Mandible allometry in extant and fossil
Balaenopteridae (Cetacea: Mammalia): the largest
vertebrate skeletal element and its role in rorqual
lunge feeding
NICHOLAS D. PYENSON1,2*, JEREMY A. GOLDBOGEN3 and ROBERT E. SHADWICK4
1Department of Paleobiology, National Museum of Natural History, Smithsonian Institution, P.O.
Box 37012, Washington, DC, 20013-7013, USA
2Departments of Mammalogy and Paleontology, Burke Museum of Natural History and Culture,
Seattle, WA 98195, USA
3Cascadia Research Collective, 218? West 4th Avenue, Olympia, WA, USA
4Department of Zoology, University of British Columbia, 6270 University Boulevard, Vancouver, BC,
Canada V6T 1Z4
Received 4 July 2012; revised 10 September 2012; accepted for publication 10 September 2012
Rorqual whales (crown Balaenopteridae) are unique among aquatic vertebrates in their ability to lunge feed.
During a single lunge, rorquals rapidly engulf a large volume of prey-laden water at high speed, which they then
filter to capture suspended prey. Engulfment biomechanics are mostly governed by the coordinated opening and
closing of the mandibles at large gape angles, which differentially exposes the floor of the oral cavity to oncoming
flow. The mouth area in rorquals is delimited by unfused bony mandibles that form kinetic linkages to each other
and with the skull. The relative scale and morphology of these skeletal elements have profound consequences for
the energetic efficiency of foraging in these gigantic predators. Here, we performed a morphometric study of rorqual
mandibles using a data set derived from a survey of museum specimens. Across adult specimens of extant
balaenopterids, mandibles range in size from ~1?6 m in length, and at their upper limit they represent the single
largest osteological element of any vertebrate, living or extinct. Our analyses determined that rorqual mandibles
exhibit positive allometry, whereby the relative size of these mandibles becomes greater with increasing body size.
These robust scaling relationships allowed us to predict mandible length for fragmentary remains (e.g. incomplete
and/or fossil specimens), as we demonstrated for two partial mandibles from the latest Miocene of California, USA,
and for mandibles from previously described fossil balaenopterids. Furthermore, we showed the allometry of
mandible length to body size in extant mysticetes, which hints at fundamental developmental constraints in
mysticetes despite their ecomorphological differences in feeding styles. Lastly, we outlined how our findings can be
used to test hypotheses about the antiquity and evolution of lunge feeding. ? 2012 The Linnean Society of
London, Biological Journal of the Linnean Society, 2013, 108, 586?599.
ADDITIONAL KEYWORDS: bone ? Cetacea ? Mysticeti.
INTRODUCTION
Baleen whales (or crown Mysticeti) are the only
known mammalian filter-feeders. Unlike odon-
tocetes, which feed on single prey items, mysticetes
process large quantities of prey suspended in water
using baleen plates, which allows them to filter
large volumes of prey-laden water (Pivorunas, 1979;
Werth, 2000; Goldbogen, 2010). A group of baleen
whales known as rorquals (crown Balaenopteridae),
which include some of the largest vertebrates ever,
exhibit a specialized filter feeding mode called lunge
feeding.*Corresponding author. E-mail: pyensonn@si.edu
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Biological Journal of the Linnean Society, 2013, 108, 586?599. With 6 figures
? 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2013, 108, 586?599586
This feeding mechanism involves the engulfment of
prey-laden water in a single, rapid gulp (Goldbogen,
2010; Pyenson et al., 2012; Fig. 1). During a single
lunge, rorqual mandibles rotate through three
orthogonal axes, which were defined by Lambertsen,
Ulrich & Straley (1995) as follows: delta rotation, or
the depression of mandibles; alpha rotation, or the
inner or outer roll of the mandible along its main axis;
and omega rotation, or right to left yaw of the man-
dible (Fig. 1). At the apogee of the lunge, the overall
gape angle approaches 90? (Brodie, 1993; Brodie,
2001), as a hyper-expandable ventral blubber layer
provides an enhanced capacity for the oropharyngeal
cavity (Orton & Brodie, 1987).
Because rorqual mandibles exhibit significant cur-
vature, their overall rotation dramatically increases
the area of the mouth and the flux of water into
the ventral pouch. The integration of such morpho-
logical data with kinematic data from animal-borne
recording systems has increased our understanding of
the mechanics, hydrodynamics and energetics of this
unusual feeding mechanism (Potvin, Goldbogen &
Shadwick, 2009, 2010; Goldbogen et al., 2011, 2012).
These studies have demonstrated the crucial role of
mandibles in the dynamics of the engulfment process,
although it remains unclear how the dimensions of
these structures vary across the scale of living and
extinct balaenopterids.
Unlike other vertebrates that are capable of simi-
larly large gapes, such as macrostomatan snakes
(Vincent et al., 2006), balaenopterids feed using man-
dibles composed of single bony elements, derived from
the embryonic dentaries (Mead & Fordyce, 2009: 42).
These mandibles are unfused at the distal, mandibu-
lar symphysis, a condition that has persisted in mys-
ticetes since the Oligocene (Fitzgerald, 2012; Pyenson
et al., 2012). Posteriorly, the articular condyles of each
ramus are enveloped by fibrous temporomandibular
joints (Brodie, 2001) that articulate with the glenoid
fossae of the squamosal bones in the skull. These
specialized joints dramatically increase the kinetic
freedom of the skull, and the manner in which they
envelop the entire articular condyle probably accom-
modates shear forces within the joint during major,
rapid excursions of the mandible during a lunge
(Brodie, 2001), much like an intervertebral joint
(Currey, 2002).
Ventrally, the mandibles are connected by muscles
and derived tissues of the floor of the mouth, external
to the oral cavity and throat, including the accordion-
like ventral groove blubber (Pivorunas, 1977; Lam-
bertsen, 1983). Balaenopterid mandibles also exhibit
a prominent, laterally deflected coronoid process,
which serves as an attachment point for the tempo-
ralis muscle (Brodie, 1993). However, the detailed
myology and functional anatomy of the engulf-
ment apparatus remain poorly understood in adult
balaenopterids because of the logistical difficulties in
accessing, manipulating, and conducting experiments
on these taxa. Nonetheless, the mandibles represent
key indicators of engulfment performance, as delim-
iters of the oral cavity, and thus demonstrably have a
bearing on lunge-feeding kinematics and energetics
(Goldbogen et al., 2011).
