The utility of cranial ontogeny for phylogenetic inference: a case study in crocodylians using geometric morphometrics


  • A. Watanabe,

    Corresponding author
    1. Department of Biological Science, Florida State University, Tallahassee, FL, USA
    Current affiliation:
    1. Division of Paleontology and Richard Gilder Graduate School, American Museum of Natural History, New York, NY 10024,, USA
    • Correspondence: Akinobu Watanabe, Department of Biological Science, Florida State University, Tallahassee, FL 32306-4295, USA.

      Tel.: 212 313 7951; fax: 212 769 5842; e-mail:

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  • D. E. Slice

    1. Department of Scientific Computing, Florida State University, Tallahassee, FL, USA
    2. Department of Anthropology, University of Vienna, Vienna, Austria
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The degree to which the ontogeny of organisms could facilitate our understanding of phylogenetic relationships has long been a subject of contention in evolutionary biology. The famed notion that ‘ontogeny recapitulates phylogeny’ has been largely discredited, but there remains an expectation that closely related organisms undergo similar morphological transformations throughout ontogeny. To test this assumption, we used three-dimensional geometric morphometric methods to characterize the cranial morphology of 10 extant crocodylian species and construct allometric trajectories that model the post-natal ontogenetic shape changes. Using time-calibrated molecular and morphological trees, we employed a suite of comparative phylogenetic methods to assess the extent of phylogenetic signal in these trajectories. All analyses largely demonstrated a lack of significant phylogenetic signal, indicating that ontogenetic shape changes contain little phylogenetic information. Notably, some Mantel tests yielded marginally significant results when analysed with the morphological tree, which suggest that the underlying signal in these trajectories is correlated with similarities in the adult cranial morphology. However, despite these instances, all other analyses, including more powerful tests for phylogenetic signal, recovered statistical and visual evidence against the assumption that similarities in ontogenetic shape changes are commensurate with phylogenetic relatedness and thus bring into question the efficacy of using allometric trajectories for phylogenetic inference.


Virtually all organisms undergo substantial changes in form throughout ontogeny. Natural selection is expected to operate across these transitions, promoting evolutionary changes in ontogenetic trajectories that ultimately lead to differences in adult phenotypes (Gould, 1977; Frankino et al., 2005). Presumably, less phenotypic divergence has occurred in closely related taxa compared with those that are more distantly related (Blomberg et al., 2003; Revell et al., 2008). As such, closely related taxa are predicted to exhibit similar ontogenetic changes. If true, morphological characters from ontogenetic data may hold enormous potential to enhance our phylogenetic understanding of organisms.

For well over a century, evolutionary biologists have argued the relationship between ontogeny and phylogeny (e.g. Haeckel, 1866; de Beer, 1958; Nelson, 1978; de Queiroz, 1985; Wake, 1989; Mabee, 2000; Laurin & Germain, 2011). The famed Recapitulationist Theory (‘ontogeny recapitulates phylogeny’) championed by Haeckel (1866) proposed the first major mechanistic explanation for the potential link between ontogeny and phylogeny. As Haeckel himself was aware, however, its universal adoption was deterred due to known occurrences of heterochrony, or forward and backward shifts in relative rates and timing of developmental processes (Gould, 1977; Alberch et al., 1979; McKinney & McNamara, 1991; Klingenberg, 1998). Organisms that follow decelerated or truncated development, for instance, could form clusters based on their ontogenetic trajectories despite being distantly related phylogenetically (e.g. Wiens et al., 2005). However, studies have also found that ontogenetic data mirror phylogenetic relationships (e.g. Larson, 2005; Laurin & Germain, 2011). Despite these competing expectations, some studies have presumed that similar or concordant ontogenetic trajectories reflect phylogenetic and taxonomic affinity (e.g. Piras et al., 2010; Campione & Evans, 2011). Therefore, the degree to which ontogeny is phylogenetically informative warrants a more comprehensive examination.

Geometric morphometrics (Rohlf & Marcus, 1993; Adams et al., 2004, 2013; Slice, 2005), or statistical analysis of shape, provides an effective approach for modelling and analysing ontogenetic shape changes. It commonly involves the collection of coordinate data of landmark points, which are then subjected to Procrustes superimposition that normalizes the position, orientation and scale of digitized specimens (Gower, 1975). By sampling a growth series, the superimposed (i.e. shape) data allow the construction of allometric trajectories that model the shape changes that occur during ontogeny (Klingenberg, 1998). Previous studies have compared allometric trajectories of various taxa, but statistical tests of interspecific differences did not directly incorporate phylogenetic trees (e.g. Klingenberg & Froese, 1991; Viđarsdóttir & Cobb, 2004; Cardini & O'Higgins, 2005; Wilson & Sánchez-Villagra, 2010; Klenovšek & Kryštufek, 2013). In most instances, the use of phylogenetic information has been limited to visual comparisons between topologies of phylogenic trees and phenograms constructed from conducting unweighted pair group method with arithmetic mean (UPGMA; Sneath & Sokal, 1973) on interspecific distances between trajectories (e.g. Cardini & O'Higgins, 2005; Piras et al., 2010). Accordingly, these studies have not been able to directly test for phylogenetic information in these ontogenetic trajectories. Furthermore, UPGMA could produce erroneous phenograms for data that deviate from ultrametricity (Felsenstein, 2004: Fig. 11.7), which could lead to spurious comparisons with phylogenetic trees. Here, we integrate modern morphometric and comparative phylogenetic approaches to explicitly test for phylogenetic signal in the ontogeny of crocodylians.

