Content uploaded by Chris J Law
Author content
All content in this area was uploaded by Chris J Law on Dec 17, 2017
Content may be subject to copyright.
Ontogenetic Scaling of Theoretical Bite Force in
Southern Sea Otters (Enhydra lutris nereis)
Chris J. Law
1,
*
Colleen Young
2
Rita S. Mehta
1
1
Department of Ecology and Evolutionary Biology, University
of California, 100 Shaffer Road, Santa Cruz, California 95060;
2
California Department of Fish and Wildlife, Marine Wildlife
Veterinary Care and Research Center, 1451 Shaffer Road,
Santa Cruz, California 95060
Accepted 6/29/2016; Electronically Published 8/18/2016
ABSTRACT
Sexual dimorphism attributed to niche divergence is often linked
to differentiation between the sexes in both dietary resources and
characters related to feeding and resource procurement. Although
recent studies have indicated that southern sea otters (Enhydra
lutris nereis) exhibit differences in dietary preferences as well as
sexual dimorphism in skull size and shape, whether these inter-
sexual differences translate to differentiation in feeding perfor-
mances between the sexes remains to be investigated. To test the
hypothesis that scaling patterns of bite force, a metric of feeding
performance, differ between the sexes, we calculated theoretical
bite forces for 55 naturally deceased male and female southern
sea otters spanning the size ranges encountered over ontogeny.
We then used standardized major axis regressions to simulta-
neously determine the scaling patterns of theoretical bite forces
and skull components across ontogeny and assess whether these
scaling patterns differed between the sexes. We found that pos-
itive allometric increases in theoretical bite force resulted from
positive allometric increases in physiological cross-sectional area
for the major jaw adductor muscle and mechanical advantage.
Closer examination revealed that allometric increases in tempo-
ralis muscle mass and relative allometric decreases in out-lever
lengths are driving these patterns. In our analysis of sexual di-
morphism, we found that scaling patterns of theoretical bite force
and morphological traits do not differ between the sexes. How-
ever, adult sea otters differed in their absolute bite forces, re-
vealing that adult males exhibited greater bite forces as a result of
their larger sizes. We found intersexual differences in biting ability
that provide some support for the niche divergence hypothesis.
Continued work in this field may link intersexual differences in
feeding functional morphology with foraging ecology to show
how niche divergence has the potential to reinforce sexual di-
morphism in southern sea otters.
Keywords: biomechanics, cranial musculature, durophagy, feed-
ing performance, Mustelidae, niche divergence, sexual dimor-
phism.
Introduction
Dietary specialization by some individuals within the same
population is a prevalent phenomenon that is not well under-
stood (Bolnick et al. 2011). The sex structure of populations
introduces natural variability in morphology and behavior that
may contribute to feeding differences between individuals. While
sexual selection may drive morphological disparity between the
sexes (Darwin 1871; Clutton-Brock 2007), natural selection may
also select for traits that reduce competition for food resources
(Darwin 1871; Hedrick and Temeles 1989; Shine 1989). The latter
hypothesis is known as niche divergence and suggests that sexual
dimorphism is linked to dietary partitioning (Darwin 1871). Sex-
ual dimorphism attributed to niche divergence is often expressed
as differences in cranial size and shape (Darwin 1871; Camilleri
and Shine 1990; Radford and Plessis 2003; Thom and Harring-
ton 2004), which further translates to differences in feeding per-
formances between the sexes (Herrel et al. 1999, 2007; Bulté et al.
2008; McGee and Wainwright 2013; Thomas et al. 2015).
In many vertebrates, biting is the primary mechanism to cap-
ture, kill, and consume prey (Kardong 2014). Bite force, a widely
used measure of feeding performance, has been shown to be
a strong link between cranial morphology and dietary ecology
(Herrel et al. 2007; Anderson et al. 2008; Bulté et al. 2008; San-
tana et al. 2010). Greater bite forces also strongly correlate with
reduced handling times for both prey capture and consumption
(Herrel et al. 2001; Verwaijen et al. 2002; van der Meij and Bout
2006; Anderson et al. 2008). In most cases, individuals with
larger heads exert greater forces and can therefore expand their
dietary breadth by consuming larger or more robust food items
(Verwaijen et al. 2002; Herrel et al. 2006; Bulté et al. 2008).
Therefore, by growth alone, both males and females exhibit in-
creases in bite force that can lead to increased foraging effi-
ciency and net energy intake (Binder and Valkenburgh 2000;
Huber et al. 2006; Pfaller et al. 2011; Marshall et al. 2014).
The ability to generate large forces during feeding is partic-
ularly important for durophagous vertebrates, those that spe-
cialize on hard items such as bones, seeds, or shelled organisms
*Corresponding author; e-mail: cjlaw@ucsc.edu.