Balaenopteridae are also abundantly represented
in the fossil record, in marine sedimentary rock
units from the late Miocene through the Pleistocene,
although the taxonomy and systematics of fossil
balaenopterids remain work in progress (Dem?r?,
Berta & McGowen, 2005; Bisconti, 2007a; Bisconti,
2010a). Since the mid-19th century, cetacean systema-
tists described many different extinct mysticete
genera that share general features with living
rorquals, but their phylogenetic relationships remain
ambiguous. These 19th century taxa may in fact
belong to distantly related lineages, although resolv-
ing their systematic position is hindered by non-
comparable elements, inaccessible or lost specimens,
and ambiguous original diagnoses (Bisconti, 2007b).
Extinct balaenopterids described in the late 20th
century, such as Parabalaenoptera bauliensis, are
known from relatively complete skeletal material,
including cranial, mandibular, and postcranial ele-
ments (Dem?r? et al., 2005). Although the taxonomic
membership for many fossil balaenopterids remains
unresolved, phylogenetic analyses have recovered
some fossil taxa as members of crown Balaenopteri-
dae, lending legitimacy to inferences of lunge-feeding
modes in these extinct taxa (Dem?r? et al., 2008).
Figure 1. Engulfment morphology in balaenopterids,
exemplified by a fin whale (Balaenoptera physalus), with
mandible morphology highlighted by a translucent mask.
Mandibles rotate through three axes: delta, alpha, and
omega. Abbreviations: so, sensory organ; VGB, ventral
groove blubber; YSF, Y-shaped fibrocartilage. Art by
C. Buell.
RORQUAL MANDIBLE ALLOMETRY 587
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Such fossil data play important roles in evaluating
hypotheses about the evolution of lunge feeding,
although much of the available morphological data for
balaenopterids (both living and extinct) has not been
analysed in a comparative, phylogenetic context.
Given their fundamental importance as a key
element in lunge feeding, we undertook a comparative
study of balaenopterid mandibles to better understand
their scaling properties. We amassed a data set across
the size range of nearly all living rorqual species by
generating a specimen-based data set that includes
mandibles ranging from ~1 to 6 m in length. We
quantified the dimensions of rorqual mandibles and
used allometric and comparative phylogenetic analy-
ses to assess the scaling of the engulfment apparatus.
We then used our allometric equations to predict
mandible length for fragmentary fossil balaenopterid
mandibles. Furthermore, we compiled a second
specimen-based data set to determine mandible
scaling relationships among all mysticetes. Lastly, we
address the implications of such scaling relationships
for filter feeding in these gigantic cetaceans, as well as
understanding the antiquity, ecomorphology, and evo-
lution of lunge feeding in rorquals.
MATERIAL AND METHODS
COMPARATIVE DATA SET
We constructed two data sets for this study: (1) a
mandibular data set exclusively using museum speci-
mens (regardless of attendant body size data); and
(2) a broader data set, including mandibular meas-
urements and total length (TL) data from museum
specimens. Measurements and museum specimens
are listed in Appendix S1.
For the first data set, we collected data from 34
individual specimens of living balaenopterids, com-
prising six species: Balaenoptera acutorostrata,
Balaenoptera borealis, Balaenoptera edeni/brydei,
Balaenoptera musculus, Balaenoptera physalus, and
Megaptera novaeangliae (see Appendix S1). The
resultant data set thus included the full size range of
extant balaenopterids, including neonatal specimens
of B. acutorostrata. Although we did not sample
Balaenoptera bonaerensis and Balaenoptera omurai
because of their extreme rarity in museum collec-
tions, these size categories were represented by
closely related species (B. acutorostrata and B. edeni/
brydei, respectively). Adult TL for B. bonaerensis is
slightly larger than B. acutorostrata (Konishi et al.,
2008), but the specimens of the former were unavail-
able for study. We also note that we considered the
allometry of B. brydei to effectively represent the
same as B. edeni, despite the phylogenetic status of
these poorly established taxa (Sasaki et al., 2006;
Kato & Perrin, 2009). For the first data set we
restricted one subset of regression analyses to include
subadult to adult (mature) specimens only; another
subset of regression analyses included all mature,
juvenile, and neonatal specimens. Skeletal maturity
for mandibles was largely assessed by the condition of
the bone surface (i.e. smooth in mature individuals),
attendant voucher data, and whether TL was con-
gruent with reported mature values from previous
literature (e.g. Pyenson & Sponberg, 2011). Because
mandibles undergo intramembranous ossification
(Drake, Vogl & Mitchell, 2010), we could not use other
ontogenetic metrics available for balaenopterid oste-
ology (e.g Walsh & Berta, 2011).
For the second data set, we collected data from 59
individual specimens of 11 species of living mysti-
cetes, except for the aforementioned omissions. This
second data set included mandibular length measure-
ments and TL data (Mackintosh & Wheeler, 1929)
that were recorded with the vouchers. Its taxonomic
scope comprises all extant families of mysticetes. As
with the first data set, we restricted the sample to
subadult to adult specimens only.
Collecting morphometric data from osteological col-
lections of large cetaceans presents several logistical
challenges. Large cetaceans are rarely curated in
museum collections with attendant natural history
data (i.e. provenance, condition, sex, and ontogenetic
stage), and the large size of their skeletal remains
(> 6 m in length; > 500 kg in total, dry weight; see
Discussion) make museum voucher specimens diffi-
cult to clean, store, and access for detailed examina-
tion and measurement (True, 1904). Second, extant
balaenopterid diversity is not equally represented
in museum collections, necessitating extensive travel
to collect data from immovable specimens. Lastly, to
generate a sufficient sample size for this study, we
included specimens that lacked attendant size data
(the first data set) as well as those that were collected
from individuals with known TLs (the second data
set). Although such data are relevant for many mor-
phological investigations, TL is inconsistently repre-
sented in the accessioned remains of most cetaceans
stored in natural history collections (see Pyenson &
Sponberg, 2011: 271?272).
