vertebral osteology and complexity in lagenorhynchus acutus

VERTEBRAL OSTEOLOGY AND COMPLEXITYIN LAGENORHYNCHUS ACUTUS

(DELPHINIDAE) WITH COMPARISONTO OTHER DELPHINOID GENERA

EMILY A. BUCHHOLTZ

ELIZABETH M. WOLKOVICH

Department of Biological Sciences, Wellesley College,Wellesley, Massachusetts 02481, U.S.A.

RICHARD J. CLEARY

Department of Mathematical Sciences, Bentley College,Waltham, Massachusetts 02452, U.S.A.

ABSTRACT

The vertebral column of the Atlantic white-sided dolphin, Lagenorhynchus acutus,reflects the radical reorganization of the cetacean column for locomotion in water.Both posterior thoracic and anterior caudal vertebrae have been ‘‘lumbarized,’’ anddiscontinuities occur within the caudal series at the synclinal point and fluke base.Morphology changes subtly as body size increases. Neural process height increasesmore rapidly, and centrum length more variably, than other vertebral parameters.As a result, large animals have disproportionately tall neural processes, short necks,long mid-body regions, and short flukes. Vertebral columns of large animals alsoshow greater complexity (range, irregularity, and polarization) of centrum lengththan do those of smaller animals. Comparisons among dolphins reveal that com-plexity trends with respect to differentiation of parts run counter to the trend withrespect to number of parts, a relationship predicted by Williston in 1914.

Key words: vertebrae, Atlantic white-sided dolphin, Lagenorhynchus acutus, dol-phins, ontogeny complexity.

Descriptive and comparative analysis of vertebral osteology in the cetacean familyDelphinidae was pioneered by E. J. Slijper (1936, 1946, 1961). In the years sincehis work, the postcranial skeleton of delphinids has received minimal attention, andits ontogenetic variation has been ignored. Here we describe the vertebral osteologyof the Atlantic white-sided dolphin, Lagenorhynchus acutus, and examine changes inthat osteology during ontogeny. We ask whether observed ontogenetic changes invertebral dimensions represent changes in complexity and compare the complexityof the adult L. acutus column to that of other delphinids.

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MARINE MAMMAL SCIENCE, 21(3):411–428 (July 2005)� 2005 by the Society for Marine Mammalogy

Lagenorhynchus acutus is a relatively small and robust dolphin with a short broadbeak and distinctive white lateral patches. It lives in subarctic North Atlanticshelves, slopes, and submarine canyons where it occurs in small to large herds,possibly reflecting feeding and migration groups, respectively (Sergeant et al. 1980,Gaskin 1992, Palka et al. 1997, Reeves et al. 1999, Weinrich et al. 2001, Cipriano2002). There is slight sexual dimorphism; maximum adult body length is 243 cmin females and 267 cm in males (Sergeant et al. 1980).

Ontogenetic data are quite limited. Guldberg and Nansen (1894) noted changesin fluke shape during development. Sergeant et al. (1980) correlated body lengthwith a variety of maturational parameters, including dentinal growth-layer counts,body mass, corpora lutea count, and testis weight. Sexual maturity occurs at201–222 cm (6–8 yr) in females, and 230–250 cm (8–9 yr) in males (Sergeant et al.1980, Gaskin 1992). Maximum age, estimated from dentinal studies, is at least 22years for males and 27 yr for females (Sergeant et al. 1980).

Vertebrae of the mammalian spinal column are classically allocated to cervical,thoracic, lumbar, sacral, and caudal series. These series have been dramaticallyremodeled during the evolution of whales from terrestrial ancestors (Slijper 1936,1946; Buchholtz 1998, 2001). Cetacean cervical vertebrae have been radicallyforeshortened, and are in many cases partially or completely fused. Counts of cervicaland thoracic series are very similar to those of terrestrial mammals, but lumbar andcaudal counts are markedly higher, especially among delphinids (Slijper 1936).Although variation between adjacent vertebrae in the elongated lumbar and anteriorcaudal series is typicallymuted, the posterior tail is interrupted by discontinuities, themost prominent of which occur at the synclinal point and the fluke base (Buchholtzand Schur 2004). Vertebral count and morphology in L. acutus have been interpretedas highly derived relative to other delphinids (Buchholtz and Schur 2004).

McShea (1993) summarized the complexity of biological series as being ‘‘somefunction of the number of different parts it has, or the degree of differentiation amongparts, and of the irregularity of their arrangement.’’ He speculated that the number ofparts and the differences among parts might well be related, as large morphologicaldifferences can be built up by a large number of small increments or by a smallnumber of large increments. McShea (1992, 1993) proposed several metrics for theevaluation of differences among parts of a series, using them to address the possibilitythat complexity of the mammalian vertebral column has increased over evolutionarytime. He found nearly equal numbers of increases and decreases in column com-plexity in a survey of mammalian ancestor descendant lineages. His extinct/extantcetacean pair was between the mysticetes Aetiosaurus (Oligogene) and Balaenoptera(Recent), for which centrum width and centrum length were examined.