Physiological and Biochemical Zoology 89(5):347–363. 2016. q2016 by The
University of Chicago. All rights reserved. 1522-2152/2016/8905-6037$15.00.
DOI: 10.1086/688313
347
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
(Van Valkenburgh 2007; Collar et al. 2014). Unsurprisingly, a
plethora of studies have revealed that bite force in durophagous
species scales with positive allometry relative to body size through
ontogeny (Erickson et al. 2003; Pfaller et al. 2011; Marshall et al.
2012; Kolmann et al. 2015). Ontogenetic increases in bite force
can occur from a disproportionate increase in (1) head size (An-
derson et al. 2008); (2) physiological cross-sectional area (PCSA)
of the jaw adductor muscles, which can be altered by changing
various components of muscle architecture including mass, pen-
nation angle, and muscle fiber lengths (Pfaller et al. 2011; Kol-
mann et al. 2015); (3) mechanical advantage, which can be en-
hanced by shifting muscle insertion points or the bite point
(Grubich 2005; Huber et al. 2008); or (4) any combination of the
aforementioned changes (Hernandez and Motta 1997; Huber
et al. 2006; Kolmann and Huber 2009). Although an increasing
number of studies have examined the differential scaling of head
size, jaw muscle force, mechanical advantage, and their contri-
butions to bite force, few studies have examined these param-
eters in mammals (Santana and Miller 2016). Furthermore, even
fewer studies have investigated whether scaling patterns of bite
force and its underlying components differ between the sexes,
particularly within mammals.
Southern sea otters (Enhydra lutris nereis) are an excellent
mammalian system with which to examine scaling patterns of
bite force and dimorphism in biting ability. These durophagous
marine mustelids feed on a variety of hard-shelled invertebrates
such as chitinous crabs and calcifying bivalves and gastropods
(Riedman and Estes 1990). Like many durophagous mammals,
sea otters exhibit several cranial adaptations that facilitate duro-
phagy including short, blunt skulls (Riley 1985); taller and wider
mandibular rami (Timm-Davis et al. 2015; bunodont dentition
(Fisher 1941; Constantino et al. 2011); and fracture-resistant
dental enamel (Ziscovici et al. 2014). Recent work on adult south-
ern sea otters indicated that although size is the primary axis of
craniomandibular variation, a handful of craniomandibular traits
demonstrated significant shape differences between the sexes (Law
et al., forthcoming). These size-corrected differences in jaw ad-
ductor muscle in-levers, cranial height, and postorbital constric-
tion breadth suggest differences in biting ability between the sexes
for a given body size.
In this study, we tested the hypothesis that the scaling patterns
of muscle dissection–based estimations of bite force and the un-
derlying anatomical components differ between the sexes. To test
our hypothesis, we first investigated the anatomical traits that
contribute to bite force generation in southern sea otters. We
then simultaneously determined the scaling patterns of theo-
retical bite forces and skull components across ontogeny and
assessed whether these scaling patterns differed between the
sexes. Last, we elucidated which of these factors are responsible
for the strong allometric patterns of bite force production.
Methods and Material
Specimens and Gross Dissections
We obtained 55 naturally deceased southern sea otters (24 fe-
males and 31 males; table A1) from the California Department
of Fish and Wildlife (CDFW) Marine Wildlife Veterinary Care
and Research Center from October 2013 to February 2016.
The age class of each specimen was determined using a suite
of morphological characteristics including total body length,
tooth wear, and closure of cranial sutures (table A2; Hatfield
2006). Body mass was also measured for each specimen. All
specimens stranded along the central California coast, within
and throughout the current southern sea otter range (Pigeon
Point in the north to Gaviota in the south).
We dissected the major jaw adductor muscles (superficial
temporalis, deep temporalis, superficial masseter, deep masse-
ter, and zygomaticomandibularis) following Scapino’s(1968)
cranial musculature description of various mustelids including
the northern sea otter (Enhydra lutris kenyoni). While there was
distinct separation between the superficial and deep temporalis,
there was inadequate separation between the superficial masse-
ter, deep masseter, and zygomaticomandibularis muscles (Sca-
pino 1968). Therefore, we treated the three subdivisions as one
muscle, the masseter (fig. 1A). Furthermore, because the medial
pterygoid is positioned deep along the medial side of the man-
dible and cannot be excised intact, we did not include this mus-
cle in our analyses. Muscles were removed from the left side of
the skull, blotted dry, and weighed to the nearest 0.1 g using a
digital scale.