Among vertebrates, the clade Crocodylia (Norell, 1989; Clark, 1994; Brochu, 1997, 2001), which includes alligators, crocodiles and slender-snouted Indian and Malay gharials, provides an excellent system for studying ontogenetic changes in morphology: (i) extant crocodylians undergo remarkable 1000- to 13 000-fold increases in body mass, whereas at the same time experiencing substantial changes in shape (Grenard, 1991; Erickson et al., 2004); (ii) robust sampling of growth series is possible for many extant species; (iii) in addition to morphological trees (Brochu, 1999, 2000), a time-calibrated phylogenetic tree based on genetic sequences from all 23 extant species (Oaks, 2011) provides a tree on which comparative phylogenetic analyses can be conducted; and (iv) molecular and fossil evidence places the genesis of the clade in the late Cretaceous (~85 Ma), allowing macroevolutionary analysis on a broad temporal scale (Brochu, 2001; Oaks, 2011).

Using cranial specimens of 10 extant crocodylian species, we tested the assumption that ontogenetic shape changes are more similar among closely related species. In contrast to linear distance measurements used in previous macroevolutionary studies on allometric trajectories (e.g. Wilson & Sánchez-Villagra, 2010, 2011; Wilson, 2013), three-dimensional (3-D) shape data of cranial landmarks were collected from a post-natal size series. These shape data were then utilized to construct multiple types of allometric trajectories for each species. With these allometric trajectories and time-calibrated molecular and morphological trees, we employed several comparative phylogenetic methods to statistically analyse whether allometric trajectories contain significant phylogenetic signal, including (i) the K-statistic (Blomberg et al., 2003); (ii) a likelihood ratio test using Pagel's λ (Pagel, 1999); (iii) permutational regression analysis on a phylogenetic tree (Laurin, 2004); and (iv) a Mantel test (Mantel, 1967; Sokal & Rohlf, 1995). In addition, we further confirmed our results by testing the topological congruence between UPGMA phenograms and the phylogenetic trees, which were only carried out visually in previous studies (e.g. Cardini & O'Higgins, 2005; Piras et al., 2010). Results indicating significant phylogenetic signal would imply a strong link between ontogeny and phylogeny and give support to the use of ontogenetic shape data as phylogenetic characters.

Materials and methods

Morphometric data

Post-natal growth series of 10 extant crocodylian species were sampled for this study that represent the morphological and phylogenetic breadth of the clade (Fig. 1; Table S1). A MicroScribe G2 digitizer (Immersion Corporation, San Jose, CA, USA), provided by the Florida State University Morphometrics Lab (Tallahassee, FL, USA), was used to amass a 3-D coordinate data set of 78 landmarks on 208 articulated crania (Fig. 2; Tables S1 and S2). These landmarks were determined based on consistent and reliable identification of the points on all sampled species across their post-natal developmental series. The dorsal and ventral landmark points were digitized separately and were subsequently merged in the programme Morpheus et al. (Slice, 2011; available at by superimposing three landmarks common to both sets (Landmarks 1–3; see Appendix S1). To prevent analytical conflicts associated with missing data, coordinate values for limited number of missing and erroneous points were estimated based on regression analysis of raw coordinates and skull length for respective species, as well as symmetry (see Appendix S1). All digitizations were performed by the same author (A.W.).

Figure 1.

Time-calibrated (a) molecular and (b) morphological phylogenetic trees used in this study. Molecular tree is based on a published ultrametric tree (Oaks, 2011). Morphological tree is based on published consensus tree (Brochu, 1999, 2000) with fossil calibrations (Brochu, 2004a,b). Taxa were pruned to include only the species sampled in this study. Note disagreement in the position of Gavialis gangeticus between the molecular and morphological trees.

Figure 2.

Landmarks used in this study (see Table S2 for details) shown on cranial specimens from the American Museum of Natural History, New York, USA (AMNH) and National Museum of Natural History, Washington, DC, USA (USNM). (a) Dorsal and (b) ventral view of Alligator mississippiensis (AMNH 8058); (c) postero-dorsal and (d) postero-ventral view of A. mississippiensis (AMNH 12572); (e) ventro-lateral view of Crocodylus niloticus (USNM 195783). Dorsal landmarks are shown in (a) and (c); ventral landmarks are shown in (b), (d), and (e).

Generalized Procrustes superimposition was then conducted on the pooled coordinate data to minimize the sum of squared differences between homologous landmarks via translation, rotation and scaling of the digitized specimens to unit centroid size (Gower, 1975; Rohlf & Slice, 1990). This procedure converts the three-dimensional coordinates into Procrustes shape coordinates, which were then used to compare the shape of specimens (Data S1).

Allometric trajectories

Allometric trajectories for each species were constructed following two approaches. These procedures differ from analysing disparity in ‘allometric space’ used in other studies (Gerber et al., 2008; Wilson & Sánchez-Villagra, 2010, 2011; Wilson, 2013) that involves an ordination of the first eigenvectors from morphometric data of each taxon. To keep the morphometric data in the same multivariate space throughout the analyses, we instead used principal component (PC) scores from a principal components analysis (PCA) on the pooled shape data and regressed them onto log-transformed centroid size (log CS) (Darroch & Mosimann, 1985; Baab et al., 2012). Because many available tools for testing phylogenetic signal are restricted to univariate traits, we used angles of the regression lines on PC scores and log CS to characterize ontogenetic trajectories. Two sets of allometric trajectories were constructed by conducting ordinary least squares (LS) regression analysis of PC1 and PC2 scores of the Procrustes shape data onto log CS for each species (hereby ‘PC1 trajectories’ and ‘PC2 trajectories,’ respectively). The angles, in radians, of these regression lines were calculated by solving the arctangent of the regression coefficient and adding π/2 to avoid negative angles.