Williston (1914) asserted that count and differentiation of elements in mor-phological series are inversely correlated. This assertion is particularly interestingbecause it links an increase in one aspect of complexity (number of parts) to adecrease in another (differentiation among those parts). It also runs counter toa suggestion (McShea 1992) that selection might favor increase in the number ofparts because high counts allow more specialization and internal division of laboramong parts. Williston’s prediction has only rarely been tested quantitatively(but see Gregory 1927, 1929; McShea 1992, 1993; Sidor 2001). Delphinoidea isa particularly good taxon for such a test because it is both speciose and highlyvariable with respect to count. Maintenance of the correlation anticipated byWilliston predicts that dolphin species with high counts, such as Lagenorhynchusacutus, should display less vertebral differentiation than those with lower counts.

412 MARINE MAMMAL SCIENCE, VOL. 21, NO. 3, 2005

Williston also noted an evolutionary trend toward reduction in count. In delphinoidevolution, and in cetacean history in general (Slijper 1936, Mead 1975, Barnes 1984,Muizon 1988, Perrin 1989, Buchholtz 1998, Buchholtz and Schur 2004), vertebralcount is typically higher in more derived taxa, a reversal of the common pattern.

METHODS

Vertebral columns of Lagenorhynchus acutus and of a comparative cetacean set weremeasured at the American Museum of Natural History (AMNH), the Museum ofComparative Zoology (MCZ), Northeastern University (NUVC) and the UnitedStates National Museum (USNM) (Table 1).

Although L. acutus is a common species, complete disarticulated postcranialskeletons are quite rare in museum collections. In this study specimens wereconsidered complete if vertebral counts fell within the range published for thespecies (77–82, Reeves et al. 1999) and the terminal vertebra was present. Thisdiminutive vertebra is often of triangular shape and varies in dimension fromroughly subequal to the preceding vertebra to a miniature nubbin; it lacks aposterior articulation surface. One individual (MCZ 62380) with a count (83) thatexceeds the published range and a terminal vertebra was also evaluated as complete.Vertebrae were allocated into series, using rib counts and rib articulation facets toidentify the thoracic/lumbar boundary. The first caudal vertebra was definedfollowing DeSmet (1977) as the first vertebra with discernable hemal arch articularfacets on its posterior margin. Recognition of the lumbar/caudal boundary isdifficult in museum specimens. There is no discontinuous anatomical marker of thetransition on the centrum or attached processes. The first chevron bones areexceptionally small, rarely preserved, and leave almost no indication of their ar-ticulation with the centrum base. On the basis of nerve distributions, Slijper (1936)suggested that homologues of the sacral series (‘‘sacral lumbars’’) of terrestrialmammals exist among the posterior lumbars of whales. He therefore inferred thepresence of several apparent lumbar vertebrae (which he called ‘‘caudal lumbars’’)homologous to the anterior caudals lacking hemal arches that commonly occurimmediately posterior to the sacrum in terrestrial mammals.

Many of the specimens available for this study had nearly or completely fusedvertebral epiphyses and were of nearly uniform size, presumably corresponding tothe adult ontogenetic stage, but almost certainly to a wide range of ages, becausemaximum body size is reached before maximum age (Sergeant et al. 1980).Specimens from the midsize range were rare, and juvenile specimens were both rareand incomplete, although the fetal specimen (USNM 571828) was complete.

Lack of age data compelled assessment of ontogenetic stage from size alone; totalcentrum length (TCL, sum of centrum length values for each vertebra includingepiphyses) was used as a proxy. This value is not the same as total postcranial lengthduring life, because it does not include lengths of the intervertebral disks, whichwere either absent or desiccated in all specimens studied. TCL was not measurablein incomplete specimens, but can be predicted with great accuracy from the averagediameter of vertebral centra 8–21, typically coincident with the thoracic series (y¼65.7x � 750.14, r2 ¼ 0.95 where y ¼ TCL in mm and x ¼ average diameter ofvertebral centra 8–21 in mm, n¼ 15). With the exception of the fetus, variation inspecimen TCL is relatively continuous. Specimens were divided into three arbitrary

413BUCHHOLTZ ET AL.: VERTEBRAL OSTEOLOGY

Table 1. Specimens of Lagenorhynchus acutus and comparative species examined in thisstudy. L. acutus specimens are listed in order of increasing TCL; comparative specimens arelisted in order of increasing count. TCL values for incomplete specimens are in parentheses,and were estimated from the regression of TCL on average thoracic diameter.

