PHYLOGENETIC ANALYSIS OF ONTOGENETIC SHAPE TRANSFORMATIONS: A REASSESSMENT OF THE PIRANHA GENUS PYGOCENTRUS (TELEOSTEI)

Transcription

1 St/sl. Biol. 44(3): , 1995 PHYLOGENETIC ANALYSIS OF ONTOGENETIC SHAPE TRANSFORMATIONS: A REASSESSMENT OF THE PIRANHA GENUS PYGOCENTRUS (TELEOSTEI) WILLIAM L. FINK 1-3 AND MIRIAM LEAH ZELDITCH 2 x Museum of Zoology and Department of Biology, University of Michigan, Ann Arbor, Michigan 48109, USA ^Museum of Paleontology, University of Michigan, Ann Arbor, Michigan 48109, USA Abstract. Despite the potential information that may lie in phylogenetic analyses of ontogenies of body form, few studies have examined methods for extracting and analyzing ontogenetic shape characters. We propose and exemplify a procedure for phylogenetic shape analysis. We use the thin-plate spline decomposed by its partial warps, a method that has several critical advantages over available alternatives. Most notably, shape variables extracted by this method refer to localizable features of the morphology. We demonstrate how these characters can be coded and include them in a phylogenetic analysis of the piranha genus Pygocentrus, using a data set also comprising meristic, myological, and osteological characters. Using ontogenies of these localized shape variables, we have corroborated the monophyly of Pygocentrus. Although we found no new characters corroborating the proposed sister-group relationship of P. nattereri and P. cariba, our characters are all congruent with this hypothesis. Several ontogenetic shape characters serve to diagnose the previously undiagnosed P. nattereri. Independence of ontogenetic shape features is assessed in the same manner as for any other features: by examination of their distributions on the corroborated cladogram. In addition to inspecting associations among characters that changed multiple times, character independence was assessed using the information in the kinds of ontogenetic modifications (gain, loss, reorientation, reversal) and the information in observed development. Most of the geometrically independent features extracted during this study are phylogenetically independent of each other. We also found that region-specific ontogenetic allometries are phylogenetically independent of each other. In addition, localized ontogenetic changes along orthogonal body axes (anteroposterior and dorsoventral in this case) are usually phylogenetically independent. Although these findings of character independence may be specific to this study, the method for assessing this independence can be applied generally. Evolution of both spatial and temporal patterns of growth is an inference that depends upon using methods, such as the one employed here, capable of describing the spatial patterning of ontogeny. [Ontogeny; phylogeny; character independence; geometric morphometrics; piranhas; Pygocentrus.] Systematists have been urged to look for cations of development that create novel characters in ontogenetic transformations morphologies (Fink, 1981; Mabee, 1993). instead of restricting their studies to fea- Comparisons of the ontogenies of form tures of comparable stages in the life cycle may add considerably to the information (Danser, 1950; Moser et al v 1984; de Quei- available in morphology when taxa share roz, 1985; Kluge and Strauss, 1985; Creigh- common anatomical parts but differ in ton and Strauss, 1986). This recommenda- form. Comparative studies of ontogenetic tion can be justified in principle because it transformations of shape have been esavoids subdividing a continuously chang- pecially recommended in part because of ing morphology. In addition, ontogenetic increasing interest in heterochrony and the transformations can also be more infor- evolution of allometry (e.g., Gould, 1977; mative than static analyses, even when Alberch et al., 1979; Alberch and Alberch, multiple stages of the life cycle are includ- 1981; Creighton and Strauss, 1986; Strauss ed in a single analysis (O'Grady, 1985; and Fuiman, 1985; McKinney, 1988; Hall, Klompen and OConnor, 1989). Further- 1992). Despite this wide interest, there are more, comparisons of ontogenies may major unresolved questions regarding just yield insights into the particular modifi- how to extract characters from such comparisons. In some cases, descriptors of shape ontogenies were judged as promis- 3 wfink@umich.edu. ing features for cladistic studies, but the 343

2 344 SYSTEMATIC BIOLOGY VOL.44 particular descriptors have not yet been shown to be characters suitable for cladistic analysis nor have methods been developed for assessing their historical independence (e.g., Richtsmeier et al., 1993). In addition, although any use of quantified shape descriptors presupposes that their homology can be assessed, this is a difficult problem because some methods for extracting characters from shape comparisons preclude application of the standard tests of homology (conjunction, similarity, and congruence [Patterson, 1982]; a critique of morphometric methods based on the potential for applying these tests of homology to quantified shape features was presented by Zelditch et al. [1995]). Before attempting to address specific problems arising from the use of ontogenetic shape data, such as methods for transforming shape variables into cladistic data, these more fundamental issues must be explored. We have argued that comparisons of shape using the thin-plate spline (TPS) decomposed by its partial warps can yield characters suitable for cladistic analysis (Zelditch et al., 1995). We focus here on the problem of transforming these quantified shape characters into cladistic data. The shape variables obtained by this method are appropriate for phylogenetic studies and are particularly useful in the cases when changes in shape are developmentally integrated, i.e., when the ontogenetic transformations in shape of a particular region of the body are associated with changes elsewhere on the body (Zelditch et al., 1992). Comparisons that ignore developmental integration could produce a large number of redundant measures of the same character. Equally problematic are comparisons that cannot distinguish among localized changes because they may confound several spatially distinct transformations. For example, one traditional character of teleost body shape is depth of the caudal peduncle relative to standard length (SL). But the ontogeny of this character may combine several distinguishable features, including (1) deepening of the caudal peduncle as part of a general deepening of the whole body (an overall increase in depth relative to length), (2) deepening of the posterior body relative to the more anterior body (a transformation in which the changes of caudal peduncle cannot be distinguished from changes of the more general posterior body), and (3) deepening of the peduncle relative to the subdorsal fin region (a transformation localized to this region). Methods such as TPS that can dissect this deepening in terms of its spatial distribution can detect its general and region-specific aspects and thereby substantially enhance the information contained in the ontogenetic comparisons. As we show herein, there is phylogenetic information in the ontogenetic spatial distribution of deepening of the caudal peduncle. We have also argued that the shape variables obtained by TPS are suitable for cladistic analysis and useful for describing the spatial distribution of ontogenetic transformations. However, methods for characterizing these shape variables have been neither proposed nor debated in the literature. Such issues were raised but not addressed in early discussions of the use of geometric morphometrics in systematic studies (Rohlf and Bookstein, 1990). More recent publications (e.g., Jensen, 1993; Rohlf and Marcus, 1993) and discussions (on MorphMet, an INTERNET LISTserv) suggest that the coding of characters remains a mysterious matter. Bookstein (1994) even denied that it is possible to code or polarize geometric characters, insisting that we must first obtain the cladogram from other data before analyzing the evolution of shape. We hope to begin a more focused debate by suggesting a conservative method similar to that used for coding ontogenetic transformations in other aspects of morphology (e.g., Wake, 1989; Mabee, 1993). We examined these methodological issues empirically by applying TPS to a comparison of ontogenies of several piranhas: Pygopristis denticulata, Serrasalmus gouldingi, Pygocentrus cariba, P. nattereri, and P. piraya. A recent revision of the genus Pygocentrus provided evidence of the monophyly of the