MEASUREMENTS
For mandibular measurements (Fig. 2), we reported
curvilinear and chord lengths for right or left mandi-
bles, or, when both were present, we calculated the
mean. Curvilinear lengths (Cu) followed the ventral
margin of the mandibles from their anteromedial
termination near the gnathion, ventral to the sym-
physeal surface, and extending to the posterior apex
of the angular condyle. The keeled ventral margin
588 N. D. PYENSON ET AL.
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along most of the mandibular ramus length provided
a consistent landmark for measuring curvilinear
length, although this measurement is inconsistently
explained in the literature. Chord lengths (Ch) rep-
resent the straight-line distance between the anteri-
ormost and posteriormost points. Because many fossil
balaenopterid mandible specimens are fragmentary,
we used a measurement that is usually preserved on
incomplete, but taxonomically diagnostic mandibular
material. This measurement, termed C?C, was meas-
ured as the linear distance from the articular condyle
to the midpoint of the coronoid process, along the
corpus of the mandible, which Bisconti (2010a, b)
described as the condyle?coronoid distance. Measure-
ments were collected directly from the specimens or,
when necessary, from images digitized with a scale
bar using ImageJ (Rasband, 2012).
INSTITUTIONAL ABBREVIATIONS
CASG, Department of Invertebrate Zoology and
Geology, California Academy of Sciences, San Fran-
cisco, California, USA; CM, Canterbury Museum,
Christchurch, New Zealand; LACM, Natural History
Museum of Los Angeles County, Los Angeles, Califor-
nia, USA; MB, Museum f?r Naturkunde, Berlin,
Germany; SBAER, Inventory of the Soprintendenza
per i Beni Archeologici dell?Emilia Romagna at the
Museo Paleontologico di Salsomaggiore Terme, Italy;
MVZ, University of California Museum of Vertebrate
Zoology, Berkeley, California, USA; UBC, University
of British Columbia Beaty Biodiversity Museum, Van-
couver, British Columbia, Canada; UCMP, University
of California Museum of Paleontology, Berkeley,
California, USA; USNM, Department of Vertebrate
Zoology, National Museum of Natural History, Smith-
sonian Institution, Washington, DC, USA (see Appen-
dix S1 for institutional abbreviations from other
specimens in the data sets).
BIVARIATE LINEAR REGRESSIONS
We regressed the curvilinear and chord lengths
against C?C for our first data set of extant
Figure 2. A, mandible length measurements for CM Ma 608, an adult blue whale (Balaenoptera musculus). Chord length
(Ch), curvilinear length (Cu), and the distance from the coronoid process to the articular condyle (C?C) were either
measured as illustrated, collected from the literature, or measured in ImageJ; see Material and methods for further
description. Photograph by R.E. Fordyce. B, composite photo of a mandible from an adult B. musculus (LACM 72562),
representing the upper size limit in mysticetes (chord length = 5.13 m), versus the mandible of an adult minke whale
(Balaenoptera acutorostrata; MVZ 134463), representing the smallest size of extant rorquals (chord length = 1.02 m).
RORQUAL MANDIBLE ALLOMETRY 589
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balaenopterid mandibular measurements. Right and
left measurements from individual specimens were
averaged and then the data were log-transformed. We
conducted bivariate ordinary least squares (OLS)
lineage regressions (McArdle, 1988) for three versions
of this data set: all specimens; species values (means
for all mature specimens); and independent contrasts
for species values, which used intraspecific means. To
determine differences between correlations of C?C
with Cu and Ch, we compared the slopes of the lines
from both bivariate plots, which was essentially
equivalent to an F-test.
PHYLOGENETIC INDEPENDENT CONTRASTS
In comparative biology, values for taxonomic data are
not independent; instead, they are related to one
another by history, as indicated by phylogenetic
relationships (Garland, Harvey & Ives, 1992; Garland
& Ives, 2000). Phylogenetic comparative methods
provide a robust set of tools to assess how phylogeny
impacts relationships for traits among taxa that are
related to one another by different phylogenetic
hypotheses (i.e. phylogenetic trees). Among various
approaches, we examined correlated trait evolution
in our data sets using phylogenetically independent
contrasts (PICs; Felsenstein, 1985). We calculated
these contrasts using log-transformed data entered
into MESQUITE 2.6 (Maddison & Maddison, 2011)
with the phenotypic diversity analysis program
module (PDTREE), with all branch lengths set to
1.0 (Midford, Garland & Maddison, 2005). Among
the available mysticete phylogenies, we based our
balaenopterid topology (for the first data set) on a
previously published molecular tree (Sasaki et al.,
2005), pruning it to the six balaenopterid species that
we sampled. Recent molecular studies (McGowen,
Spaulding & Gatesy, 2009; Steeman et al., 2009)
reveal congruent relationships among these six
taxa, although not for other unsampled taxa (e.g.
B. omurai) (Marx, 2011). For the second data set,
we used a consensus tree for 11 species of mysticetes,
the structure of which most closely parallels that
of Sasaki et al. (2005: fig. 5). Again, as with the
balaenopterid consensus tree, the mysticete consen-
sus tree places Eschrichtius in a polytomy with other
Balaenopteridae, rendering this clade potentially
paraphyletic; Caperea is sister to this latter polytomy,
with Balaenidae as the basal group. All other subc-
lade relationships are uncontroversial among the 11
species sampled herein. Plots of phylogenetically
correct (OLS) regression and associated confidence
intervals were then mapped onto the original tip data
space (Garland & Ives, 2000).