Specimen TCL, mm TC Vertebral formula Complete? Sex

Lagenorhynchus acutus

USNM 571828 334.3 79 C7T14L?Ca? COM FNUVC 2694 (957.1) 73þ C7T14L23Ca29þ INC FUSNM 22934 (993.9) 65þ C7T14L24Ca20þ INC MUSNM 504082 1,014.2 79 C7T14L24Ca34 COM MNUVC 1968 1,023.8 82 C7T14L22Ca39 COM FNUVC 2702 (1,100.2) 77þ C7T14L23Ca33þ INC MMCZ 62383 (1,123.9) 81þ C7T14L21Ca39þ INC FNUVC 2461 (1,133.1) 71þ C7T15L23Ca26þ INC UMCZ 62377 1,159.4 81 C7T14L20Ca40 COM FNUVC 2701 (1,259.8) 78þ C7T14L23Ca34þ INC MNUVC 2712 1,296.5 80 C7T14L23Ca36 COM FMCZ 62382 (1,364.9) 79þ C7T14L23Ca33þ INC FNUVC 2706 (1,384.2) 81þ C7T14L23Ca37þ INC UUSNM 22942 (1,406.2) 75þ C7T13L25Ca30þ INC UNUVC 2715 (1,410.9) 78þ C7T14L22Ca35þ INC FAMNH 143513 1,453.7 82 C7T14L24Ca37 COM UUSNM 484922 1,548.1 80 C7T13L24Ca36 COM FNUVC 2707 (1,536.9) 79þ C7T14L20Ca38þ INC FNUVC 4167 (1,595.5) 76þ C7T14L23Ca32þ INC FUSNM 504754 1,613.0 79 C7T13L22Ca37 COM FMCZ 62380 1,692.0 83 C7T14L22Ca40 COM MMCZ 60939 1,704.6 82 C7T14L25Ca36 COM MMCZ 61008 1,757.6 82 C7T13L20Ca42 COM MNUVC 2696 (1,767.4) 78þ C7T16L21Ca34þ INC MNUVC 2711 (1,784.5) 79þ C7T14L22Ca36þ INC UUSNM 504153 (1,819.3) 78þ C7T13L22Ca36þ INC MUSNM 571391 1,841.0 81 C7T14L24Ca36 COM UMCZ 62384 1,848.0 81 C7T14L23Ca37 COM MMCZ 62379 1,870.9 81 C7T14L20Ca40 COM M

Lipotes vexilliferAMNH 57333 1,476 44 C7T10L7Ca20 COM U

Delphinapterus leucasUSNM 571021 2,864 50þ C7T11L7Ca25þ INC U

Orcinus orcaAMNH 34276 5,533 53 C7T11L11Ca24 COM M

Globicephala macrorhynchaUSNM 22571 2,849 54 C7T8L13Ca26 COM U

Neophocoena phocaenoidesAMNH 57332 957 60 C7T12L13Ca28 COM M

Steno bredanensisUSNM 550221 1,372 62 C7T12L15Ca28 COM U

Cephalorhynchus commersoniiUSNM 550156 894 63 C7T12L13Ca31 COM U

Phocoena phocoenaUSNM 550312 1,128 65 C7T13L14Ca31 COM U


TCL size classes (,1,200 mm, between 1,200 and 1,600 mm, .1,600 mm), andaveraged to allow ontogenetic comparisons.

Vertebral count (VC), centrum length (CL), centrum width (CW) centrumheight (CH), neural process (¼ neural arch þ neural spine) height (NPH), andneural spine inclination (NSI) were measured for each vertebra of all specimens. CLwas measured ventrally, CW and CH anteriorly. When epiphyses were detached(some juvenile specimens) they were sorted and reattached before measurement;lengths of missing epiphyses were estimated from that of the other face of the sameor from the immediately adjacent vertebra. Measurements were made in mm withdigital calipers and were rounded to one decimal point. Each vertebra was placedindividually in a jig that clamped anterior and posterior centrum faces andphotographed perpendicular to the axis of the vertebra; NPH and NSI weremeasured from these images. NPH is the length of the line drawn from the dorsaltip of the neural process to its perpendicular intersection with the (extended) linealong the dorsal centrum surface (Fig. 1). NSI is the angular inclination of the spineto this same line, with anterior inclination represented by values ,908 andposterior inclination by values .908. The line of inclination was drawn betweenmidpoints of the spine’s lateral surface at the points of its neural arch attachmentand preattenuation distal tip. Measurements were made to the nearest half-degree.Transverse process width (TPW) and transverse process inclination (TPI) weremeasured for a smaller subset of specimens with analogous methods from dorsalimages.

Table 1. Continued.