3 1995 PHYLOGENIES OF SHAPE ONTOGENIES 345 genus and proposed that P. cariba and P. nattereri are sister taxa (Fink, 1993). However, only two characters supported the hypothesized relationships within the genus and, even more troubling, no characters were found to diagnose P. nattereri. We propose a method for comparing ontogenies of shape and reassess the monophyly of Pygocentrus, the postulated relationships within the genus, and the status of P. nattereri. We include evidence from several sources, including ontogenies of shape. To highlight the approach, we first describe all ontogenetic features and then discuss which ones were judged phylogenetically informative and how they were coded. We conclude with a phylogenetic analysis of the combined data set, an evaluation of the information contained within ontogenetic shape characters, and a discussion of tests of character independence. MATERIALS AND METHODS Data Samples. Species from the genera Pygopristis and Serrasalmus served as outgroups for the analysis of Pygocentrus based on the work of Machado-Allison (1985) and studies by Machado-Allison and Fink (in prep.). Juvenile Pygopristis denticulata (MBUCV 10690, specimens 8 and 9; MCNG 3243, specimen 1) were averaged to obtain the starting form. Specimens of Pygocentrus nattereri from many localities in the Amazon and Parang/Paraguay rivers were treated as a single sample; no pattern of geographic variation in form was found among these populations, confirming the conclusion of Fink (1993). See Appendix 1 for information about specimens examined. Our analysis of ontogenetic transformations examined changes in shape associated with changes in size. We have no information regarding chronological ages of the specimens; however, in the case of poikilotherms, size may be an estimate of biological age more closely tied to growth than chronological time (Strauss, 1987). Sizes ranged from posttransformation juveniles with undeveloped pectoral fins 10 FIGURE 1. Landmarks used for description of ontogenetic shape change drawn on an adult Pygocentrus (see Appendix 2 for landmark descriptions). (20.5 mm SL [snout tip to base of caudal fin]) to large breeding adults (277 mm SL). Landmarks. Discrete points (landmarks) that can be recognized as the same point in individuals at all sizes and that can be argued to sample homologous parts of all piranhas were digitized on the left side of each individual (Fig. 1; Appendix 2). Because these individuals are laterally flattened, little information is lost or distorted when they are projected onto a plane. To compute an average of the three juvenile Pygopristis denticulata for the starting form for the shape analyses, we constructed and averaged shape coordinates (Bookstein, 1986,1991) to a baseline with landmarks 1 and 7 at the endpoints. Morphometric Analysis of Ontogenetic Change Size. As our size measure we used root centroid size, the square root of the summed squared distances of all landmarks to the center of the form (Bookstein et al, 1985; Bookstein, 1986, 1991). Centroid size is the only size variable uncorrelated with shape in the absence of allometry (Bookstein et al., 1985; Bookstein, 1991). Because centroid size in the piranha samples increases by more than a factor of 10 and most shape change occurs over a fairly small range of sizes, the log transform of root centroid size was used as the size variable. Measurement of shape change. The ontogenetic change in body form was described using TPS, modeling shape change

4 346 SYSTEMATIC BIOLOGY VOL rcttl t ( r u Bit UJXt _ -~ * " '? X Ml "T LI ^* -^ i xlll t JJaJi Pygopristis denticulata - 4 -ft Serrasalmus gouldingi - V \\ v [h - r TTrn Pygocentrus cariba -. - ^ -y P. nattereri E - P. piraya i i FIGURE 2. Net ontogenetic shape change for five piranha taxa, depicted as Cartesian transformations. as a deformation between landmarks (Fig. 2; technical details supplied by Bookstein [1989,1991]; the physical metaphor and its application to studies of shape change were discussed less technically by Zelditch et al. [1992, 1995] and Swiderski [1994]). The deformation is decomposed into affine (uniform) and nonaffine (nonuniform) components. The uniform component describes changes that are geometrically uniform over the body; every small square of a grid superimposed on one form would be transformed to the same parallelogram in the same orientation. The nonuniform component describes transformations that are different among regions of the body. The nonuniform component can be decomposed further into a series of components ordered by their eigenvalues. The eigenvalues can be interpreted as inversely related to the spatial scale of the corresponding principal warp. That is, a smaller eigenvalue is associated with a principal warp at a higher spatial scale. The biological signal does not lie in the number of these components nor in the pattern of landmark displacements they describe both are entirely a matter of the location of landmarks in the starting form. The number of nonuniform components is three less than the number of landmarks. The pattern of landmark displacements described by each component is determined by the configuration of landmarks in the

5 1995 PHYLOGENIES OF SHAPE ONTOGENIES 347 starting form (representing the canonical form, or mode, of relative landmark displacements for shape changes at that spatial scale of localization). These geometrically independent features ordered by spatial scale are called principal warps in reference to the metaphorical bent steel plate, the mathematics of which underlies the analysis. The biological interpretation of shape change comes from inspection of the partial warps (vectors multiplying each of these principal warps), which express the contribution that each principal warp makes to the realized landmark displacements in the x, y plane. Thus, although principal warps are geometric terms in which morphological differences can be described, partial warps describe realized changes in those terms. Most real biological shape changes incorporate both uniform and nonuniform components. In these analyses of piranha form and ontogeny, an average small juvenile Pygopristis denticulata (Cuvier) was used as the starting form. A single starting form ensures that shape changes of homologous regions of the body are compared (Zelditch et al., 1995) to the extent that the points sampled are homologous in this clade. Not only are the landmarks homologous at the level of the whole clade examined, but also the components of shape change are homologous at that same level. Because all individuals were compared with the same starting form and the principal warps are a function of the configuration of landmarks on this form, we have a common basis for all comparisons. We estimated the uniform component by the factor-approximation formula given by Bookstein (1991:279). TPS analysis was done with two programs. F. J. Rohlf's TPSPLINE (version dated 12/17/91; available with Rohlf and Bookstein, 1990) and J. M. Humphries' Jspline (version 1.0) both compute principal warps and the partial warp scores. We used TPSPLINE to depict the shape changes as Cartesian deformations and Humphries' Vector Spector (version 1.0) to depict the shape changes as a pattern of relative landmark displacements (to obtain current versions of these programs, contact the program authors at rohlf@sbbiovm.bitnet and jmhl@cornell. edu). We used the Format Conversion program (available with Rohlf and Bookstein, 1990) for converting digitized coordinates into the format required by TPSPLINE. The association between size and the partial warps was analyzed by multiple regression of size on the two-dimensional partial warps to determine if the aspects of shape described at that scale changed ontogenetically. Features were considered to exhibit ontogenetic change at a particular spatial scale when the associations between size and shape were statistically significant table wide, a = 0.05 (the table comprised the regressions of the partial warps on log root centroid size of each species analyzed separately by a sequential Bonferroni test [Rice, 1986]). The coefficients describing the size-related change in each direction (anteroposterior [x], dorsoventral [y]) were obtained by simple regression of each component of the two-dimensional partial warp on log centroid size. Characterizing Ontogenetic Shape Variables For the phylogenetic analysis, each spatial scale and each component of the vector (the anteroposterior and dorsoventral components) were analyzed separately. Ontogenetic changes were compared with respect to two criteria: (1) the existence of ontogenetic change and (2) the direction of ontogenetic change. When we found evidence of a statistically significant relationship between size and shape change at a particular spatial scale, the ontogenetic changes were compared by examination of the partial warp scores. Two taxa were considered to exhibit the same ontogenetic change along a particular body axis if they both changed at a particular spatial scale and in the same direction. We did not compare regression coefficients (or constants) statistically, although there may be additional information in these features. With larger samples and further study of methods for assessing individual variation in

