) or with high variability (dometsticated dog breeds)will help to clarify whether this pattern is specific to bats oris generalizable across functional limb categories.

Future Approaches to the Study of Covariation Structure

This model of limb covariance structure focuses on sim-ilarities in the outgrowth and proximo-distal patterning oftetrapod (specifically mammalian) limb elements, but it canbe further expanded to include other patterning axes, seriallyhomologous structures, or taxonomic groups. The success ofthis model will be in its ability to predict how developmentalfactors affect patterns of covariation. For example, the pat-terning of the anterior-posterior axis of the limb involvesprogressively more complex series of Hox genes and inde-pendent regulatory inputs (Carroll et al. 2001). In bats, hind-limb digits are uniform in length and virtually indistinguish-able from one another, whereas their forelimb digits are high-ly heterogeneous in length (Swartz 1997). Insects exhibiteven greater appendicular specialization than in tetrapods(Carroll et al. 2001), and other serially homologous structuressuch as vertebrae have different functions depending on lo-


cation. In all of these cases, constraints imposed by commondevelopmental factors would likely have had to be overcometo enable these specialized morphologies.

The model presented here predicts that phenotypic co-variation will be affected by common developmental factors.As such, changes in developmental factors that affect eitherone or both limbs would be predicted to have different effectson phenotypic covariation. This hypothesis can be tested inmutant or knockout phenotypes by measuring changes in co-variance structure relative to controls from the same strain.For example, knockout of Ptx1 in mice caused marked re-ductions in hindlimb length but not in forelimbs (Lanctot etal. 1999; Shapiro et al. 2004), whereas knockout of Gdf5 ledto reductions in both limbs (Gurrieri et al. 2002). In theformer case, covariation between limbs is predicted to bereduced, whereas in the latter case covariation would be un-affected. Targeting regulatory elements that differentially af-fect gene expression within or between limbs will be a nec-essary refinement of this approach. As is true of other ques-tions about complex phenotypic patterns, success in unrav-eling the developmental genetics of vertebrate limbcovariation structure will require an integrated approach thatcombines current experimental approaches with refined mor-phometric analysis of phenotypic variability. Such an ap-proach will greatly facilitate our understanding of how thearchitecture of limb development has constrained and enabledthe diversification of vertebrate limb morphology.

ACKNOWLEDGMENTS

This research was funded by postdoctoral fellowships fromthe American School of Prehistoric Research and the AlbertaIngenuity Fund to NY and National Science and EngineeringResearch Council grant 238992-02, Canada Faculty Initiativegrant 3923, and Alberta Innovation and Science grant URSI-01-103-RI to BH. Data from Macaca specimens were ob-tained with the support of the Caribbean Primate ResearchCenter, the University of Puerto Rico, Medical SciencesCampus, and the National Institutes of Health (grantRR03640). The authors thank J. Chupasko (Museum of Com-parative Zoology); B. Patterson and W. Stanley (Field Mu-seum of Natural History); J. Cant and T. Kensler (Universityof Puerto Rico, Laboratory of Primate Morphology and Ge-netics); and L. Leamy (University of North Carolina-Char-lotte) for use of specimens in this study. The associate editor,two anonymous reviewers, and D. Pilbeam provided helpfulcriticism that greatly improved this paper.

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Corresponding Editor: C. Janis

SERIAL HOMOLOGY AND THE EVOLUTION OF MAMMALIAN LIMB COVARIATION STRUCTURE

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