Specimen TCL, mm TC Vertebral formula Complete? Sex

Grampus griseusUSNM 504328 2,095 66 C7T12L16Ca31 COM M

Feresa attenuataMCZ 51458 1,708 69 C7T11L17Ca34 COM M

Phocoena spinipinnisUSNM 395751 1,169 69 C7T13L15Ca34 COM U

Stenella frontalisUSNM 571139 1,230 72 C7T12L20Ca33 COM U

Lagenorhynchus obliquidensUSNM 504851 1,341 75 C7T12L24Ca32 COM U

Peponocephala electraUSNM 504948 1,601 78 C7T12L19Ca40 COM U

Stenella coeruleoalbaUSNM 504350 1,585 79 C7T14L20Ca38 COM U

Lissodelphis borealisUSNM 484929 1,906 85 C7T14L33Ca31 COM U

Lagenorhynchus albirostrisMCZ 5322 1,725 91 C7T14L24Ca46 COM U

Phocoenoides dalliUSNM 504969 1,472 97 C7T17L26Ca47 COM U

Abbreviations: C¼ cervical; Ca¼ caudal; F¼ female; L¼ lumbar; M¼male; T¼ thoracic;U ¼ unknown; TC ¼ total vertebral count; (þ) indicates that vertebrae are missing froma series or count.


Anatomical descriptions are presented by vertebral series. Diagrams of mid-seriescervical, thoracic, and lumbar vertebrae, as well as vertebrae from three distinctivecaudal regions were drawn from digital images of an adult male (MCZ 60939).Dimensional variation along the column is described by graphical presentation andby factor analysis.

Relationships among CL, CW, CH, NPH, and NSI are presented by graphingaverages of these variables for the largest TCL size class. Factor analyses ofthe vertebrae from single individuals were run using the Minitab statisticalpackage to discover relationships among vertebral parameters and to identifydiscontinuities in vertebral morphology along the column. Separate analyses wererun on the vertebrae of six complete individuals (MCZ62377, NUVC 2712,AMNH 143513, MCZ62380, MCZ262384, MCZ61008) that span almost theentire range of TCL. Variables used were CL, CW, CH, NPH, and NSI. Lineardimensions of CL, CW, CH, and NPH were normalized to those of vertebra 22(typically the first lumbar vertebra) to make animals of different TCL more directlycomparable. Vertebrae without neural processes were coded as having NPH ¼ 0.For this analysis, raw NSI measurements were recoded so that inclinations weremeasured in degrees, with 08 representing a spine perpendicular to thelongitudinal axis of the vertebra. Anterior inclination was indicated with values,0, and posterior inclination with values .0. Vertebrae lacking neural processeswere coded as having NSI ¼ 0.

Ontogenetic variation along the column is presented by comparison of averagevalues of CL, CW, CH, NPH, and NSI in the three size classes. CL was also graphedby vertebral series because of marked variability in size increments among differentcolumn regions. Rates of CL, CW, CH, and NPH change during ontogeny werecompared by graphing raw measurements against TCL for those vertebrae (8–55)

Figure 1. Vertebral parameters measured in this study. CH ¼ centrum height, CL ¼centrum length, CW¼ centrum width, NPH¼ neural process height, NSI¼ neural spineinclination.


for which all four parameters were measurable (neural spines are absent fromposterior caudal vertebrae).

Three metrics developed by McShea (1992) were used to evaluate columncomplexity. As defined, all three measures have the same theoretical maximumvalue in cases of extreme differentiation, and all have a value of zero when there isno differentiation. The McShea metrics are: (1) range (a measure of maximumdifference among elements),

range ¼ logðxmax � XminÞ;(2) irregularity, or local differentiation (a measure of average absolute differencebetween adjacent elements),

irregularity ¼ logXN�1

i¼1

jXiþ1 � Xij !,

ðN � 1Þ !

; and

(3) polarization, or global differentiation (a scaled measure of average absolutedifference of elements from the element mean),

polarization ¼ log 2XNi¼1

jXi � �Xj=N !

Because vertebral count is stable across ontogeny, evaluation of complexity withrespect to count was applicable only across taxa.

Range, irregularity, and polarization were calculated for CL, CW, CH, and NPHfor animals of different TCL to determine whether morphological changes re-presented changes in column complexity. Because magnitudes of differences amongvertebrae tend to be greater in larger animals, McShea (1993) suggested severalprocedures for minimizing the possible effects of size. Here we follow his procedureof log transforming the data before calculating the metrics and omitting the logoperation from the equations cited above. Differences in size are therefore log ratios.CL, CW, and CH calculations omit cervicals 1–4 (because of fusion) and the terminalvertebra (because of irregular size). NPH calculations include all postcervicalprocesses greater than 5 mm in height. Estimates of NPH for vertebrae with brokentips were interpolated from those of immediately anterior and posterior columnposition; specimens with more than one broken process were eliminated from thecalculations. Cumulative CL complexity was calculated from anterior to posteriorlocations along the column for all complete specimens and graphed by size group.

Complexity metrics for CL and NPH were also calculated for adult individuals of18 delphinoid (delphinapterid, phocoenid, and delphinid) genera. This data setincludes animals of a wide range of vertebral count (44–97) and body TCL (957–5,533 mm) and allows a test of Williston’s prediction that greater differentiation(complexity) occurs in series of lower count.