6 348. SYSTEMATIC BIOLOGY VOL P. nattereri i o. o 0 o U ' 9 1 P. piraya Size o o o fi 0 0 O o 5 Size 6 7 FIGURE 3. Change in relative length of the caudal peduncle, PW9x, with increasing body size. The Cartesian transformations for the piranha taxa depict decreasing relative length of the caudal peduncle, the change implied by decreasing scores on the y-axis, as in Pygopristis denticulata and Serrasalmus gouldingi. O O ~% O - - these aspects of growth, these features may also become useful. Here, we exemplify our procedure by describing one of the more localized features of ontogenetic shape change and giving our interpretation of the characters. Partial warp 9 (PW9) (see Figs. 3, 4) describes a contrast between point 5 (and to a lesser degree points 7 and 8) and point 6, implying localized changes within the posterior back and peduncle region (Fig. 1). In Pygopristis denticulata, we found change along the anteroposterior body axis: elongation of the region between the dorsal and adipose fins relative to the caudal peduncle and the predorsal fin back (r

7 1995 PHYLOGENIES OF SHAPE ONTOGENIES a > » *-- r - FIGURE 4. Change in relative depth of the caudal peduncle, PW9y, with increasing body size. The Cartesian transformations for the piranha taxa depict relative shallowing of the peduncle region, the change implied by increasing scores on the y-axis, as in Pygopristis denticulata and Serrasalmus gouldingi. = 0.647, P < ) (Fig. 3). We also observed change along the dorsoventral axis: r = 0.837, P < ). No evidence of onterior: r = 0.761, P < ; dorsoventral: deepening of the region between dorsal togenetic change at this scale was found in and adipose fins relative to the depth of any of the three Pygocentrus. For Pygocentrus cariba, the correlations between size the caudal peduncle (r = 0.894, P < ) (Fig. 4). In S. gouldingi, ontogenetic change and shape are nonsignificant in both directions (anteroposterior: r = 0.037, P = is as described for Pygopristis denticulata (correlation in size and change anteropos ; dorsoventral: r = 0.288, P = 0.205).

8 350 SYSTEMATIC BIOLOGY VOL * (a) 1 (b) H * ' 1 V" ^,. i - ^. 1 ^., 1 -». ^ ^, ^ - [» *" ' FIGURE 5. Reorientation of PW2y. (a) Primitively, the head shallows relative to the more posterior body, (b) In the piranha Pygocentrus nattereri, the head deepens relative to the more posterior body. The correlations are nonsignificant also in Pygocentrus nattereri (anteroposterior: r = 0.023, P = 0.828; dorsoventral: r = 0.033, P = 0.760) and Pygocentrus piraya (anteroposterior: r = 0.054, P = 0.765; dorsoventral: r = 0.099, P = 0.585). In some cases, we found that taxa differ not only in the presence or absence of ontogenetic change at a particular spatial scale but also in the direction of change along a single body axis. For example, ontogenetic shallowing of the head relative to, the posterior body (Fig. 5a) is a primitive feature of piranha ontogeny that is lost in Pygocentrus; in Pygocentrus nattereri there is an ontogenetic deepening of the head relative to the posterior body (Fig. 5b). In these cases, features were treated as unordered multistate characters. This preliminary comparison of the individual vector coefficients does not require that ontogenetic changes at each spatial scale or along each body axis be developmentally or historically independent. As in any case when there is no a priori reason to doubt that characters are independent, the characters are analyzed under the assumption of independence and this assumption is reconsidered once the pattern of changes inferred by the phylogenetic analysis has been established. This assumption of phylogenetic independence can be rejected if change in both directions occurs at the same node of the cladogram, which would be evidence for lack of independence, both ontogenetic or phylogenetic. Table 1 shows the data matrix of all features used in the analysis, and Appendix 3 includes abbreviated descriptions of the features. The codings for the comparisons of ontogenetic change in PW9 were presence of ontogenetic change (0) in the anteroposterior direction (PW9x, character 19) in Pygopristis denticulata and S. gouldingi (elongation of the region between dorsal and adipose fins relative to the caudal peduncle) and absence of change in this direction (1). For ontogenetic changes in the dorsoventral direction (PW9y, character 20), we coded presence of ontogenetic change (0) observed in Pygopristis denticulata and S. gouldingi (deepening of the re- TABLE 1. Data matrix for five species of piranhas. Characters Taxon Pygopristis denticulata Serrasalmus gouldingi Pygocentrus cariba Pygocentrus nattereri Pygocentrus piraya