To remove the overall size-dependent shape changes, another set of trajectories were constructed by (i) conducting LS regression of group mean-centred Procrustes coordinates on log CS of pooled shape data; (ii) calculating the residuals from the regression line; (iii) performing a PCA on pooled residual data; and (iv) running LS regression analysis of PC1 of residuals on log CS for each species (hereby ‘PCR trajectories’). The PCR trajectories were constructed and analysed to determine whether shape changes independent of common allometric component are phylogenetically informative (Mitteroecker et al., 2004, 2005). The angles of the regression lines were calculated in the same manner as PC1 and PC2 trajectories.

Although approaches employing the first few PC axes allow the allometric trajectories to be easily visualized, could discard a substantial amount of shape information from the original data. Therefore, multivariate trajectories were also constructed that maintain the statistical dimensionality of the original shape data. These trajectories were each represented by a vector of coefficients from multivariate LS regression analysis on shape variables and log CS (Klingenberg, 1998; Baab et al., 2012). One set of multivariate allometric trajectories comprised 234 regression coefficients (78 sets of x, y, and z coordinates) obtained from the multivariate LS regression analysis that describe the positional changes of each landmark through ontogeny (hereby ‘MV trajectories’). Another set of multivariate trajectories also incorporated intercept values from the multivariate regression analysis to investigate whether the addition of extrapolated starting position of coordinate points generates contrasting results (‘initial trait value’ in Klingenberg, 1998). This set of trajectories included 234 intercept values in addition to the 234 regression coefficients (hereby ‘MVI trajectories’).

Pairwise distances were used to quantify interspecific differences in allometric trajectories. Angular distances for PC1, PC2 and PCR trajectories were calculated as arithmetic difference. Those for MV and MVI trajectories were calculated using the formula θ = arccos[(a•b)(||a|| ||b||)−1], in which a and b represent two multivariate trajectories being compared, is the dot product, and || || is the vector length. Additional set of analyses was performed using Euclidean and Mahalanobis distances between pairs of MV and MVI trajectories to investigate whether different distance metrics could yield contrasting results.


To test for phylogenetic signal, we used published time-calibrated molecular and morphological trees of Crocodylia (Fig. 1). The longstanding disagreement between molecular and morphological trees of crocodylians centres on the phylogenetic position of Gavialis (Indian gharial). Among extant taxa, molecular data strongly support the sister group relationship of the slender-snouted Gavialis and Tomistoma, which together form a sister clade to all other extant crocodylids (e.g. Harshman et al., 2003; Oaks, 2011). Conversely, morphological data and the current fossil record point to Gavialis being sister group to all other extant members of Crocodylia (Brochu, 1997, 2003). Here, we used a recently published time-calibrated molecular tree inferred from 10 nuclear loci of all 23 crocodylian species (Oaks, 2011), which was pruned of unsampled species for this study (Fig. 1a). Median estimated ages from the original study were used for divergence times. For a time-calibrated morphological tree (Fig. 1b), we referred to the divergence times based on established fossil calibration points (Brochu, 2004a,b), with the phylogenetic split of Gavialis from other crocodylians placed at 85 Ma as inferred from the rich fossil record of alligatoroids known from the Campanian and Maastrichtian (Brochu, 2004b).

Analyses were performed in R v2.15.1 (R Developmental Core Team, 2012), unless otherwise noted. The ‘picante’ R package (Kembel et al., 2010) was used to calculate the K-statistic for univariate angles of PC1, PC2 and PCR trajectories. Likelihood ratio test of phylogenetic signal was conducted by employing the tree transformation parameter λ (Pagel, 1999), in which the internal nodes of a phylogenetic tree are shifted deeper as λ → 0. First, the ‘geiger’ R package (Harmon et al., 2008) was used to calculate the most likely λ value (λML) given a Brownian motion model of trait evolution. A P-value was calculated by comparing the log likelihoods of trait evolution on tree transformed by λML and λ = 0, which approximates a χ2 distribution with degrees of freedom equal to the difference in number of parameters (i.e. 1).

To perform a permutational regression analysis on trees, a script was written in Python (van Rossum, 1995) that, for each iteration, (i) randomizes the species at the tips of a phylogeny while keeping the topology and branch lengths constant; (ii) calculates and records the pairwise differences between univariate trait values and pairwise phylogenetic distance, measured as the total branch length separating two species (equivalent to twice the estimated divergence time at the most recent common ancestor); and (iii) runs a LS regression analysis on the trait and phylogenetic distances and records the regression coefficient. The significance of correlation was determined based on the proportion of obtaining a regression coefficient as or more distant from zero than coefficients recovered after 9999 randomizations.

A Mantel test was conducted on phylogenetic distances, calculated as the branch length separating a pair of species in millions of years, and pairwise distances between allometric trajectories, including angular distances, as well as Euclidean and Mahalanobis distances for multivariate trajectories. Mahalanobis distances were calculated by subjecting the Procrustes shape data to a PCA and removing PC axes with zero or nearly zero eigenvalues to avoid undefined values. The test was performed with the ‘ade4’ R package (Dray & Dufour, 2007) with 9999 randomizations to determine the significance of covariation between phylogenetic and trajectory distances.