FOSSIL DATA
We incorporated fossil balaenopterid data into this
study in two ways. First, subsequent to the regression
analyses, we plotted measurements from the com-
plete mandibles belonging to known fossil balaenop-
terids. After a survey of known taxa, we selected
Plesiobalaenoptera quarantellii (SBAER 240505) and
Parabalaenoptera bauliensis (CASG 6660) from the
late Miocene of northern Italy and northern Califor-
nia, respectively. Second, we applied predictive equa-
tions to estimate the size of fragmentary fossil
balaenopterid mandibles not included in the afore-
mentioned data sets. These incomplete specimens
derive from three specimens: the partial mandibles
belonging to ?Megaptera? hubachi (MB.Ma. 28570), a
fossil balaenopterid putatively from the late Miocene
of Chile; and isolated, partial mandibles from two
separate localities of the Purisima Formation, in
central California, USA (Figs 3, 4). The mandibles of
?M.? hubachi are reconstructed with plaster to give the
impression of being complete (Dathe, 1983), although
Bisconti (2010b) clarified that the posterior ~25% are
Figure 3. Examples of partial fossil balaenopterid mandibles. A, UCMP 81001, referred to Balaenopteridae;
B, UCMP 194914, also referred to Balaenopteridae. Note that both specimens are incomplete, lacking anterior or distal
portions. Abbreviations: an, angular process; ar, articular process; cp, coronoid process; mc, mandibular corpus; mf,
mandibular foramen; ptf, pterygoid fovea.
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real, including all of the morphology along the C?C
distance. The first isolated specimen, UCMP 81001,
represents an incomplete, proximal left mandible
(Figs 3A, 4A), which was collected from exposures of
the Purisima Formation along Drakes Beach, in the
Point Reyes National Seashore, Marin County, Cali-
fornia, USA, at UCMP locality V6858 (Barnes, 1976).
The sea cliffs along Drakes Beach preserve sections of
late Neogene marine units that Galloway (1977)
referred to Drakes Bay Formation. Clark et al. (1984)
correlated the upper units of Drakes Bay with litho-
logically similar rocks of the Purisima Formation,
much further south along the San Andreas Fault, in
Santa Cruz County, California (Clark et al., 1984).
Here, we follow their determination in referring to
the sequence of rocks above the basal glauconitic
greensand along Drakes Beach as the Purisima
Formation.
The second specimen, UCMP 194914, represented
by an incomplete right mandible (Figs 3B, 4B), origi-
nates from the Opal Cliffs locality (UCMP locality
V6875), in the city of Santa Cruz, Santa Cruz County,
California, USA. Opal Cliffs is one of many localities
of the Purisima Formation exposed along the sea cliffs
in Santa Cruz (Powell et al., 2007). These sandstone
exposures have produced an abundance of fossil
marine mammal material, although much of it is
incomplete and fragmentary. Based on similar rela-
tionships, lithologies and fossil content between the
Drakes Bay Formation and rock units in San Mateo
County, California, Clark et al. (1984) correlated the
lower greensand unit of the Drakes Bay Formation
with the Santa Margarita Formation in San Mateo
County. Clark et al. (1984) also correlated the overly-
ing mudstone unit with the Santa Cruz Mudstone,
and the uppermost unit with the Purisima Formation.
Although correlating fault-bounded rocks at a
regional level is difficult, Powell and Powell et al.
designated the upper units of Galloway?s (1977)
Drakes Bay Formation as the Purisima Formation
(Powell, 1998; Powell et al., 2007).
RESULTS
ALLOMETRY OF BALAENOPTERID AND
MYSTICETE MANDIBLES
Scaling relationships of total mandible length versus
the distance from the articular condyle to the coronoid
process (C?C) were positively allometric (Fig. 5), as
well as being significantly correlated (P < 0.001;
R2 = 0.97). Overall, C?C decreased with larger man-
dible lengths (slope = 1.23 and 1.24, for both Cu and
Ch lines, respectively), indicating that the position
Figure 4. Comparative morphology of proximal (i.e. posterior) ends of fossil and extant balaenopterid mandibles: from
left to right, lateral, posterior, and lingual views of the proximal mandible. A, UCMP 81001, fossil specimen referred to
Balaenopteridae; B, UCMP 194914, fossil specimen also referred to Balaenopteridae; C, living Balaenoptera acutorostrata,
composite views from the right and left mandibles of MVZ 126873. All specimens are scaled to approximately the same
C?C distance. Abbreviations: an, angular process; ar, articular process; cp, coronoid process; mf, mandibular foramen;
pcf, postcoronoid fossa; ptf, pterygoid fovea.
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of the coronoid process in larger balaenopterids is
located further posteriorly than in smaller balaenop-
terids. We included two metrics of mandible length in
our analysis (Cu and Ch), and we found no statistical
difference between the slopes of their lines. Our
bivariate plots included all specimens (n = 34), as well
as species averages, for the six species assessed
(Fig. 5). To assess the phylogenetic underpinnings of
these scaling relationships, we regressed the PICs of
these bivariate plots, mapped back onto original data
space (Garland & Ives, 2000). In this analysis, both
Cu and Ch exhibited the same scaling relationships,
indicating that phylogeny had no effect on rorqual
mandible scaling (see Appendix S1). For some taxa
(e.g. B. acutorostrata), we included neonatal and juve-
nile specimens within the first data set to evaluate
the role of early ontogeny. Interestingly, the presence
of these specimens did not change the allometric
results presented herein (Fig. 5B, D).
Plotting fossil values for C?C from the fossil speci-
mens reported herein revealed that some fossil
balaenopterids possessed mandible lengths smaller
than the adult mandibles of the smallest extant
balaenopterids in this data set, B. acutorostrata. Fol-
lowing equations from the slope of the line for Ch
versus C?C, using mature specimens, we estimate
that UCMP 81001, 194914, and ?M.? hubachi pos-
sessed complete mandibles that measured approxi-
mately 0.82, 1.23, and 1.45 m, respectively, in chord
distance (see calculations in Appendix S1). The calcu-
lated chord length for ?M.? hubachi is slightly less
than the estimated length of 1.57 m published by
Bisconti (2010b: table 1).
Our second data set examined the relationship
between mandible length (Ch) and TL across nearly
all species of living mysticetes (Fig. 6; Table 1). We
determined that Ch scaled closely with TL (P < 0.001;
R2 = 0.94), and its slope (0.87) deviated from isometry.