9 1995 PHYLOGENIES OF SHAPE ONTOGENIES 351 gion below the dorsal and adipose fins relative to the caudal peduncle) and absence of ontogenetic change (1). These two features were judged nonindependent based on their distribution on the cladogram. The data were analyzed using the branch-and-bound algorithm of PAUP 3.1.1(Swofford, 1993), rooting the network between the outgroups (Pygopristis denticulata and S. gouldingi) and the ingroup. Character changes were examined with MacClade 3.1 (Maddison and Maddison, 1992). Monophyly of Pygocentrus was not assumed nor were polarities of characters assigned a priori. RESULTS Comparisons of Ontogenies Uniform component of ontogenetic shape change. Pygopristis denticulata undergoes a slight posteriad shift of dorsal landmarks (and anteriad shift of ventral landmarks) proportional to their location along the dorsoventral body axis; we also observed dorsoventral deepening. The same ontogenetic transformations were observed in S. gouldingi and Pygocentrus cariba. In Pygocentrus nattereri, there is an anteriad shift of dorsal landmarks (and a posteriad shift of ventral landmarks); change in the dorsoventral direction is as described for Pygopristis denticulata. We found no uniform ontogenetic change in Pygocentrus piraya. Nonuniform components of ontogenetic shape change. At the highest spatial scale (the component with the least bending energy), partial warp 1 (PW1) refers to a contrast between the midbody points and those at the anterior and posterior of the form. (Following the numbering convention of Zelditch et al. [1992], we number warps in order of decreasing spatial scale.) Pygopristis denticulata exhibits an anteroposterior axial gradient of smoothly increasing growth rates towards the posterior end; there is no evidence of change oriented along the dorsoventral body axis. In S. gouldingi, change in both directions is as described for Pygopristis denticulata. In Pygocentrus cariba, change along the anteroposterior body axis is as described for Pygopristis denticulata; we also observed change along the dorsoventral body axis: increasing convexity of the dorsal profile associated with a decreasing concavity of the ventral profile. In Pygocentrus nattereri, there is no evidence of change in either direction (lack of ontogenetic change along the dorsoventral axis is as described for Pygopristis denticulata). In Pygocentrus piraya, change in both directions is as described for Pygopristis denticulata. With a slightly higher eigenvalue, hence at a slightly lower spatial scale, PW2 describes contrasting displacements of the landmarks at the anterodorsal and posteroventral "corners" and the landmarks at the anteroventral and posterodorsal "corners" of the form. The landmarks delineate a region posterior to the snout and extending to below the dorsal fin termination. In Pygopristis denticulata, we observed change oriented along the anteroposterior body axis: shortening of the dorsal relative to the ventral body profile. In addition, we observed change along the dorsoventral body axis: relative deepening of the posterior body compared with the head. In S. gouldingi, there is no evidence of change along the anteroposterior body axis; change along the dorsoventral axis is as described for Pygopristis denticulata. In Pygocentrus nattereri, lack of evidence of change along the anteroposterior axis is as described for S. gouldingi; along the dorsoventral axis, we observed shallowing of the posterior body relative to the head and anterior back. In Pygocentrus cariba and Pygocentrus piraya, there is no evidence of change along either axis (lack of evidence of change along the anteroposterior direction is as described for S. gouldingi). At an almost equally high spatial scale, PW3 describes contrasting displacements of points within the midbody region with those in the anterior and posterior ends of the body. In Pygopristis denticulata, we observed change at this scale along the anteroposterior direction: elongation of the midbody compared with the head and posterior body regions, with resultant steepening of the anterior head profile; there is no evidence of change at this scale

10 352 SYSTEMATIC BIOLOGY VOL. 44 along the dorsoventral body axis. Serrasalmus gouldingi and the three Pygocentrus are as described for Pygopristis denticulata. At the next smaller spatial scale, PW4 describes contrasting displacements of points 4, 7, and 12 with points 2 and 15 anteriorly and points 5 and 6 on the posterior back. In Pygopristis denticulata, there is no evidence of change along the anteroposterior body axis at this scale. We observed a change at this scale along the dorsoventral axis: an increase in the curvature of the back with increasing convexity of head and posterior body profiles. In S. gouldingi, change is as described for Pygopristis denticulata. In Pygocentrus cariba, lack of evidence of change along the anteroposterior axis is as described for Pygopristis denticulata; there is no evidence of change along the dorsoventral body axis. In Pygocentrus nattereri, lack of evidence of change along the anteroposterior axis is as described for Pygopristis denticulata; along the dorsoventral axis, we observed reduction in the concavity of the back and decreasing convexity of the head and posterior back profiles. In Pygocentrus piraya, changes are as described for Pygocentrus cariba. PW5 describes contrasting displacements of points 9, 12, 13, and 15 with points 1 and 10. In Pygopristis denticulata, there is no evidence of change in either direction at this scale. In S. gouldingi, lack of evidence of change along the anteroposterior axis is as described for Pygopristis denticulata; along the dorsoventral axis, we observed change: lessening relative depth of the anterior dorsal head profile compared with the lower jaw and suborbital head and a decreasing convexity of the postpelvic belly. In all three Pygocentrus, lack of evidence of change is as described for Pygopristis denticulata. PW6 describes contrasting displacements of point 3 with point 4 dorsally and of point 12 with point 16 ventrally. In Pygopristis denticulata, there is no evidence of any change along the anteroposterior axis. Dorsally, we observed increasing convexity of the anterior head and back and decreasing steepness of the dorsal fin base, and ventrally we observed a relative shallowing of the posterior ventral head profile. Ontogenetic change in S. gouldingi is as described for Pygopristis denticulata. In Pygocentrus cariba, lack of evidence of change along the anteroposterior axis is as described for Pygopristis denticulata; there also is no evidence of change along the dorsoventral body axis. Changes in Pygocentrus nattereri are as described for Pygopristis denticulata, and lack of change in Pygocentrus piraya is as described for Pygocentrus cariba. PW7 describes contrasting displacements of points 1, 3, 8, and 16 with points 2, 7, 10, and 15. In Pygopristis denticulata, we observed change at this scale in the anteroposterior direction: expansion of the postorbital head, nape, and postpelvic belly relative to the anterior head and prepelvic belly; in the dorsoventral direction, we observed decreasing convexity of the dorsal head profile along with relative expansion of the snout tip and an increase in relative depth of the area between the pelvic fin and posterior head. Change along the anteroposterior axis in S. gouldingi and in all three Pygocentrus is as described for Pygopristis denticulata. In S. gouldingi, change in the dorsoventral axis is as described for Pygopristis denticulata. Change along the dorsoventral axis in Pygocentrus cariba is as described for Pygopristis denticulata. In Pygocentrus nattereri, there is no evidence of change along the dorsoventral axis at this scale. In Pygocentrus piraya, change along the dorsoventral axis is as described for Pygopristis denticulata. PW8 describes contrasting displacements of points 7 and 9 with points 8 and 10. In Pygopristis denticulata, we observed change in the anteroposterior direction: shortening of the anal fin base relative to the ventral body anteriorly and posteriorly. In addition, there is evidence of change along the dorsoventral axis: relative narrowing of the ventral region of the peduncle and deepening of the more anterior belly. There is no evidence of change at this scale in S. gouldingi. In Pygocentrus cariba, lack of evidence of change in the anteroposterior direction is as described for S.