RESULTS

Descriptive Anatomy

Diagrams of a representative vertebra of each series were drawn fromMCZ 60939,an adult male (snout–fluke notch length¼ 2,490 mm, TCL¼ 1,704.59, VC¼ 82;Fig. 2). As in most mammals, the cervical series of L. acutus (Fig. 2A–C) is composed


of seven vertebrae. The first four cervicals are typically fused both ventrally (centra)and dorsally (neural processes) into a single unit. Vertebrae 3–6 have extremely shortCL and short, posteriorly oriented neural spines. In measurable (i.e., separate)vertebrae, CW exceeds CH and centrum faces are nearly flat. Zygapophyses arepresent and oblique in orientation.

The thoracic series (Fig. 2D–F) is composed of 14 (rarely 13, 15, or 16) vertebrae,all with articulations for moveable ribs. The six anterior thoracics commonly havetwo rib facets (parapophyseal, diapophyseal); the remaining thoracics have a single

Figure 2. Anterior, lateral, and dorsal views of vertebrae of Lagenorhynchus acutus MCZ60939, TCL ¼ 1704.6. A–C, cervical 5 (vertebra 5), D–F, thoracic 8 (vertebra 15); G–I,lumbar 10 (vertebra 31); J–L, caudal 5 (vertebra 51); M–O, caudal 15 (vertebra 61); P–R¼caudal 31 (vertebra 77). Scale bars ¼ 2 cm.


facet (diapophyseal). CL is smaller than either CW or CH, but increases rapidlythrough the series. Centrum faces are flat and nearly round, with CW marginallygreater than CH. Neural spines are posteriorly inclined and increase in heightthroughout the series. Transverse processes are thick with a slightly posteriororientation. Zygapophyses are distinct in only the first half of the series, each pairprogressively more medial in location than that of the previous vertebra. In posteriorthoracics, anteriorly projecting metapophyses overlap but do not articulate with theneural spines of the preceding vertebra. Location of metapophysis attachment isprogressively more dorsal throughout the series.

The lumbar series (Fig 2G–I) is composed of 20–25 vertebrae; a significant portionof this variability may reflect difficulty in locating the lumbar/caudal boundary.Lumbar vertebrae lack zygapophyses, rib facets, and chevron facets. Centrum length isnoticeably shorter than in the thorax. CWand CH are subequal, and both dimensionsincrease throughout the unit. Neural processes are very tall, and very nearly erect. Inthe anterior part of the series, metapophyses are large and located near the base of theneural spine; posteriorly they diminish in size and are progressively more dorsal inlocation, a continuation of the trend seen in the thoracics. Metapophyses are absent onposterior lumbars. Transverse processes are nearly perpendicular to the vertebral axisand reach their greatest length in the most anterior lumbars.

The caudal series has the highest and greatest range in count, with 34–40vertebrae in complete specimens. Gradational anatomical variation is interruptedby discontinuities at the synclinal point and at the base of the fluke. Anteriormostcaudals are difficult to distinguish from posterior lumbars: CL and CH aresubequal, CL is short, neural processes are tall, transverse processes areperpendicular, and metapophyses are lacking. Posteriorly (Fig. 2J–L), metapophyseslocated high on the neural processes reappear. Neural spines have progressivelymore anterior, and transverse processes progressively more posterior, inclinations.At the synclinal point (at about vertebra 60) neural spines shorten, thicken, andabruptly reverse direction of inclination consistent with the discontinuity firstnoted by Slijper (1936). Posteriorly oriented spines are therefore mounted onanteriorly oriented arches, with the result that neural processes appear to be ‘‘bent’’(Fig 2M–O). Transverse processes are short and again perpendicular to thelongitudinal axis of the centrum. Centrum faces posterior to the synclinal point arerounded and CL increases between the synclinal point and the fluke base. Inimmediately prefluke vertebrae, CW drops rapidly to produce laterally compressedcentra. At the fluke base, the transitional vertebra has equal width and height, andhighly convex centrum faces. Fluke vertebrae (Fig. 2P–R) have very short CL andlack neural and transverse processes. They are of nearly rectangular cross-section andhave irregularly rounded faces.

Dimensional change of vertebrae along the column follows a consistent patternin all animals, presented as parameter averages for the largest size class in Figure 3.CW and CH are subequal throughout the column, peaking in the middle of thecaudal series. Immediately anterior to the fluke base CH . CW, and in the flukeCW. CH. CL is always less than CWand CH, and is particularly short in the neck,the anterior tail, and the fluke. A local peak in CL occurs immediately anterior tothe fluke base. NPH peaks in the mid-lumbos, and declines uniformly posteriorly.Neural processes have posterior orientations in the cervical and thoracic regions, asdo most terrestrial mammals. Vertebrae from the mid-lumbos to the synclinal pointof the tail have marked anterior inclinations; posterior to the synclinal point incli-nations are again posterior.