Finally, the ‘phangorn’ R package (Maechler et al., 2002) was used to construct UPGMA phenograms based on angular pairwise distances between all sets of allometric trajectories, in addition to Euclidean and Mahalanobis distances for the multivariate trajectories. A script was written for the TNT phylogenetic programme (Goloboff et al., 2008) to test whether the topology of these phenograms is more similar to that of published molecular and morphological trees than expected from randomly generated tree topologies. To quantify topological differences, we used subtree pruning and regrafting (SPR) distance (Goloboff, 2007), defined as the minimum number of SPR moves needed to convert one tree to another, with 100 replications for the heuristic search of distances. First, the SPR distance between a phenogram and the molecular and morphological trees was calculated. This observed distance was then compared with the distribution of SPR distances between the phenogram and 999 999 randomly generated tree topologies. Significance was determined based on the proportion of times that the SPR distances from randomized tree topologies were shorter than or as short as the observed distance. A more commonly used tree dissimilarity metric, the Robinson-Foulds (RF) distance (Bourque, 1978; Robinson & Foulds, 1981), was not used because based on this metric, some phenograms were maximally distant from molecular and morphological phylogenies (RF distance = 1). In these situations, the P-value (i.e. P = 1) would reflect the limitation of the metric rather than a genuine significance of tree similarity.

Despite the assumption of ultrametricity, UPGMA was used in this study due to its prevalence in the current morphometric literature as a method for visualizing underlying patterns in shape variation (e.g. Cardini & O'Higgins, 2005; Piras et al., 2010). We did not perform a phylogenetic analysis on the angles of PC1, PC2 and PCR trajectories because we did not sample an outgroup and because the number of taxa would exceed the number of characters. Similarly, phylogenetic analyses were not conducted on MV and MVI trajectories because the individual regression coefficients that comprise the trajectories are dependent on the orientation of the superimposed specimens (i.e. the orientation of the x, y, and z axes are arbitrary). The regression coefficients and intercepts therefore are not grounded on a biological principle when treated as individual phylogenetic characters. Moreover, landmarks, particularly those in close spatial proximity, are unlikely to be independent, violating a key aspect of phylogenetic characters.



Principal components analysis was performed on the pooled Procrustes shape data to construct a PC bivariate plot that shows the underlying pattern of variation in cranial shape (Fig. 3). The first PC reflects interspecific variation and is primarily associated with narrowness of the snout (Landmarks 1, 37–42), generally separating the alligatorids, the slender-snouted Gavialis and Tomistoma, and remaining crocodylids, whereas PC2 largely accounts for changes in the shape of the orbit (Landmarks 8–15) and temporal fenestrae (Landmarks 16–21) (Fig. 4), both of which characterize key morphological changes in cranial ontogeny. Thus, with broad sampling of extant crocodylians, the trajectories of most taxa are represented by their alignment with the PC2 axis (i.e. neonates occupy more positive PC2 values, whereas adults occupy more negative values). Taken together, the morphospace indicates that alligatorids undergo narrowing of the snout throughout ontogeny, whereas crocodylids, with the exception of Gavialis and Tomistoma, undergo a narrowing, followed by a broadening of the snout during ontogeny, which has been previously documented in Crocodylus acutus and Mecistops cataphractus (Piras et al., 2010).

Figure 3.

Bivariate plot of the first two principal components (PC) of pooled Procrustes coordinate data (n = 208). Triangles and squares indicate smallest and largest specimens in each species, respectively. PC1 is primarily associated with the narrowness of the snout. With the exception of Gavialis, the growth series align with PC2, in which neonates occupy more positive PC2 values and adults occupy more negative values. Images of hatchling (AMNH 7128; top) and adult (AMNH 9043; bottom) Alligator mississippiensis and adult Gavialis gangeticus (AMNH 7138; left) highlight ontogenetic and interspecific cranial variation in dorsal view.

Figure 4.

Shape changes in the crocodylian crania in dorsal view along the first two principal components (PC). Rostral and posterior directions are to the left and right, respectively. The points denote the position of the pooled mean shape and respective lines represent the direction and magnitude of positional shift corresponding to an increase of 0.1 units along (a) PC1 and (b) PC2 axis (see Fig. 3). Numbers refer to landmark number listed in Table S2. Images visualized in MorphJ v1.05f (Klingenberg, 2011).

Allometric trajectories

Allometric trajectories of all types were constructed for each species by regressing shape variables on log CS. Because PC2, instead of PC1, largely accounts for shape changes along a size series (PC2: R2 = 0.726; PC1: R2 = 0.175), ontogenetic trajectories were characterized as the angles of regression lines on PC2 scores and log CS (Fig. 5), and angular differences between regression lines were used to measure dissimilarities between pairs of allometric trajectories. These trajectories show that alligatorids and crocodylids collectively undergo similar post-natal shape changes. However, those of Gavialis and Tomistoma each follow distinct shape changes in cranial morphology relative to each other and to all other crocodylian species sampled. These trajectories also indicate that crocodylian species gradually diverge in cranial shape with larger size.

Figure 5.

Bivariate plot of the second principal component (PC2) of Procrustes coordinates and log centroid size. Lines indicate regression lines for each species. Centroid size in mm.