11 1995 PHYLOGENIES OF SHAPE ONTOGENIES 353 gouldingi; observed changes along the dorsoventral body axis include relative deepening of the ventral region of the peduncle and shallowing of the more anterior belly. In Pygocentrus nattereri, change along the anteroposterior direction is as described for Pygopristis denticulata, and change along the dorsoventral direction is as described for Pygocentrus cariba. In Pygocentrus piraya, ontogenetic change is as described for Pygocentrus cariba. For description of PW9, see Materials and Methods section. PW10 describes contrasting displacements of points 2 and 16 with points 11 and 15. There is no evidence of ontogenetic change in either direction in Pygopristis denticulata. In S. gouldingi, we observed change in the anteroposterior direction: steepening and relative elongation of the dorsal head profile compared with the postorbital head. There is no evidence of change in the dorsoventral direction. In Pygocentrus cariba and Pygocentrus nattereri, change is as described for S. gouldingi. In Pygocentrus piraya, lack of evidence of change along the anteroposterior direction is as described for Pygopristis denticulata; dorsoventrally there is lessening of the convexity of the dorsal head profile relative to the suborbital head along with a relatively ventrad displacement of the pectoral fin. PW11 describes contrasting displacements of points 2, 12, and 16 with points 11 and 15. There is no evidence of ontogenetic change at this scale in Pygopristis denticulata. In S. gouldingi, we observed change in the anteroposterior direction: slight shortening of the postorbital region relative to the snout and orbital regions. In addition, we observed change in the dorsoventral direction: moderately decreasing convexity of the head profile. In Pygocentrus cariba, we observed elongation of the postorbital region relative to the more anterior snout and orbital regions; there is no evidence of change along the dorsoventral axis. In Pygocentrus nattereri, change in the anteroposterior direction is as described for Pygocentrus cariba; change in the dorsoventral direction is as described for S. gouldingi. In Pygocentrus piraya, ontogenetic change is as described for Pygocentrus cariba. PW12 describes contrasting displacements of point 14 with points 1 and 15. There is no evidence of ontogenetic shape change at this scale in Pygopristis denticulata. In S. gouldingi, along the anteroposterior direction we observed an increase in snout length relative to eye diameter. In addition, there is evidence of change in the dorsoventral direction: an anterodorsal rotation of the snout relative to the anteroposterior body axis. In all three Pygocentrus, change in the anteroposterior direction is as described for S. gouldingi; lack of evidence of change along the dorsoventral axis is as described for Pygopristis denticulata. The most localized warp, PW13, describes contrasting displacements of point 13 with points 12 and 14 in the head region. There is no evidence of ontogenetic change at this scale in Pygopristis denticulata or S. gouldingi. In Pygocentrus cariba, there is evidence of change in the anteroposterior direction: a relative displacement of the infraorbital anteriorly, a shift partially reversed at larger size. In Pygocentrus nattereri, change in the anteroposterior direction is as described for Pygocentrus cariba. In addition, there is evidence of change in the dorsoventral direction: a decrease in the extent of the anterior suborbital region relative to the depth of the lower jaw. In Pygocentrus piraya, change is as described for Pygocentrus cariba. Phylogenetic Results and Character Independence Some characters (Table 1) were invariant and therefore contributed no information to the phylogenetic analysis (characters 7, 8, 9,11,13,15 [PW3x, PW3y, PW4x, PW5x, PW6x, PW7x]). However, the original numbering scheme has been retained for consistency. We also included several osteological and myological features that have been surveyed broadly in piranhas and found to be unique features of the group comprising Pygocentrus, Serrasalmus, and Pristobrycon.

12 354 SYSTEMATIC BIOLOGY VOL. 44 Pygopristis 2x 8x(1) 12x 5y 8y(1) 12y I I I I I I 2y(1)4y(1)8y(2)9x,y 11x 13x I I I Ux(2) Uy 10y I I I I I Ux(1) 1x 2y(2)4y(2) 7y 8x(0) S. gouldingi P. piraya f- P. nattereri 13y (a) P. cariba (b) (C) (d) 2x 8x(1) 12x 2x 8x(1) 12x 2x 8x(1)12x 5y 8y(1) 12y 2y(1)4y(1) 8y(2) 9x,y 11x 13x I I I 5y 8y(1) 12y I I I I I I 2y(1)4y(1) 8y(2) 9x,y 13x I I I 5y 8y(1) 12y 2y(1)4y(1) I I I I 8y(2)9x,y 11x 13x I I I Ux(2) Uy 10y Ux(2) 4-H- Uy 10y I I I Ux(2) Uy 10y I I I I I Ux(1) 1x 2y(2)4y(2) 7y 8x(0) 13y I II I I I I 1x 2y(2) 4y(2) 7y 8x(0) 13y 4-f Ux(1) 1x 2y(2) 4y(2) 7y 8x(0) 13y Pygopristis S. gouldingi P. piraya -f- P. nattereri P. cariba Pygopristis S. gouldingi P. p/raya I P. nattereri P. cariba Pygopristis S. gouldingi P. piraya P. nattereri P. carfoa FIGURE 6. Assessing independence of characters that change multiple times on the cladogram of piranha taxa. A box encloses each change of a particular character. Of these, only PW2y and PW4y have the same distributions and thus fail the test of independence. S. = Serrasalmus; P. = Pygocentrus. state 1 of character 6 [PW2y(l)], and characters 10, 19, 20, and 27 [PW4y, PW9x, PW9y, PW13x] are unique). No ontogenetic shape characters with unambiguous distributions corroborate the proposed sistergroup relationship between Pygocentrus nattereri and P. cariba, nor do they imply an alternative hypothesis of relationships within Pygocentrus; they are congruent with this hypothesis but simply fail to ad- The one cladogram (length = 42 steps; consistency index [CI] excluding uninformative characters = 0.826; retention index = 0.750; rescaled CI = 0.679) clearly supports the monophyly of Pygocentrus (Fig. 6). Seven ontogenetic shape characters with unambiguous distributions corroborate this hypothesis (characters 6, 10, 18, 19, 20, 23, 27 [PW2y(l), PW4y(l), PW8y(2), PW9x, PW9y, PWllx, PW13x]; of these,

13 1995 PHYLOGENIES OF SHAPE ONTOGENIES 355 dress it. Several ontogenetic characters with unambiguous distribution diagnose P. nattereri (1, 3, 6, 10, 17, 24, 28; of these, state 2 of characters 6 and 10, and characters 1, 3, and 28 are unique; character 6 is ambiguous). Pygocentrus cariba and P. piraya are also each diagnosed by unique ontogenetic characters: P. cariba by character 4 and P. piraya by characters 1, 2, 22, and several others that also diagnose other taxa. In this analysis, we began with the assumption that each spatial scale could be treated as an independent character. This assumption was assessed by examining the patterns of character change on the cladogram to determine if the geometrically independent features exhibit the same pattern of character changes. Several partial warps jointly diagnose Pygocentrus, and multiple partial warps diagnose each of several taxa. This examination of character patterns reveals cases in which independence is clearly supported, others where the evidence is equivocal, and yet others where independence is doubtful. Our strategy for examining independence is as follows. First, examine features that change more than once on the cladogram, such as PW8x in Figure 6a, which initially changes at node Serrasalmus + Pygocentrus. Then, ask whether any other characters that diagnose that node also change in concert with PW8x at the next node where it changes (P. nattereri). In this case, there are two other features diagnostic of Serrasalmus + Pygocentrus (PW2x and PW12x) that do not change in P. nattereri and thus were judged independent of PW8x. We come to a similar conclusion for PW8y (Fig. 6b) and Ux (Fig. 6c), which exhibit independent change in two sister taxa that have no other characters in common. In contrast, Figure 6d shows two features whose independence is in doubt. PW2y and PW4y both change at Pygocentrus and change together again in P. nattereri. For characters that only change once, this strategy cannot be used. However, ontogeny can be used to judge the independence of such features. Whenever we had several characters diagnosing a node and we wished to examine their independence we looked to see whether they originated by the same modifications of ontogeny. Gains and losses of ontogenetic transformations are the two major categories used. One special type of gain, reorientation, merits extra attention. Reorientation refers to a modification of the orientation of the ontogenetic change, such as the transformation from a shallowing of the head relative to the posterior body to a deepening of the head (Fig. 5). Reorientations are treated as different from simple gains or reversals because they involve modifications in addition to gain or reversion to primitive states. Another category is reversal, which refers to change (whether by loss or gain) resulting in reappearance of an apparently primitive ontogeny. There are other possible refinements of this classification of changes. For example, given information of specific heterochronic modifications, we might then wish to classify characters in those terms. The objective is to determine whether characters that change at a single node fall into the same types. When they do, they may be nonindependent. When they differ, in contrast, different ontogenetic processes may have generated the novelties and they should be interpreted as independent in origin. This approach to characters that change multiple times on the cladogram places the independence of PW2y and PW4y. in doubt because both are lost in Pygocentrus and reoriented in P. nattereri. The combination of their multiple occurrence and the commonality of the type of ontogenetic modification strongly suggests that these partial warps should be considered as a single character. Although some features appear to be nonindependent, we have no reason to doubt the independence of the majority of the characters because of the different patterns of character associations in ontogeny and phylogeny. Developmentally coordinated features (changing over the same time interval in ontogeny) usually do not have an identical phylogenetic distribution in this analysis; we discuss those with unambiguous distributions here. For example, there is a suite of ontogenetic transformations coor-