Factor analysis of the dimensional parameters for individual vertebrae of sixindividuals generated the same general pattern regardless of TCL (Fig. 4). Valuesfor the first two factors, representing between 79.4 and 83.7 percent of thevariation in each data set, are presented graphically. Loadings for vertebralparameters (Table 2) suggest that factor 1 reflects primarily centrum and neuralprocess size and factor 2 reflects primarily neural spine inclination. The closecorrespondence between vertebral sequence and plot location emphasizes the

Figure 3. Vertebral morphology and dimensions in Lagenorhynchus acutus. A, diagram ofan articulated vertebral column in lateral view, drawn from photos of MCZ 61008. B, C,average dimensions of TCL . 1,600 mm; standard errors, omitted here for legibility, maybe found in Figure 5. Solid vertical lines indicate transitions between classical series; hatchedlines indicate transitions within the caudal series at the synclinal point and fluke base. Seriesboundaries in A do not coincide with those in B and C because of variable centrum lengthalong the column. C¼ cervical, Ca ¼ caudal, L¼ lumbar, T ¼ thoracic.


gradational nature of variation along the column. Vertebrae of small size (cervical,anterior thoracic, immediately prefluke caudals, and fluke) have negative values offactor 1, while the larger and nearly uniform vertebrae of the posterior thoracic tomid-caudal series have a narrow range of positive factor 1 scores. Vertebrae withposteriorly inclined spines typically have positive values of factor 2, while thosewith anteriorly inclined spines are negative. Marked transitions in plot location(and by inference in vertebral morphology) occur both at locations between(cervical/thoracic) and at locations within (mid-thoracic/posterior thoracic,synclinal point of caudals, and at the fluke base) series as defined for terrestrialanimals.

Figure 4. Factor analyses of vertebral variation in Lagenorhynchus acutus. Each markerrepresents an individual vertebra; the continuous line connects vertebrae in sequence. þ¼cervical, u¼ thoracic, �¼ lumbar, s¼ caudal vertebrae; fluke base¼ gray bar; synclinalpoint ¼ black bar.


Ontogenetic Changes in Size and Complexity

Vertebral CL, CW, CH, and NPH all increase as TCL increases, but increase inaverage NPH is almost three times that of average CL, CW, or CH (Fig. 5). Increasesalso vary by column location (Fig. 6A–F). CL increases are largest from the posteriorthorax to the mid-tail (Fig. 6A). Cervical and fluke vertebrae are of nearly the samelength in all animals (Fig. 6B). Increases in CWand CH are nearly uniform from thethoracic/lumbar boundary to the fluke; the smallest increments of increase occurwithin the fluke (Fig. 6C, D). Increases in NPH are minimal in the thorax, but

Table 2. Factor loadings and percent variance for each factor analysis.

Factor CL CW CH NPH NSI %variance

MCZ 62377, total variance explained: 81.2%

1 0.7954 0.9133 0.9178 0.7510 �0.0301 57.52 0.4235 �0.2111 �0.1999 0.1919 0.9393 23.7

NUVC 2712, total variance explained: 79.4%

1 0.6140 0.9162 0.9188 0.7207 �0.2054 52.42 0.6825 �0.1746 �0.1267 0.2849 0.8686 27.0

AMNH 143513, total variance explained: 82.6%

1 0.7443 0.9149 0.9155 0.7799 �0.1315 57.12 0.5553 0.1993 �0.2009 0.1158 0.9337 25.5


1 0.8990 0.8354 0.8278 0.8137 �0.0649 57.22 0.2564 �0.4283 �0.3404 �0.0675 0.9390 25.0


1 0.7947 0.9149 0.9270 0.7945 �0.0297 59.22 0.4848 �0.2318 �0.0942 0.2053 0.9402 24.5


1 0.8354 0.8950 0.8951 0.8250 �0.0687 59.72 0.4120 �0.2402 �0.2245 0.05634 0.9443 23.5

Figure 5. Average CL, CW, CH and NPH as a function of TCL for vertebrae 8–55, n¼28. CL, y¼ 0.02x� 1.5, r2¼ 0.95; CW, y¼ 0.02xþ 13.7, r2¼ 0.95; CH, y¼ 0.02xþ 8.7,r2 ¼ 0.98; NPH, y ¼ 0.06x� 12.9, r2 ¼ 0.89.