Although PC1 does not reflect ontogenetic changes for most taxa in the pooled shape data, PC1 trajectories (Fig. S1a) were also constructed and analysed for possible phylogenetic signal. Similar to PC2 trajectories, PC1 trajectories show that Gavialis and Tomistoma undergo particularly different ontogenetic shape changes relative to those of other species. In contrast to PC2 trajectories, however, PC1 trajectories show minor convergence in cranial shape among species at larger sizes, most notably in the snout. Although the data points of PC1 and PC2 scores against log CS largely align with their respective allometric trajectories, the data points of PC1 scores of residuals from the common allometric component against log CS are highly scattered with respect to their corresponding allometric trajectories (Fig. S1b). Furthermore, these data points form two distinct trajectories for several species across Crocodylia (e.g. Crocodylus porosus, Melanosuchus niger, Tomistoma schlegelii). This result appears to be decoupled from sexual dimorphism and ontogenetic variation, and whether it is due to other biological factors could not be determined.

Important to consider is that the use of regressions assumes a linear relationship between shape and log CS, which may not be justified. Nonlinear allometric trajectories have been observed in vertebrate groups, in which the orientation of the trajectory changes during the course of development (e.g. Zelditch et al., 1993; Fink & Zelditch, 1995; Mitteroecker & Bookstein, 2009). Here, bivariate plots of PC1 and PC2 of the pooled shape data against size show no observable shifts in the orientation of the data points within species (Figs 5 and S1a). In addition, regression lines model size-dependent shape changes along PC2 with high degree of fit (R2 > 0.93 for all species). However, PC1 and PCR trajectories model their respective size series with variable fidelity (PC1: R2 range 0.0834–0.822; PCR: R2 range 0.0132–0.742), indicating that PC1 scores of pooled shape and residuals from the common allometric component poorly characterize ontogenetic shape changes. Therefore, PC2 trajectories were considered the principal models of ontogenetic shape changes among these trajectories, although the results for PC1 and PCR trajectories are also reported. When PCA is conducted on shape data of each species separately, the plot of PC1 of Procrustes shape coordinates (reflecting ontogenetic shape changes within species) against log CS also shows a continuous linear relationship in species with robust sampling (i.e. Alligator, Caiman, Crocodylus), but the pattern is ambiguous for taxa with more limited sample size (i.e. Gavialis, Osteolaemus, Tomistoma).

Based on pairwise distances, MV and MVI trajectories show generally congruent patterns (Table S3). Multivariate trajectories of Gavialis and Tomistoma are comparatively more distant from those of other taxa, although Tomistoma shows a closer trajectory to other crocodylids according to pairwise distances among MVI trajectories. Alligatorids, on average, have more similar trajectories among one another than crocodylids although the degree of similarity ranges widely. For the two types of multivariate trajectories, a vast majority of the regressions of shape variables on log CS had R2 values > 0.80, implying that the regression coefficients are good proxies for describing relative positional changes of individual landmarks.

Phylogenetic signal

The K-statistic is a descriptive parameter that measures the degree of interspecific similarity in trait values relative to the similarity expected from a Brownian motion model of trait evolution (Blomberg et al., 2003). A K value between 0 and 1 denotes a more disparate trait distribution across a given phylogeny than predicted, whereas K > 1 indicates more similar trait values among closely related taxa than expected. The PC2 trajectory angles, as did PC1 and PCR trajectories, yielded K < 1 with both molecular (=0.711; Table S4) and morphological trees (=0.876; Table S4). Because available analytical tools do not allow multivariate trait data, K values were not calculated for multivariate trajectories.

Likelihood ratio tests with Pagel's λ compare the likelihoods of a Brownian motion model of trait evolution on phylogenies with topological structure (λ > 0) to those on entirely polytomous trees (λ = 0), in which species are treated as independent observations without genealogical relationships (Pagel, 1999). Consistent with the observed K values, the likelihood ratio tests generated nonsignificant results for PC2 trajectories (molecular tree: P = 0.162; morphological tree: P = 0.268), implying that allometric trajectories of crocodylians are within expectation of a random distribution. Both PC1 and PCR trajectories produced even greater P-values with both molecular and morphological phylogenies (Table S4). Again, only univariate trajectory angles were analysed for the same reason stated above.

Permutational regression analysis (Laurin, 2004; Baab et al., 2012) randomizes the trait values among species, while keeping the tree topology and branch lengths constant, and it determines the significance of the observed correlation between interspecific angular and phylogenetic distances. This produced nonsignificant results for PC2 trajectory angles (molecular tree: P = 0.394; morphological tree: P = 0.093), as well as for PC1 and PCR trajectories (Table S4). A poor correlation between trajectory and phylogenetic distances is also apparent from the low R2 values obtained from regression analysis on the observed data (PC1: R2 = 0.060; PC2: R2 = 0.127; PCR: R2 = 0.118).

With few exceptions, the Mantel test (Mantel, 1967; Sokal & Rohlf, 1995) failed to find a significant correlation between phylogenetic distance and angular distance between allometric trajectories (Table S4). For PC1, PC2 and PCR trajectories, the Mantel test generally recovered lower, but nonsignificant, P-values relative to other tests with one exception (i.e. likelihood ratio test on PC2 trajectories). Although the P-values are well above significance level with the molecular phylogeny (i.e. P > 0.05), all three types of PC trajectories generated lower P-values when analysed with the morphological tree, in which PC1 and PCR trajectories approach significance (PC2: P = 0.053; PCR: P = 0.062). For MV and MVI trajectories, none of the results, including tests with Euclidean and Mahalanobis distances, are significant with the molecular tree. Similar to the PC trajectories, Mantel tests with the morphological tree generally produced lower P-values, with the exception of angular distances between MV trajectories. Interestingly, all results, besides the angular distances between MV trajectories, are slightly above or below significance at the 0.05 level with the morphological tree (MVEuclidean: P = 0.059; MVMahalanobis: P = 0.045; MVIangular: P = 0.018; MVIEuclidean: P = 0.033; MVIMahalanobis: P = 0.062), suggesting that these trajectories contain a signal that is more compatible with the morphological than the molecular tree.