14 356 SYSTEMATIC BIOLOGY VOL. 44 dinated in the ontogeny of P. nattereri: Ux and Uy, PW2y, PW3x, PW4y, PW6x, PW6y, PW7x, PW8x, PW8y, PWlOx, PWllx, PWlly, PW12x, PW13x, PW13y. Some of these are retained primitive features of piranhas (Uy, PW3x, PW6x, PW6y, PW7x). One character is found in Pygocentrus + Serrasalmus (PW12x[l]), some are found only in Pygocentrus (PWllx[l], PW8y[2], PW13x), and others are unique to P. nattereri (Ux[l], PW2y[2], PW4y[2], PW8x[0], PW13y). Thus, ontogenetically integrated characters can have different histories. In all cases, some ontogenetic transformations are retained from, some are added to, and others are deleted from the primitive ontogeny. There is no global modification of ontogenetic processes causing, for example, an overall acceleration of growth. Even when characters appear to respond to a common modification of ontogeny, such as that leading to loss of both PW2x and PW8x, the subsequent (and thus historically independent) reversal of PW8x suggests that these two features are not a single developmental unit. The gain of both PWllx and PW13x at Pygocentrus suggests that these two partial warps comprise a single developmental unit; they both describe localized features within the head. However, PW12x, which describes a transformation of a region including that spanned by PW13x, does not change in association with PWllx and PW13x. There may be combinations of inhibitory and stimulatory phenomena that could give rise to a complex coordination among gains and losses. A single modification of development could indeed create a complex derived spatial patterning of ontogeny. However, such scenarios can always be constructed to explain any variety of patterns, and although they are testable in principle, in the absence of tests there is no reason to eliminate character evidence based on these grounds. We have also presumed that changes in ontogenies along the anteroposterior body axis are independent of changes along the dorsoventral body axis at a single scale. This assumption appears amply justified; in only one case do changes in both directions at one scale have the same distribution (characters 19 [PW9x] and 20 [PW9y]). All other nonuniform components and the uniform component demonstrate independent phylogenetic modifications in these anteroposterior and dorsoventral directions. DISCUSSION We have previously argued that unlike most multivariate methods, TPS decomposed by its partial warps can, in principle, provide data suitable for cladistic studies (Zelditch et al., 1995). Here, we have shown that the method is also useful for obtaining systematic information from comparisons of body form ontogeny. Our data corroborate the hypothesis proposed by Fink (1993), although they are not informative regarding relationships among the species of Pygocentrus. However, they amply support the proposed monophyly of the genus and suggest some additional derived characters shared by Pygocentrus and Serrasalmus (but these characters are ambiguous because they might be uniquely derived in Pygopristis; further testing requires additional sampling of more outgroups and more representatives of Serrasalmus). Fink (1993) was unable to diagnose the widespread P. nattereri with features from either morphology or traditional morphometric procedures. Our analysis shows that P. nattereri can be diagnosed by the following features (Fig. 7; Table 1): reorientation of Ux, PW2y, and PW4y; loss of PWlx and PW7y; reversal of PW8x; and gain of PW13y. Although it has long been argued that ontogeny should be included in systematic analyses, few studies have incorporated comparisons of body form ontogeny together with more conventional osteological and meristic characters. Our argument is not that ontogenetic transformations are inherently more informative than other morphological characters, but rather that they should be and can be examined. The method proposed here is one for extracting this information from ontogeny. Other methods have recently been proposed as suitable for this kind of study (such as Eu-

15 1995 PHYLOGENIES OF SHAPE ONTOGENIES 357 *-D-t- 5y 8y(1) 12y 2x 8x(1) 12x Ux(2) Uy 10y Pygopristis S. gouldingi P. piraya 2y(1) 4y(1) 8y(2) 9x,y 11x 13x Ux(1) 1x 2y(2) 4y(2) 7y 8x(0) 13y Gain Q Reorientation Q Loss ^ Reversal P. cariba FIGURE 7. Cladogram of piranha taxa illustrating gains, losses, reorientations, and reversals of unambiguous characters. S. = Serrasalmus; P. = Pygocentrus. clidean distance matrix analysis [EDMA], Richtsmeier et al., 1993), but none of them have been shown to yield characters suitable for cladistic analysis in principle. More importantly, no method for assessing character independence has been developed for the ontogenetic characters discovered by those methods. Criticisms have been raised against methods such as EDMA on biometric grounds as well (Bookstein, 1991). Given these objections, the methods should not be pursued as sources of ontogenetic characters unless they can be shown to be superior for extracting cladistic data. Bookstein (1994) objected to the use of morphometric characters in systematics. In a paper entitled "Can biometrical shape be a homologous character?" he answered in the negative. We find his arguments unconvincing. In part, we disagree over semantics, most importantly over the meaning of homology. His arguments apply to his meaning of homology, which is not taxic homology, the concept of homology relevant in cladistic analysis. In addition, as is evident by the title of that paper, he regards shape as a unit character, with the consequence that a shape comparison describes a net, or overall, shape difference. Thus, terminal taxa would be coded as having a different state of shape whenever they differ at all in form. Conceivably, each one of our specimens could be coded as having a different state of shape. Such a view of shape as a single character renders shape useless for cladistic analysis. The same holistic approach to any other data, including qualitative morphology and nucleotide sequences, would similarly limit cladistic analysis. However, we certainly agree that biometric methods cannot test homology. Hypotheses of homology for morphometric features must be subjected to the same cladistic tests applied to all other characters (Zelditch et al., 1995). Unlike other morphometric methods, the partial warps provide a set of geometrically independent features for comparison. This geometric independence, however, does not imply that the components are phylogenetically independent. If it were necessary to assert the independence of the characters a priori and impossible to test this assumption empirically, the method would be fatally flawed because systematic analyses depend upon the independence of characters. Nor can we assert that the components of the two-dimensional vectors multiplying the partial warps are phylogenetically independent. If this assumption of the independence of the two directions at each spatial scale had to be valid but could not be tested, the method would be furthter disqualified from consideration for phylogenetic studies. However, even though we coded these vector components as independent features, we tested the assumption of independence empirically. We were thus able to identify characters comprising geometrically independent features. The problem of independence, however, is not a complication unique to this method. The possibility that a single ratio comprises multiple phylogenetically independent features is just as problematic, but it cannot normally be tested. Standard mea-