Figure 5. Allometric relationships of balaenopterid mandibles using different linear measurements. Chord length (Ch)
versus the distance between the coronoid process and the articular condyle (C?C): (A) mature specimens only; (B) both
immature and mature specimens. Curvilinear length (Cu) versus the distance between the coronoid process and the
articular condyle: (C) mature specimens only; (D) both immature and mature specimens. Black dots represent extant
specimens, and white circles represent extant species means. Dotted and solid lines represent 95% confidence intervals
and slopes, respectively. Grey diamonds represent partial fossils with C?C values, and open, white diamonds represent
complete fossils, both plotted after regressing extant data. See text for statistical results.
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As with the first data set, PICs of this second data
set produced no discernible difference (slope = 0.88;
R2 = 0.94; see Appendix S1), which likewise suggests
that the scaling of mandible length with body size
in living mysticetes is independent of phylogeny (but
see Discussion). Because the inclusion of neonatal
and juvenile specimens in this first data set did
not change the allometric results, we included juve-
nile specimens in this second data set to increase
sampling.
RECONSTRUCTED TOTAL LENGTH FOR
FOSSIL BALAENOPTERIDAE
Conducting a regression analyses on the second data
set allowed us to develop balaenopterid-specific equa-
tions for predicting body size using mandible meas-
urements of museum specimens (see calculations in
Appendix S1 based on balaenopterid Ch and TL data).
Based on its smooth bone surface, we argue that
UCMP 81001 probably represents a subadult to
mature individual, despite its small size (estimated
TL = 3.26 m). We estimate that UCMP 194914
belonged to an individual with a TL of 4.83 m, which
was larger than an adult Caperea, but smaller than
an adult B. acutorostrata (Fig. 6). By contrast, we
estimate TLs of ?M.? hubachi, Parabalaenoptera, and
Plesiobalaenoptera as 5.62, 7.70, and 8.54 m, respec-
tively, which are all specimens based on mature indi-
viduals, and fall within the size range for extant
balaenopterids (Fig. 5).
DIAGNOSIS AND AGES OF FOSSIL BALAENOPTERIDAE
Both partial fossil mandibles reported here are
assigned to Balaenopteridae on the basis of a suite
of morphological features that they share with
extant balaenopterid mandibles, to the exclusion of
other mysticetes. This suite of features includes: an
elevated, finger-like, and laterally deflected coronoid
process (Lambertsen et al., 1995; Bouetel, 2005); a
posteriorly directed and hemispherically shaped
articular condyle that is separated from a compara-
tively smaller, angular process by a pterygoid fovea
(Bisconti, 2010b); and a relatively small, tubular bony
aperture for the mandibular foramen (Zeigler, Chan
& Barnes, 1997; Dem?r? et al., 2005; Steeman, 2007).
Both fossils also have a reduced postcoronoid fossa
(see Bisconti, 2010a: 952, for a discussion), relative
to the elevated crest observed in more basal, fossil
mysticetes, such as Aglaocetus or Pelocetus. Other
non-balaenopterid taxa possess some of these
aforementioned characters, but only balaenopterids
possess the entire suite.
One of the fossils used in the analysis,
UCMP 194914, compares favourably with extant
balaenopterids in the shape and deflection of its coro-
noid process. Also, UCMP 194914 has an articular
condyle that is proportionally larger than its angular
condyle, which has a surface that broadens and is
exposed posterolaterally, and which is separated from
the angular condyle by a clear pterygoid fovea (sensu
Bisconti, 2010b) that rings the posterior end of the
mandible from lateral to medial sides. UCMP 194914
shares strong overall similarities in lateral profile
with the fossil taxa ?M.? hubachi and Plesiobalaenop-
tera, but it is unlike Parabalaenoptera, which has a
Figure 6. Bivariate plot of body size (total length, TL)
against mandible length (chord length, Ch) across living
mysticetes. The solid black line represents the slope of all
data combined, and white circles represent extant species
means. Key: Caperea, gold; Eschrichtius, green; Balaeni-
dae, purple; Balaenopteridae, red. See Appendix S1 for
regression results.
Table 1. Ratio of mandible length (Ch, or chord length) to
body size (TL, or total length) in extant mysticetes, sup-
ported by data from museum specimens in this study
Clade Taxon Ch : TL N
Eschrichtiidae Eschrichtius robustus 0.19 11
Neobalaenidae Caperea marginata 0.19 3
Balaenopteridae Balaenoptera
acutorostrata
0.20 8
Balaenopteridae Balaenoptera edeni 0.22 4
Balaenidae Eubalaena glacialis 0.23 3
Balaenopteridae Balaenoptera musculus 0.23 6
Balaenopteridae Balaenoptera physalus 0.23 4
Balaenopteridae Balaenoptera borealis 0.23 4
Balaenopteridae Megaptera
novaeangliae
0.25 4
Balaenidae Eubalaena japonica 0.28 1
Balaenidae Balaena mysticetus 0.28 9
N, number of specimens per taxon.
RORQUAL MANDIBLE ALLOMETRY 593
? 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2013, 108, 586?599
higher and more gradually sloping anterior margin to
the coronoid process.
Notably, UCMP 81001 has a pterygoid fovea that
extends only from the medial side of the proximal end
of the mandible to the posterior side. In contrast, all
extant balaenopterids (and many putative fossil
balaenopterids) exhibit a clear division between the
articular and angular condyles, with a clear pterygoid
fovea that extends from the lateral surface all the
way to the medial surface. The dorsoventral height
of the coronoid process (from the ventral margin
of the mandibular corpus) is close to the same
height of the angular and articular condyles, which
contrasts with most other extant balaenopterids and
UCMP 194914. Lastly, the aperture of the mandibu-
lar foramen in UCMP 81001 is similar to that of some
fossil balaenopterids, especially Plesiobalaenoptera.
Although UCMP 81001 possesses hallmark balaenop-
terid traits, it probably belonged to an extinct, and
presently unknown, balaenopterid taxon.