Despite some marginally significant results from the Mantel test, the phenograms constructed from UPGMA show topologies that differ markedly from the time-calibrated molecular and morphological trees for both PC and multivariate trajectories (Figs 6 and S2). In fact, four of the nine phenograms (Figs 6b,g and S2) do not share a single node with molecular and morphological trees. Only three of the nine phenograms are able to recover alligatorids as a monophyletic group, but no further phylogenetic relationships within the clade (Fig. 6c–e). Few localized congruences exist, including the grouping of (i) Caiman crocodilus, Mniger and Paleosuchus trigonatus (Fig. 6a), (ii) Cracutus and Crocodylus niloticus (Fig. 6c–e), (iii) all three sampled Crocodylus species (Fig. 6e), and most notably, (iv) the position of Gavialis as the most divergent taxon in PC2, MV and MVI phenograms (Fig. 6a,c–e), which support the topology of the morphological tree (Fig. 1b). Beyond these isolated cases of congruence, however, the phenograms do not show species-level resolution and exhibit disparate topologies among themselves, indicating a lack of common signal. Oddly, phenograms constructed from pairwise Mahalanobis distances are perfectly pectinate and resemble an entirely polytomous tree except for the relatively close association between Crniloticus and Cr. porosus (Fig. 6f,g).

Figure 6.

Phenograms constructed via unweighted pair group method with arithmetic means (UPGMA) from pairwise distances between allometric trajectories. Phenogram constructed from (a) pairwise distances between trajectories based on the second principal component (PC2) of Procrustes coordinates; pairwise (b, c) angular, (d, e) Euclidean, and (f, g) Mahalanobis distances between multivariate trajectories without intercept values (MV) and with intercept values (MVI).

The results of the tree congruence test corroborate these observations. When compared to the topology of both molecular and morphological trees, all phenograms produced nonsignificant results (Table 1). This outcome implies that a phenogram based on ontogenetic shape changes is not significantly more similar to molecular and morphological trees than expected from comparisons with randomly generated trees.

Table 1. Results of the topological congruence test. The observed subtree pruning and regrafting distance (SPRobserved) measures the topological differences between a UPGMA phenogram and phylogenetic trees based on molecular and morphological data. Significance (P) of the observed similarity is determined relative to the distribution of distances between the phenograms and 999 999 randomly generated tree topologies.
UPGMAMolecular treeMorphological tree
SPRobserved P SPRobserved P
  1. MV, mutivariate trajectories without intercept values; MVI, multivariate trajectories with intercept values; PC1, trajectories based on the first principal component (PC1) of Procrustes shape data; PC2, trajectories based on PC2 of Procrustes shape data; PCR, trajectories based on PC1 of residuals from the common allometric component; UPGMA, Unweighted Pair Group Method with Arithmetic Mean.

MV (angular distance)50.88250.882
MV (Euclidean distance)40.38740.385
MV (Mahalanobis distance)50.90950.909
MVI (angular distance)30.06240.385
MVI (Euclidean distance)40.38130.062
MVI (Mahalanobis distance)50.91050.910

To further explore the potential link between ontogeny and phylogeny, pairwise phylogenetic and trajectory distances were plotted to seek possible correlations restricted to particular time intervals or nonlinear relationships between ontogenetic shape changes and phylogeny (Figs 7 and S3). Bivariate plots using three different distance metrics (i.e. angular, Euclidean and Mahalanobis distances) do not show correlations occurring within any particular temporal segment. However, with the exception of the bivariate plot of PC1 trajectories (Fig. S3a), angular distances between MV trajectories (Fig. 7c,d), and Mahalanobis distances (Fig. 7c–f), the upper bound of angular trajectory distances increases in conjunction with phylogenetic distance at least within ~100 Myr. Thus, the variance in trajectory distances appears to increase gradually with phylogenetic distance. This result suggests that more closely related species tend to exhibit similar ontogenetic trajectories and disparate trajectories are generally restricted to comparisons between distantly related taxa. However, distantly related species could also show very similar trajectories. Analogous shape changes during ontogeny therefore do not imply close evolutionary relationships among taxa.

Figure 7.

Bivariate plots of pairwise trajectory and phylogenetic distances based on (a, c, e) molecular and (b, d, f) morphological tree. The former is calculated using angular, Euclidean and Mahalanobis distances, and the latter is calculated as the total branch length, in estimated million years, separating a pair of species. Bivariate plots of (a) angular against phylogenetic distances of univariate trajectories based on the second principal component (PC2) of Procrustes coordinates (n = 45); angular, Euclidean and Mahalanobis distances against phylogenetic distances of multivariate trajectories (c, d) without intercept values (MV) (n = 45 for each distance metric); and (e, f) with intercept values (MVI) (n = 45 for each distance metric).