16 358 SYSTEMATIC BIOLOGY VOL. 44 sures used in systematic ichthyology make use of such ratios as a matter of course, e.g., the ratio of caudal peduncle depth relative to standard length. In the piranhas we examined, differences in this region of the body result from changes at several spatial scales. This analysis indicates why such a decomposition can be useful; several of these aspects of ontogenetic deepening appear to evolve independently in piranhas. At the largest spatial scale, the caudal peduncle is indivisible from any other region of the body; deepening is uniform in its rate everywhere. Still at a high spatial scale (PW2), deepening of the caudal peduncle occurs as part of a more general deepening of the posterior body relative to the anterior body. At a more localized scale, PW8 describes a relative narrowing of the ventral region of the peduncle and deepening of the more anterior belly. There is an even more localized deepening of the peduncle (PW9) relative to the region below the dorsal and adipose fins. Our phylogenetic analysis shows that only two of these features (PW2y, PW4y) are historically associated. Thus, comparisons that examine only depth of the peduncle relative to standard length risk confounding independently evolving characters. Two aspects of the method we have used warrant further examination and debate. First, we have taken a conservative approach to the analysis of the ontogenetic comparisons, using only presence or absence of ontogenetic change as characters. There might be additional information in rates and timings of ontogenetic changes. As yet, we have no criteria for coding differences in rates and timing; as with other characters that show quantitative variation and overlap, such details are problematic. Furthermore, rates and timings should not be compared until the transformations themselves are shown to be homologous. The second issue of concern is that the basis for the comparisons comes from the location of landmarks on the starting form. If the deformations are to be interpreted as actual evolutionary transformations, the starting form must represent the primitive morphology. Usually, the starting form will possess both primitive and derived features, so the mathematical transformations cannot be interpreted as actual historical transformations. What is more problematic is that in the cases in which multiple outgroups are included in the analysis, only one outgroup can be selected as the starting form (although some studies have used an average of the variable outgroups [Swiderski, 1994]). If the comparisons are interpreted as unpolarized contrasts between forms, the choice of starting form does not matter. Perhaps the most critical question is whether choosing different starting forms or even choice of an alternative basis for shape space would result in different phylogenies. The utility of ontogenetic shape characters in systematics cannot be asserted as a general rule. Pygocentrus has a distinctive form that must have arisen by modifications of ontogeny, so it is not surprising that we found diagnostic ontogenetic shape characters at this level. There may well be many cases in which ontogenetic transformations are invariant, are unique to each taxon, or are difficult to distinguish as distinct character states. Even in cases in which no new systematic insights are gained from ontogenetic shape transformations, these features still can be valuable for exploring the evolution of development, an area of wide interest. We can describe changes in both spatial and temporal patterning of growth. The work on piranhas indicates that spatial changes are a major source of novelties. ACKNOWLEDGMENTS We thank J. Birch, F. L. Bookstein, A. G. Kluge, and the Systematics Discussion Group of the University of Michigan for their invaluable contributions to and discussion of this work. Margaret Van Bolt prepared the final drafts of the figures. This work was supported in part by NSF grant DEB to M.L.Z. and NSF grants BSR and DEB and a Horace H. Rackham Research Grant from the University of Michigan to W.L.F. REFERENCES ALBERCH, P., AND J. ALBERCH Heterochronic mechanisms of morphological diversification and evolutionary change in the neotropical salamander