Overall, both of these fossils from the Purisima
Formation in California are largely coeval. In Marin
County, K/Ar dates of 7.9 ? 0.3 Mya from a glauconitic
greensand unit down-section from UCMP V6858
(Clark & Brabb, 1997) constrains the age of
UCMP 81001 to the latest Miocene; the top of the
Purisima Formation in Marin County is probably
early Pliocene in age (Galloway, 1977). Similarly, in
Santa Cruz County, Powell et al. (2007) argued that
the consensus of biostratigraphic and geochronologi-
cal evidence indicated a latest Miocene to late
Pliocene age for the Purisima Formation in this area,
and thus for UCMP 194914. Powell et al. (2007) also
indicated that the base of the Purisima Formation
along the sea cliffs of Santa Cruz is geochronologically
constrained by a K/Ar date of 6.9 ? 0.5 Mya (Madrid,
Stuart & Verosub, 1986), which establishes the
maximum age of the Purisima Formation in Santa
Cruz County as latest Miocene. Thus, the fossil
balaenopterid specimens reported herein are latest
Miocene to early Pliocene in age (~6?5 Mya).
DISCUSSION
We undertook this comparative study of balaenop-
terid mandible allometry because mandibles play a
fundamental role in delimiting the size of the oral
cavity in lunge feeding. Our allometric analyses of
simple mandible dimensions, across the size range of
all living rorqual species, demonstrated a strong and
significant scaling relationship among functionally
relevant features (i.e. C?C and Ch). In the first case,
we used the allometric relationships to estimate the
original size of fragmentary fossil balaenopterid man-
dibles. In the second case, we explored how mandibles
in all other mysticetes scale with body size. Below, we
elaborate on the significance of these results, and
expand on key points that hold promise for future
work on the biomechanics and evolution of rorqual
lunge feeding.
MANDIBLE SCALING AND LUNGE-FEEDING
BIOMECHANICS
As an integral component of the craniomandibular
apparatus, mandibles play an important role in
lunge-feeding mechanics. These features include: the
perimeter of the oral cavity and thus engulfment
volume (Goldbogen, Pyenson & Shadwick, 2007; Gold-
bogen, 2010; Goldbogen et al., 2011); the large gape
angles, which rely on a flexible temporomandibular
joint (Brodie, 1993, 2001); and the lateral rotations of
the bowed rami, which can adjust the articulation of
the jaws with the rostrum independently on the right
and left sides (Lillie, 1915; Lambertsen et al., 1995).
Notably, Goldbogen et al. (2007), Goldbogen, Potvin &
Shadwick (2010), Goldbogen et al. (2011), and Potvin
et al. (2009, 2010) used mandible measurements to
model mouth area, and estimate engulfment volume
and engulfment mechanics in different species of
rorquals. However, the specific physical forces at play
during the engulfment process remain poorly under-
stood in an empirical way because of the logistical
and legal barriers in dealing with large marine ver-
tebrates such as rorquals. Although adult rorquals
were the targets of sustained hunting in the early
through to the late 20th century (Reeves & Smith,
2006), our understanding of their basic cranio-
mandibular anatomy is deficient in specifics about
joint articulations and basic morphometrics, which
excludes the possibility of using standard approaches
for analysing feeding biomechanics in marine verte-
brates (Westneat, 2004). These aforementioned chal-
lenges in large part affected our original intention to
record simple measurements of rorqual mandibles,
especially using a data set grounded in vouchered
museum specimens, instead of secondary or tertiary
literature.
Our analyses, with the first data set, demonstrated
that the position of the coronoid process (primary
point of attachment for the temporalis muscle) along
the length of the mandible is relatively closer to the
condyle in larger rorquals (Fig. 5). This finding sug-
gests that mechanical advantage (Currey, 2002),
when closing the mandibles against drag to complete
a single lunge, is also comparatively lower in larger
rorquals. Reduced mechanical advantage, however,
may be ameliorated in larger rorquals because they
exhibit longer time scales during engulfment, and
thus relatively lower peak drag forces (Potvin et al.,
2010). Given the small body sizes of fossil rorquals,
the even higher mechanical advantage of these
594 N. D. PYENSON ET AL.
? 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2013, 108, 586?599
diminutive, extinct balaenopterids may have been
important in the evolution of lunge feeding. Specifi-
cally, it is possible that the earliest form of lunge
feeding, which probably occurred at small body sizes,
involved largely rapid single gulps, a mode that was
later elaborated at larger body sizes with less biome-
chanically advantageous mandibles but for larger and
longer gulps. Future modelling work, using parachute
physics as an analogy (e.g. Potvin et al., 2009, 2010),
may be fruitful in clarifying this possible evolutionary
scenario.
It is important to note that the simple linear meas-
urements used in this analysis vastly oversimplify
the complex morphology of the posterior end of
the rorqual mandible. There are clear morphological
differences between the size extremes observed in
balaenopterids: for example, in lateral view, the coro-
noid process in B. actutorostrata is narrow and spatu-
late (Fig. 4C), whereas it has a broad, sloping base in
B. musculus (Fig. 2A, B). Equally, in medial view, the
margin of the articular condyle in B. acutorostrata
points posterodorsally, whereas the articular condyle
in B. musculus is depressed and nearly extends ven-
trally relative to the corpus of the mandible. These
differences underscore two important needs for future
investigations: (1) more detailed, comparative des-
criptions of the mandibular morphology across all
balaenopterids, including fossil taxa; and (2) clarifi-
cation about the relationship between soft tissue
structures (e.g. insertion of the temporalis and ptery-
goid muscles) and their bony tissue correlates (e.g.
the size and shape of the coronoid process and the
pterygoid fovea), especially for adult balaenopterids.
The latter issue will require broader comparative
studies in osteological collections with sufficient
samples to understand latent variation; the former
issue will require unique opportunities to dissect the
craniomandibular apparatus of these gigantic ceta-
ceans (e.g. see Pyenson et al., 2012).