Figure 6. Average dimensional and process inclination in small (TCL , 1,200 mm, n¼8), intermediate (1,200 mm, TCL, 1,600 mm, n¼10) and large ( TCL. 1,600, n¼10)individuals of Lagenorhynchus acutus with standard errors. A, CL; B, CL by vertebral series,with prefluke and fluke caudals analyzed separately; C, CW; D, CH; E, NPH; F, NSI.Vertical lines represent transitions between series, but are approximate as transitions occurin slightly different locations in different individuals. C¼ cervical, Ca¼ caudal. FB¼ flukebase, L¼ lumbar, S¼ synclinal point, T¼ thoracic. TCL¼ total centrum length. In graph B,where x¼TCL and y¼ series length, y¼ 0.023xþ 15.9, r2¼ 0.77 n¼ 28 for cervicals; y¼021x þ 14.19, r2 ¼ 0.87, n ¼ 28 for thoracics; y ¼ 0.37x � 32.12, r2 ¼ 0.89, n ¼ 28 forlumbars; y¼ 0.38x� 64.45, r2¼ 0.91, n¼ 28 for prefluke caudals; y¼ 0.044xþ 30.58m,r2 ¼ 0.76, n ¼ 14 for fluke caudals.


increase rapidly through the lumbars and anterior caudals (Fig. 6E). The pattern ofNSI is virtually indistinguishable across all animals (Fig. 6F).

Range, irregularity and polarization for size-corrected CL measurements allshow highly significant increases with increase in TCL (Fig. 7A). Range increasesmore than twice as fast as polarization and more than 50 times as fast asirregularity. Complexity trends for other vertebral variables were either marginallysignificant (CH irregularity, increase) or not significant (all others). CL complexitydoes not accumulate regularly along the column, but is concentrated at anterior andposterior ends of the body (Fig. 8). This pattern is more extreme in large than in smallindividuals.

Changes in Complexity with Change in Count

Interspecific comparisons of CL and NPH were used to test Williston’s pre-dictions of a negative correlation between vertebral count and complexity. Despitewide range in adult body size in these cetacean taxa, no significant changes in range

Figure 7. CL complexity in Lagenorhynchus acutus individuals of different total centrumlength (A) and in species of different total vertebral count (B). In L. acutus, range (y ¼0.015xþ 0.44, r2¼ 0.83, P , 0.001, n¼ 14), irregularity (y¼ 0.0066xþ 0.082, r2¼ 0.91,P , 0.001, n¼ 14) and polarization (y¼ 0.0003xþ 0.020, r2¼ 0.66, P¼ 0.003, n¼ 14) allincrease with increase in TCL. For comparative delphinoids, irregularity (y ¼�0.0037x þ0.55, r2¼ 0.46, P¼ 0.008, n¼ 14) and polarization (y¼�0.0002xþ 0.043, r2¼ 0.58, P¼0.002, n ¼ 14) with increase in count.


were detected after size correction. Decreases in CL irregularity and polarizationwere significant for CL (Fig. 7B).

DISCUSSION

The classical criteria by which vertebral series are defined reflect the subdivisionof the column into functional regions in animals with limb-based terrestriallocomotion. It is not surprising that modern cetaceans display different region-alization patterns that reflect the use of their columns for axial locomotion.Foreshortening of cervical vertebrae, loss of the sacral series, increase in vertebralcount, elongation of neural processes, and modification of the posterior caudals tosupport a fluke are adaptations common to all whales. The data presented hereindicate that Lagenorhynchus acutus, a derived delphinid, possesses a suite of addi-tional modifications of the ancestral terrestrial pattern.

Dimensional and factor analysis of five vertebral variables supports the inter-pretation of the L. acutus column as a long series of highly uniform vertebrae cappedanteriorly and posteriorly by units of smaller and more variable vertebrae. Vertebraewith the centrum dimensions, neural process heights, and neural spine inclinationstypical of lumbar vertebrae extend from the mid-thorax to the mid-tail. Thelumbar series is thus expanded both by high count and by ‘‘lumbarization’’ ofadjacent vertebrae. This expanded mid-body region provides the skeletal supportfor muscles that generate the forces that act posteriorly. The flexion of the tailduring locomotion is concentrated at two locations: the synclinal point and thefluke base (Slijper 1961). The tail can therefore be divided into three functionalunits: anterior vertebrae are part of the expanded lumbos where force is generated,

Figure 8. Cumulative irregularity (A) and polarization (B) of CL along the column inL. acutus individuals of different TCL. Lines are averages for complete individuals with TCL, 1,200 mm (thin, n ¼ 4), between 1,200 and 1,600 mm (medium weight, n ¼ 4) and. 1,600 mm (thick, n ¼ 6). Error bars represent standard error for small and largeindividuals, but were omitted for the intermediate size class to allow visualization of sizeclass differences. C ¼ cervical, Ca ¼ caudal, L ¼ lumbar, T ¼ thoracic.


middle vertebrae support the tail stock which is flexed at the synclinal point, andposterior vertebrae support the fluke which is flexed at the fluke base.