17 1995 PHYLOGENIES OF SHAPE ONTOGENIES 359 Bolitoglossa occidentalis (Amphibia: Plethodontidae). J. Morphol. 167: ALBERCH, P., S. J. GOULD, G. F. OSTER, AND D. B. WAKE Size and shape in ontogeny and phylogeny. Paleobiology 5: BOOKSTEIN, F. L Size and shape spaces for landmark data in two dimensions. Stat. Sci. 1: BOOKSTEIN, F. L Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Trans. Pattern Anal. Mach. Intell. USA 11: BOOKSTEIN, F. L Morphometric tools for landmark data: Geometry and biology. Cambridge Univ. Press, New York. BOOKSTEIN, F. L Can biometrical shape be a homologous character? Pages in Homology: The hierarchical basis of comparative biology (B. K. Hall, ed.). Academic Press, New York. BOOKSTEIN, F. L., B. CHERNOFF, R. L. ELDER, J. HUM- PHRIES, JR., G. R. SMITH, AND R. E. STRAUSS Morphometrics in evolutionary biology. Spec. Publ. Acad. Nat. Sci. Phila. 15:i-xvii, CREIGHTON, G. K., AND R. E. STRAUSS Comparative patterns of growth and development in cricetine rodents and the evolution of ontogeny. Evolution 40: DANSER, B. H A theory of systematics. Bibl. Biotheor. 4: DE QUEIROZ, K The ontogenetic method for determining character polarity and its relevance to phylogenetic systematics. Syst. Zool. 34: FINK, W. L Ontogeny and phylogeny of tooth attachment modes in actinopterygian fishes. J. Morphol. 167: FINK, W. L Revision of the piranha genus Pygocentrus (Teleostei, Characiformes). Copeia 1993: GOULD, S. J Ontogeny and phylogeny. Harvard Univ. Press, Cambridge, Massachusetts. HALL, B. K Evolutionary developmental biology. Chapman & Hall, New York. JENSEN, R. J The 25th International Numerical Taxonomy Conference. Syst. Biol. 42: KLOMPEN, J. S. H., AND B. M. OCONNOR Ontogenetic patterns and phylogenetic analysis in Acari. Pages in The concept of stase and the ontogeny of arthropods (H. M. Andre and J.-C. Lions, eds.). AGAR, Wavre, Belgium. KLUGE, A. G., AND R. E. STRAUSS Ontogeny and systematics. Annu. Rev. Ecol. Syst. 16: MABEE, P Phylogenetic interpretation of ontogenetic change: Sorting out the actual and artefactual in an empirical case study of centrarchid fishes. Zool. J. Linn. Soc. 107: MACHADO-ALLISON, A Studies on the subfamily Serrasalminae. Part III. On the generic status and phylogenetic relationships of the genera Pygopristis, Pygocentrus, Pristobrycon, and Serrasalmus (Teleostei Characidae Serrasalminae). Acta Biol. Venez. MADDISON, W. P., AND D. R. MADDISON MacClade, analysis of phylogeny and character evolution, version 3. Sinauer, Sunderland, Massachusetts. MCKINNEY, M Heterochrony in evolution. Plenum, New York. MOSER, H. G., W. J. RICHARDS, D. M. COHEN, M. P. FAHAY, A. W. KENDALL, AND S. L. RICHARDSON Ontogeny and systematics of fishes. Am. Soc. Ichthyol. Herpetol. Spec. Publ. l:i-ix, O'GRADY, R Ontogenetic sequences and the phylogenetics of parasitic flatworm life cycles. Cladistics 1: PATTERSON, C Morphological characters and homology. Pages in Problems of phylogenetic reconstruction (K. A. Joysey and A. E. Friday, eds.). Academic Press, London. RICE, W. R Analyzing tables of statistical tests. Evolution 43: RlCHTSMEIER, J. T, B. D. CORNER, H. M. GRAUSZ, J. M. CHEVERUD, AND S. E. DANAHEY The role of postnatal growth pattern in the production of facial morphology. Syst. Biol. 42: ROHLF, F. J., AND F. L. BOOKSTEIN (eds.) Proceedings of the Michigan morphometrics workshop. Univ. Mich. Mus. Zool. Spec. Publ. 2:i-viii, ROHLF, F. J., AND L. F. MARCUS A revolution in morphometrics. Trends Ecol. Evol. 8: STRAUSS, R. E On allometry and relative growth in evolutionary studies. Syst. Zool. 36: STRAUSS, R. E., AND L. A. FUIMAN Quantitative comparisons of body form and allometry in larval and adult Pacific sculpins (Teleostei: Cottidae). Can. J. Zool. 63: SWIDERSKI, D. L Morphological evolution of the scapula in tree squirrels, chipmunks and ground squirrels (Sciuridae): An analysis using thin-plate splines. Evolution 47: SWOFFORD, D. L PAUP: Phylogenetic analysis using parsimony, version 3.1. Illinois Natural History Survey, Champaign. WAKE, D. B Phylogenetic implications of ontogenetic data. Geobios 12: ZELDITCH, M. L., F. L. BOOKSTEIN, AND B. L. LUNDRI- GAN Ontogeny of integrated skull growth in the cotton rat Sigmodon fulviventer. Evolution 46: ZELDITCH, M. L., W. L. FINK, AND D. L. SWIDERSKI Morphometrics, homology, and phylogenetics: Quantified characters as synapomorphies. Syst. Biol.44: Received 12 April 1994; accepted 18 January 1995 APPENDIX 1 SPECIMENS EXAMINED Specimens were obtained from several museum collections: Museo de Biologia, Universidad Central de Venezuela (MBUCV); Museo de Ciencias Naturales, Guanare, Venezuela (MCNG); Museu de Zoologia, Universidade de Sao Paulo (MZUSP); and University of Michigan Museum of Zoology (UMMZ). Other institutions were listed by Fink (1993). Pygopristis denticulata MBUCV (n = 6, 44.9-

18 360 SYSTEMATIC BIOLOGY VOL mm SL), MBUCV (n = 3, mm SL), MZUSP (n = 7, mm SL), MZUSP (n = 3, mm SL), UMMZ (n = 3, mm SL [glo46-9]), and UMMZ (n = 10, mm SL [ g ]). Serrasalmus gouldingi UMMZ (n = 5, mm SL), UMMZ (n = 2, mm SL), and UMMZ («= 10, mm SL). Specimens of Pygocentrus cariba, P. nattereri, and P. piraya are the same as used by Fink (1993). APPENDIX 2 PIRANHA LANDMARKS 1. Snout tip, anteroventral junction of anteriomedial borders of premaxillaries. 2. Anterior border of epiphyseal bridge bone at dorsal midline (an insect pin was inserted into the top of the cranium to detect the border and was left in place for digitization). 3. Posterior tip of supraoccipital bone where it lies adjacent to epaxial musculature and the median dorsal septum. 4. Dorsal fin origin, not including anterior modified fin rays, marking anterior junction of fin and dorsal body midline. 5. Posterior end of dorsal fin base at dorsal body midline. 6. Posterior end of adipose fin base, where it joins with skin of posterior back on dorsal midline. 7. Posterior border of hypural bones (identified as bending axis of caudal fin base). 8. Posterior end of anal fin base at ventral midline. 9. Anal fin origin, marking junction of fin and ventral body midline. 10. Pelvic fin insertion, where fin projects laterally from pelvic girdle. 11. Pectoral fin insertion, where pectoral fin extends laterally from joint with pectoral girdle. 12. Mandible/quadrate joint (usually marked by an insect pin placed in middle of joint), marking junction between lower jaw and "face." 13. Posterior border of maxillary bone, where it intersects third infraorbital (cheek) bone. 14. Anterior border of bony orbit along horizontal body axis. 15. Posterior bony border of orbit along horizontal body axis. 16. Posterior border of bony operculum at most posterior point from snout tip. APPENDIX 3 CHARACTERS USED IN PHYLOGENETIC ANALYSIS OF PIRANHAS Data matrix is provided in Table 1. Characters are from Fink (1993). Characters are from Machado-Allison (1985); numbers in brackets correspond to character numbering in that study. 1. Uniform component, x. 2. Uniform component, y. 3. PWlx. 4. PWly. 5. PW2x. 6. PW2y. 7. PW3x. 8. PW3y. 9. PW4x. 10. PW4y. 11. PW5x. 12. PW5y. 13. PW6x. 14. PW6y. 15. PW7x. 16. PW7y. 17. PW8x. 18. PW8y. 19. PW9x. 20. PW9y. 21. PWlOx. 22. PWlOy. 23. PWllx. 24. PWUy. 25. PW12x. 26. PW12y. 27. PW13x. 28. PW13y. 29. Vertebrae: 37 or 38 (0); 36 (1). 30. Neural spines anterior to first pterygiophore: 7 (0); 6 (1); 5 (2). 31. Prepelvic serrae: >20 (0); 17 (1). 32. Gas bladder: elongate or partially truncate (0); greatly truncate (1). 33. Head width: relatively narrow (0); very wide (1). 34. Hypobranchial bones: without well-developed dermal bones (0); with such bones (1). 35. Vomer shape: nonconcave and lacking articular surfaces (0); concave, with articular surfaces (1) [character 13]. 36. Parasphenoid ventral lamina: undeveloped (0); highly developed (1) [character 14]. 37. Prootic shape: blocklike (0); elongate and laminar (1) [character 15]. 38. Exoctipital bone: convex and expanded (0); concave and laterally reduced (1). 39. Tendinous portion of inner and outer bodies of adductor muscles: not interconnected (0); with strong interconnection (1) [character 24].