The near-isometric scaling of mandibles relative to
body size across all mysticetes (Fig. 6) was a surpris-
ing finding, given the disparity among filter-feeding
modes in extant mysticetes (Werth, 2000). Our analy-
ses with the first data set demonstrated that the
inclusion of juvenile (even neonatal) specimens did
not significantly change the allometric slopes of rela-
tionships within Balaenopteridae (see Fig. 5B, D).
This uniformity in scaling indicates that the morpho-
logical bauplan for mandibular scaling is set late
in utero, hinting at the dominant role of developmen-
tal constraint in shaping the functional morphology of
balaenopterids. Our analyses of mandible scaling
relative to body size in all extant mysticete lineages
(Fig. 6), which included juvenile and immature speci-
mens, showed similar slopes, ranging in coefficients
from 0.89?0.95 across family-level groupings (all of
which were significant; see Appendix S1). This latter
finding suggests that the pattern of ontogenetic man-
dibular scaling in balaenopterids may also extend
across all mysticetes, despite different feeding modes.
In turn, these allometric data suggest that scaling
relationships of the feeding apparatus in baleen
whales might have been set at the origin of crown
Mysticeti.
Balaenids had the largest mandibles relative to
body size (Table 1), with the upper limit of the ratio
reaching nearly 0.30, providing much needed quanti-
tative data for the oft-cited claim that balaenids have
an oral cavity that is one-third their body length (e.g.
Lambertsen et al., 1995). However, it is important to
note, in this specimen-based data set, that one species
of balaenid, Eubalaena glacialis (North Atlantic right
whales) had a ratio similar to that of balaenopterids.
This unusual finding is not affected by ontogeny, as
juvenile and adult specimens (LACM 54763 and
USNM 257513, respectively) both had similar ratios
(0.20?0.23; see Appendix S1). Rorquals had ratios
closer to 0.20?0.25, with Megaptera possessing a
ratio of 0.25. Interestingly, B. acutorostrata shared
ratios close to that of Eschrichtius (the sister taxon
to Balaenopteridae) and Caperea, despite divergent
feeding modes and craniomandibular morphologies
(Werth, 2000). These mandibular proportions simplify
far more complex ecomorphological patterns that are
related to the skull (see Goldbogen et al., 2010), and a
deeper understanding of the variation of these fea-
tures in balaenopterids requires coupling mandibular
and skull measurements in future work.
SIZE EXTREMES FOR BONY ELEMENTS
As a single osteological element, the mandibles of the
largest balaenopterids (e.g. B. musculus or blue
whales) are unequivocally the largest single osteologi-
cal element for any vertebrate in the history of life,
an observation that can be attributed to Pivorunas
(1977: 299). No single osteological element from
any other vertebrate, living or extinct, compares
in terms of linear dimensions and weight. Weights
for balaenopterid mandibles derive from industrial
whaling reports, although some reports fail to clarify
the distinction between single dentaries and con-
joined dentaries in a mandible (using more traditional
nomenclature; see Mead & Fordyce, 2009: 42). For
example, Laurie (1933: 403?404) reported ?jaw bones?
of a 20.30-m blue whale weighing 928 kg, whereas
a ?jaw bone? from a 27.18-m blue whale weighed
2117 kg. Nonetheless, these estimated weights
compare favourably with weights recorded for speci-
mens in our data set (e.g. 550 kg dry weight recorded
for the right mandible of UBC 17999). To our knowl-
edge, the largest single specimen represented in
RORQUAL MANDIBLE ALLOMETRY 595
? 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2013, 108, 586?599
extant museum collections are the 6.8-m (in curvilin-
ear length) mandibles of a female B. musculus with a
TL of 28.0 m, collected from the Southern Ocean in
1939 (USNM 268731). Winston (1950: 395) reported a
6.96-m mandible from a 27.13-m female B. musculus
(metric conversions from the source data), although
no voucher material was reported and it is unknown
if any voucher material from this era of Japanese
Antarctic whaling has survived. Because pelagic
industrial whaling in the Southern Ocean decimated
the largest individual B. musculus prior to the 1950s
(Small, 1971), we suspect that USNM 268731 repre-
sents one of the largest examples for the currently
available B. musculus museum specimens anywhere
in the world.
Linear measurements presented herein are unri-
valed by the largest elements from terrestrial
mammals or sauropod dinosaurs, which rank as con-
tenders in this category; individual postcranial ele-
ments do not rank close to this size category, and
cranial and mandibular elements of other candidate
vertebrates are composed of multiple elements. For
example, many extinct marine diapsids (e.g. mosas-
aurs, ichthyosaurs, and pliosaurs) possess mandibles
greater than 1 m in length; and these mandibles are
also composed of multiple individual bones. Despite
the large absolute size of balaenopterid mandibles,
mandibles are not technically long bones, but are
actually flat bones that undergo direct, intramembra-
nous ossification, like other cranial bones (Currey,
2002). It remains an open question as to whether this
kind of developmental pathway promotes the extreme
size growth observed in rorqual mandibles; con-
versely, few authors have identified clear develop-
mental or evolutionary limits that would prevent
mandibles from attaining extreme sizes, with the
obvious exception of their use in (near-) weightless-
ness under water. Nonetheless, we foresee future
allometric analysis focusing on direct comparisons
between rorqual mandibles and traditional long bone
scaling studies (Bertram & Biewener, 1992; Garcia &
da Silva, 2004), as well as their densiometry and
bending mechanics (Field et al., 2010).
PALEOBIOLOGICAL AND COMPARATIVE APPLICATIONS
Many reported fossil balaenopterids are fragmentary
or are represented by undiagnostic material (Dem?r?
et al., 2005; Bisconti, 2007a, b, 2009, 2010a, b).