The PC morphospace (Fig. 3), as well as PC1 and PC2 trajectories (Fig. 5, S1a), highlight several aspects of cranial morphological variation in crocodylians. First, ontogenetic shape changes in the cranium contribute less to the total morphological variation than interspecific shape differences among adults of extant taxa, primarily due to the slender-snouted Gavialis and Tomistoma. Second, the ontogenetic trajectories of Gavialis and Tomistoma are disparate from all other sampled crocodylians, and each occupies different regions of the morphospace. Relative to Tomistoma, Gavialis bears a narrower snout at the beginning and at the end of its post-natal development. Meanwhile, alligatorids and other crocodylids diverge and subsequently converge along PC1 along their respective ontogenetic trajectories, suggesting that their cranial shape is more similar among adults than subadults. Third, both Paleosuchus (Schneider's dwarf caiman) and Osteolaemus (African dwarf crocodile) occupy, as their common names imply, the smaller size segment of the trajectories of other alligatorid taxa. Interestingly, the allometric trajectories of the crocodylid Osteolaemus align adjacent to those of alligatorids, instead of other crocodylids. This outcome is likely the result of the relatively broad rostrum in Osteolaemus, which resembles that of alligatorids (Grenard, 1991). Because the allometric trajectories are constructed from log CS instead of age, the type of developmental shift that contributed to the dwarfism in these taxa cannot be ascertained (e.g. later onset vs. early cessation of growth; Klingenberg, 1998). Furthermore, PCR trajectories are comparatively less resolved (PC1 of residuals account for only 19.8% of the total variation), signifying that a substantial amount of shape information was discarded when common size-dependent shape changes were removed (Fig. S1b; Jungers et al., 1995).

Despite the difference in the phylogenetic placement of Gavialis, analyses with both molecular and morphological trees largely indicate a lack of significant phylogenetic signal in the cranial ontogeny of crocodylians. Tests incorporating the molecular tree did not produce any significant P-values. Interestingly, the P-values were generally lower with the morphological tree (Table S4), which suggest that allometric trajectories contain greater phylogenetic signal when analysed with the morphological than the molecular tree. Although a critical discussion on the respective validity of morphological and molecular trees of Crocodylia is outside the scope of this study, adult morphology, on which morphological characters are based, is expected to drive the orientation of ontogenetic trajectories. For instance, taxa that exhibit similar adult morphology are anticipated to have analogous ontogenetic trajectories because vertebrates generally appear more similar early in development, and thus, adult forms are expected to reflect the general directionality of shape changes (Richtsmeier et al., 1993). As such, ontogenetic shape changes are likely correlated with morphological phylogenetic data to an extent.

Of the analyses conducted, only the Mantel test produced marginally significant results (Table S4). A Mantel test (Mantel, 1967) is a nonparametric approach to examine the degree of correlation between two distance matrices. Here, it was used to test for correlation between interspecific phylogenetic and trajectory distances. Despite some significant results, the Mantel test is known to have low power and inflated Type-I error rate (Guillot & Rousset, 2013), particularly when used in the context of a comparative phylogenetic analysis (Harmon & Glor, 2010). These shortcomings explain the conflicting results from these few Mantel tests with respect to all other analyses employed in this study. In addition, significant results from pairwise Mahalanobis distances of MV and MVI trajectories seem to be driven primarily by the relatively similar trajectories of Crniloticus and Crporosus (Fig. 7c–f), whereas other species are essentially equidistant from each other (see Fig. 6f,g). Hence, Mahalanobis distance is likely not an appropriate metric for characterizing dissimiliarities in ontogenetic shape changes, at least in crocodylians. Nevertheless, the Mantel test recovered significant results with the use of Mahalanobis distances, which support previous claims that it is weak and more prone to Type-I error relative to methods that directly incorporate phylogeny, such as the K-statistic and Pagel's λ (Harmon & Glor, 2010). In fact, all other analyses clearly show that these allometric trajectories do not contain a significant amount of phylogenetic signal, including the bivariate plots (Figs 7 and S3) that visualize the lack of correlation between phylogenetic and trajectory distances. However, the Mantel test was used because it is one of the few tests for correlations between distances, which was necessary for the multivariate trajectories employed in this study.

The methods used in this study collectively demonstrate that the allometric trajectories have little phylogenetic utility. The results therefore belie the existence of a meaningful link between ontogenetic shape changes and phylogenetic relatedness, corroborating the results of previous studies based on linear distance measurements and allometric disparity in rodents (Wilson & Sánchez-Villagra, 2010) and turtles (Wilson & Sánchez-Villagra, 2011). This lack of significant phylogenetic signal may be because allometric trajectories (i) evolve randomly with high variation that loses phylogenetic signal in the temporal and phylogenetic ranges examined in this study (i.e. 10–175 Myrs); (ii) fail to sufficiently model ontogenetic changes based on the approaches employed in this study; or (iii) are adapted to or constrained by factors (e.g. ecological, functional, size) that yield signals that contrast with molecular and morphological phylogenetic data (Martin & Bellairs, 1977; Wilson & Sánchez-Villagra, 2010; Klingenberg, 20102011; Wilson, 2013).

In crocodylians, the first possibility seems unlikely due to the constrained appearance of PC2 allometric trajectories (Fig. 5) and the relatively conserved pattern of ontogenetic shape changes observed in extant crocodylians, as suggested by Foth et al. (2013). Regarding the second possibility, other approaches for comparing allometric trajectories have been proposed, which may characterize ontogenetic shape changes with greater fidelity. The construction of ‘allometric space’ (Gerber et al., 2008; Wilson & Sánchez-Villagra, 2010, 2011; Wilson, 2013) aims to visualize the underlying variation in allometric trajectories by conducting a PCA on morphometric data of each species separately, followed by another PCA on the concatenated PC1 coefficients. This successive ordination approach, however, fails to retain shape information in a common multivariate space and assumes that the association between PC1 and size is equivalent in each species sampled. Methods based on loadings from PCA on shape variables would also be problematic because the degree of correlation with individual shape variables (i.e. x, y, and z coordinate values of each landmark) depends on the orientation of the superimposed specimens. In addition, loadings merely indicate the degree of correlation between shape and size, failing to describe the tempo of shape changes during ontogeny.