Animals of all TCL retain the same basic morphological pattern, but duringontogeny variable growth among vertebral parameters and among column regionsproduce changes in body proportions. NPH increases more rapidly than othervertebral variables, particularly in the lumbos, probably reflecting the rapid increasein attachment area for locomotor muscles in large animals. Somewhat counterintuitively, the most dramatic change in body proportions is the result of almostisometric additions to CL, CW, and CH. The cumulative total of incrementaladditions to TCL by each vertebra produces an increase of 83% in TCL, but of only60% in CH and CW across the size range of postfetal animals studied here.Although vertebral diameter may correspond only roughly to external body diam-eter, it seems reasonable to infer that, as in other small cetaceans (e.g., the harborporpoise, Curren et al. 1993) fineness ratio (body length/maximum body diameter)increases in Lagenorhynchus acutus as body length increases.

Changes in CL are particularly variable along the column, altering the relativeproportions of column regions. During ontogeny, lumbar vertebrae elongate ata rate more than three times that of thoracic and more than eight times that ofcervical vertebrae (Fig. 6B). Rates of increase vary dramatically across differenttail regions: prefluke caudals grow at rates similar to lumbars, while the flukecaudals mimic the very modest growth rates of the neck. As a result, largeanimals have shorter necks and flukes, and longer lumbar and prefluke caudalregions, than do small animals. Body length in larger animals is thereforerelatively greater where force is generated (lumbos and anterior tail) and shorterwhere force is applied (the fluke). A smaller relative length (¼ root chord) of thefluke predicts smaller fluke planform area and higher fluke aspect ratio (flukespan2/fluke area) (Fish 1998) as animals increase in TCL. This same trend hasbeen documented from external measurements of fluke area in the harbor porpoise(Curren et al. 1993).

Calculations of CL complexity at different ontogenetic stages reflect this variablegrowth. The rapid increase in CL range may be anticipated from the near stabilityof cervical and fluke CL across all body sizes and the increase in CL of remainingvertebrae. The increase in CL polarization indicates that even after size correction,the average CL value lies farther from the mean in large than in small animals.Animals become more ‘‘globally differentiated’’ as they elongate. Vertebrae makingthe largest contributions to this metric can be identified by graphing cumulativecolumn polarization: they lie anterior to the middle thorax and posterior to thesynclinal point. Irrregularity increases at a much slower rate than range or polar-ization. Nevertheless, small increases in irregularity indicate that the average dif-ferences between adjacent vertebrae are greater in large animals after size correction.The vertebrae contributing most heavily to irregularity are again those located inthe anterior and posterior extremes of the column; mid-body vertebrae vary moremodestly from each other. Increasing CL range, polarization, and irregularity are allresults of the differential growth of CL, and all identify adults as more highlyregionalized than juveniles. Increase in regionalization of morphology suggestsa parallel increase in regionalization of function.

McShea (1993) included ‘‘number of parts’’ as well as ‘‘differentiation’’ of parts inhis definition of complexity in biological series. During postembryonic devel-opment, vertebral count in vertebrates is static and, therefore, complexity withrespect to count is fixed. However, the existence of wide variation in count across


cetacean taxa presents an opportunity to test Williston’s (1914) hypothesis of aninverse relationship between series count and differentiation.

No significant change in CL or NPH range was found across a broad sample ofdelphinoid species after size correction. However, declines in CL polarization andirregularity are significantly correlated with increase in count. In these delphinoids,a greater number of parts is not associated with their specialization or differ-entiation. They show lower complexity than do animals with smaller vertebralcounts, supporting Williston’s hypothesis. This maintenance of the ‘‘Willistonrelationship’’ between count and differentiation is particularly interesting because itoccurs in a taxon in which the common evolutionary trend toward reduction incount (Williston 1914) is reversed.

Evaluation of complexity in Lagenorhynchus acutus is therefore dependent on thecontext of the comparison. In ontogeny, complexity increases; larger animals havegreater range, polarization, and irregularity of centrum length. In interspecificcomparisons, L. acutus is neither more complex nor less complex than otherdelphinoids, but rather complex in a different way. As a species with a very highvertebral count, it lies at the high end of trend of increasing complexity withrespect to number of parts, but these numerous parts show less differentiation, andtherefore lower complexity, than do those of animals of lower count.

ACKNOWLEDGMENTS

We thank these curators and collection managers for their kind hospitality and for accessto the specimens in their care: Gwillum Jones, Jim Mead, Charley Potter, Judy Chupasko,Maria Rutzmoser, and Robert Randall. We also thank Jim Mead, Charley Potter, and LindaGordon for the loan of the fetal specimen, Mauricio Solano of Tufts University School ofVeterinary Medicine for x-raying the fetal specimen, Larry Baldwin for a preliminaryversion of the factor analysis, Kate Webbink for help with the computer graphics, and twoanonymous reviewers. National Science Foundation Grant No. 9805793 to E.A.B. anda Wellesley College Faculty Grant supported travel to institutions.

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Received: 10 July 2004Accepted: 2 December 2004


vertebral osteology and complexity in lagenorhynchus acutus

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