Indeed, most of the diagnostic balaenopterid fossil
record consists solely of cranial material, which is
rarely associated with corresponding mandibular ele-
ments. In this way, functional inferences about
feeding behaviour are severely limited for extinct
balaenopterids. In contrast, the occurrence of iso-
lated mandibular elements does provide very clear
evidence for ecomorphology and the probable func-
tional aspects of the feeding apparatus (Bisconti &
Varola, 2000, 2006). In this study, we have extended
Bisconti & Varola?s (2000) suggestion for reconstruct-
ing mandible length on a partial, fossil mandible
using extant data. As a result, we have demonstrated
the utility of a strong scaling relationship for estimat-
ing the original length of partial mandibles. Because
mandible length essentially mirrors skull size in mys-
ticetes (Fig. 5; Table 1; and see Goldbogen et al.,
2010), we used the strong correlation between condy-
lobasal length and total length in living balaenop-
terids (see also Pyenson & Sponberg, 2011) as a basis
for estimating the size of extinct balaenopterids rep-
resented by incomplete material.
Interestingly, in adopting our methods for fossil
balaenopterids, we recovered surprisingly comparable
size estimates. Parabalaenoptera, the holotype and
only known specimen of which does not preserve TL,
produces similar results to those of Pyenson & Spon-
berg (2011: table 4), with a calculated TL of 8.54 m
(see Appendix S1) from the measured Ch of the com-
plete right mandible. This value is slightly smaller
than the best estimate of TL (8.85 m) presented by
Pyenson & Sponberg (2011), which used a phyloge-
netically informed equation that included data from
several skull measurements. ?Megaptera? hubachi, a
fossil balaenopterid that does not belong in the genus
Megaptera and probably represents a separate,
extinct genus, is represented by a single specimen
that is almost complete. Dathe (1983: 844) and Bis-
conti (2010b) reported a length of the total skeleton of
6.00 m, which is slightly larger than our estimated
value of 5.63 m. For the partial fossils represented
solely by mandibles, their estimated sizes represented
adult balaenopterids below the lower limit of adult
total length in extant balaenopterids, suggesting that
some of these extinct taxa were smaller than those
alive today.
Previously, Lambertsen et al. (1995) argued that
the acquisition of morphological specializations asso-
ciated with lunge feeding played a key role in the
evolutionary diversification of balaenopterids. Given
the preliminary results presented here for two fossil
balaenopterids, considered alongside other late
Miocene balaenopterids discussed by Dem?r? et al.
(2005) and Bisconti (2010b), we argue that that the
necessary bony specializations were acquired at least
by the late Miocene, and at size ranges below the
threshold for living taxa (Pyenson & Sponberg, 2011).
Moreover, the stratigraphic and geological contexts of
their occurrences provide critical data for informed
conclusions about the antiquity of balaenopterids.
Such work, especially with specimen-based data sets,
should form the basis of future fossil calibrations of
phylogenetic trees, in accordance with the guidelines
596 N. D. PYENSON ET AL.
? 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2013, 108, 586?599
proposed by Parham et al. (2012). Taken together,
these different kinds of data sets for extant and fossil
balaenopterid data will better test potential evolu-
tionary scenarios for the origin of lunge feeding.
CONCLUSIONS
Rorqual whales provide data on the upper limits of
scaling relationships that underpin many fundamen-
tal processes in vertebrate and mammalian physiol-
ogy, ecology, and evolution. Their large size directly
relates to their lunge-feeding performance, a feeding
style that efficiently maximizes their ability to access
dense aggregates of prey. As a single bony element,
rorqual mandibles ultimately constrain the volume of
prey-laden water that rorquals engulf while lunge-
feeding. Here, we demonstrated that rorqual mandi-
bles are positively allometric, where larger whales
exhibited relatively longer mandibles. Such a trend
suggests that relative engulfment capacity increases
with body size, a feeding characteristic that plays a
fundamental role in influencing prey preference, eco-
logical niche, and foraging efficiency. These results
are consistent with previous morphometric and func-
tional analyses across differently sized rorquals that
suggest a set of limiting factors controlling the upper
limit of body size in rorquals. Lastly, the strong
scaling relationships of rorqual mandibles demon-
strated here can be used to estimate the original
length in fragmentary museum specimens, including
those of partial fossil balaenopterid mandibles. The
ability to reconstruct morphometric data for key fossil
taxa, and the integration of those data with extant
taxa into comparative phylogenetic analyses, is para-
mount for understanding the evolution of body size
and specialized feeding modes in baleen whales.
ACKNOWLEDGEMENTS
We thank E. M. G. Fitzgerald, A. Werth, and an
anonymous reviewer for diligent, insightful, and con-
structive comments that improved the quality of this
article. For their assistance with museum collections
under their care, we thank: M. Flannery, B. Simison,
J. DeMouthe, and S. Mansfield (all CAS); S. Stollman
(CM); D. Casper and S. Davenport (both Long Marine
Laboratory); the staff at the Whale Interpretive
Centre, Telegraph Cove, British Columbia; J. Dynes
and D. Janiger (both LACM); C. Conroy (MVZ); A. van
Helden (Te Papa Tongarewa National Museum of
New Zealand); E. M. G. Fitzgerald (Museum Victoria);
K. A. Fahy (Santa Barbara Museum of Natural
History); E. Rickett, W. Maddison, and A. Trites,
(all UBC); P. A. Holroyd (UCMP); C. W. Potter
and J. G. Mead (both USNM); and J. Bradley
(Burke Museum of Natural History and Culture). For
additional logistical support with data collection, we
thank K. Kuker, C. Birdsall, F. Perry, R. E. Fordyce,
D. J. Field, T. A. Dem?r?, and M. deRoos. N.D.P. was
supported by a National Science Foundation Gradu-
ate Research Fellowship, a postdoctoral research
fellowship from the Natural Sciences and Engineer-
ing Research Council of Canada (NSERC), and by
funding from the Smithsonian Institution and its
Remington Kellogg Fund. J.A.G. was supported by a
University Graduate Fellowship for Research from
the University of British Columbia, a Scripps Post-
doctoral Research Fellowship and NSERC funding to
R.E.S.
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SUPPORTING INFORMATION
Additional Supporting Information may be found in the online version of this article:
Appendix S1. Supplemental institutional abbreviations for datasets, supplemental tables, and supplemental
references for morphometric and phylogenetic analyses.
RORQUAL MANDIBLE ALLOMETRY 599
? 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2013, 108, 586?599