For this study, the angles of univariate and multivariate trajectories were used to quantify ontogenetic shape changes because the trajectories more directly model the shape changes that occur throughout ontogeny. Moreover, previous studies have used the same metric to characterize allometric trajectories constructed from coordinate data. Angles of PC1, PC2 and PCR trajectories were also utilized because many available tools for comparative phylogenetic analyses only allow univariate trait values.

The third possibility that functional factors have driven the evolution of ontogenetic shape changes is probable based on previous morphometric studies on crocodylians. These studies have shown that the adult cranial morphology is associated with ecological factors, particularly their diet (Monteiro et al., 1997; Pierce et al., 2008, 2009; Sadleir & Makovicky, 2008). Therefore, the same selective forces are expected to have shaped ontogenetic trajectories, allowing co-occurring species to possess different ecomorphs. Although a functional explanation for lack of phylogenetic signal is likely, a direct confirmation of factors associated with allometric trajectories is still necessary to elucidate why these trajectories are not phylogenetically informative.

Besides ontogeny, this study did not explicitly account for other sources of intraspecific variation that may influence the allometric trajectories. Most notably, crocodylians exhibit sexual dimorphism, in which adult males attain larger asymptotic sizes than females (e.g. Andrews, 1982; Grenard, 1991). Size-independent morphological dimorphism includes the development of a nasal protuberance in male Gavialis (Martin & Bellairs, 1977; Grenard, 1991) and differences in interorbital and skull roof width in Cr. porosus (Webb & Messel, 1978). These shape differences have the potential to inflate shape variation later in ontogeny. Moreover, if males and females undergo parallel allometric trajectories or different rates of shape changes relative to size, then a differential sampling of sexes in each species is expected to inflate the variance and impact the orientation of allometric trajectories. Sexual dimorphism was not directly considered in this study because the sex of osteological specimens for noncaptive individuals is seldom recorded. Unfortunately, osteological correlates for identifying sex are currently lacking in crocodylians (Prieto-Márquez et al., 2007).

Nonetheless, sex identification was available for 20 of 52 digitized crania of Ca. crocodilus. A bivariate plot with PC1 scores of Procrustes shape data of Ca. crocodilus specimens and log CS suggests that there is no observable distinction between the male and female allometric trajectories (Fig. S4). Recently, the black caiman (M. niger) was also shown to lack significant sexual dimorphism in allometric shape trajectories (Foth et al., 2013). Yet, consistent sexual dimorphism has been reported in both hatchling (Piña et al., 2007) and captive (Verdade, 2003) specimens of the broad-snouted caiman (Caiman latirostris) based on linear distance measurements of the crania. In Ca. crocodilus, however, the magnitude of the variation due to sexual dimorphism appears to be minimal compared to ontogenetic variation. Furthermore, if sexual dimorphism is limited to size differences, it is not expected to considerably alter the results of this study because allometric trajectories here are based on size, instead of age. Hence, if the males and females of the same size exhibit similar cranial shape within species, then a differential sampling of sexes is not expected to alter the variation and direction of allometric trajectories. Nevertheless, a greater representation of sexed specimens is needed to allow for a more comprehensive understanding of the effects of sexual dimorphism on allometric trajectories in crocodylians.

Although recovering nonsignificant statistical results is not equivalent to confirming the absence of correlations, this study clearly illustrates that the use of allometric trajectories for inferring the evolutionary history of organisms, precluding tests for phylogenetic signal, is unjustified. It is worth noting, however, that these trajectories model the ontogenetic changes in the overall shape of the cranium. Hence, this study does not necessarily discredit the efficacy of individual ontogenetic characters as phylogenetically informative characters (e.g. Mabee & Trendler, 1996; Smith, 2001; Laurin & Germain, 2011). Finally, whether these findings are generalizable to other taxonomic groups remains to be examined. Additional investigations across the vertebrate clade are needed to identify common factors that impact the evolution of ontogenetic trajectories. Here, we have presented an integrated approach that is applicable to virtually any taxonomic group that exhibit ontogenetic changes in form.


We thank D. Kizirian and R. Pascocello (American Museum of Natural History, New York, NY); K. Krysko and M. Nickerson (Florida Museum of Natural History, Gainesville, FL); A. Resetar and K. Kelly (Field Museum of Natural History, Chicago, IL); J. Rosado (Museum of Comparative Zoology, Cambridge, MA); A. Wynn and K. Tigh (National Museum of Natural History, Washington, DC); and G. Schneider (University of Michigan Museum of Zoology, Ann Arbor, MI) for facilitating access to specimens. We also thank M. Palczewski for assistance with Python programming; and the Willi Hennig Society for making the programme TNT freely available. C. Brochu (University of Iowa, Iowa City, IA), G. Erickson (Florida State University, Tallahassee, FL), P. Gignac (Oklahoma State University, Tulsa, OK), E. Gold (American Museum of Natural History), M. Laurin (Muséum National d'Histoire Naturelle, Paris, France), K. J. Soda (Florida State University), S. Steppan (Florida State University), and an anonymous reviewer provided helpful comments and criticisms on earlier versions of the manuscript. This work partially forms the M.S. thesis of A.W. completed at Florida State University. The present study was supported by the National Science Foundation Graduate Research Fellowship and Sigma Xi Grants-in-Aid of Research (Grant No. G20110315156273) to A.W.