We then measured the length and pennation angle of muscle
fibers by digesting and separating the muscles in a solution of 15%
aqueous nitric acid for 3–7 d depending on muscle size (Biewener
and Full 1992). Muscle fiber lengths were measured to the nearest
0.01 mm using a digital caliper. Skulls were subsequently cleaned
by a dermestid beetle colonyat the California Academy of Sciences
or with a maceration tank at CDFW. We then photographed and
digitally measured the condylobasal length (distance from the an-
teriormost point on the premaxillae to the plane of the posterior
surface of the occipital condyles), zygomatic breadth (greatest dis-
tance across the zygomatic arches), and cranial height (distance
perpendicular to the palate plane from the lateralmost point of the
mastoid process to the point of the sagittal crest directl y superior
to the mastoid process) of each cranium using ImageJ (Schneider
et al. 2012; fig. 1C,1D).
Bite Force Model
Because of its craniostylic characteristics, the mammalian jaw
can be modeled as a static third-class lever where an axis pass-
ing through the temporomandibular joints (TMJs) serves as
the fulcrum and muscle forces generated by jaw adductor
muscle contractions create rotation of the lower jaw about this
fulcrum (Davis et al. 2010). Under static lever equilibrium, the
force of biting balances the rotation of the lower jaw created by
these muscle forces (fig. 1A,1B).
We first calculated PCSA for each muscle based on muscle
mass (m), mean fiber length ( f), muscle density (r), and fiber
pennation angle (v; Sacks and Roy 1982):
PCSA p
m
r
cos½v
f:
348 C. J. Law, C. Young, and R. S. Mehta
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
We used a mammalian muscle density of 1.06 g/cm (Mendez
and Keys 1960). Jaw muscle fibers were parallel; thus, we used a
fiber pennation angle of 07. PCSA of the temporalis muscle was
totaled as a sum of the PCSA calculated for the superficial and
deep temporalis subdivisions and modeled as a single muscle.
To estimate muscle forces of the temporalis and masseter, we
multiplied PCSA by a muscle stress value of 25 N/cm
2
(Herzog
1994), a value that is commonly used in other dissection-based
estimations of bite force (Herrel et al. 2008; Davis et al. 2010;
Santana et al. 2010; Pfaller et al. 2011). We then modeled each
muscle force as a single force vector (F
T
and F
M
) and applied
them to the insertion points of the temporalis, the top of the
coronoid process of the mandible, and the masseter, the mid-
point between the anteriormost edge of the masseteric fossa
and the angular process of the mandible. Our estimation of
muscle forces assumed that all of the jaw muscles were maxi-
mally activated.
We calculated maximum theoretical bite forces (BF
X
)by
adding the moment (product of the force vector and in-lever
length) of each jaw adductor muscle, dividing by the out-lever,
and multiplying by 2 to account for bilateral biting:
BFXp2FT#MAT 1FM#MAM
OX
,
where F
T
and F
M
are the force vectors of the temporalis and
masseter, respectively; MAT is the perpendicular in-lever length
of the temporalis, measured as the perpendicular distance from
the temporalis muscle force vector to the TMJ; MAM is the per-
pendicular in-lever length of the masseter, measured as the per-
pendicular distance from the masseter muscle force vector to the
TMJ; and O
X
is the out-lever length, measured as the distance
between the bite point and the TMJ (Davis et al. 2010). Muscle
force vectors were estimated based on gape angle measured from
the maxillary tip to the condyle to the mandibular tip. Because
data for gape angles were unavailable for all age classes, we es-
timated maximum gape angle based on measurements from os-
teological specimens. We used constant gape angles of 457,557,
607,and627for pups, immatures, subadults, and adults, respec-
tively. Our estimation of adult gape angles is similar to the mean
gape angle range (66.57) obtained from observational studies of
adult sea otter feeding (Timm 2013). We calculated theoretical
bite forces at two locations, the lower canine (BF
C
) and in be-
Figure 1. A, Photograph of the two major jaw adductor muscles of an adult male sea adult. B, Forces of the temporalis and masseter muscles (F
T
and F
M
) are applied at given distances (MAT and MAM) from the fulcrum (triangle),creatingrotationofthelowerjaw.Biteforces,atgiven
distances (O
C
and O
M
), balance these muscle forces. Using the model BF
X
p2[(F
T
#MAT 1F
M
#MAM)/O
X
], theoretical bite forces are
calculated at the canine (BF
C
)andthemolar(BF
M
). C,D, Cranial dimensions used in this study. CBL pcondylobasal length; CH pcranial
height; ZB pzygomatic breadth. A color version of this figure is available online.
Ontogeny of Sea Otter Bite Forces 349
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
tween the first and second molars of the lower jaw (BF
M
). These
two bite points represent important bite positions in prey pro-
cessing for sea otters; biting at the canine is used to pry open
hard-shelled invertebrates such as bivalves, whereas the molars
are used to crush items before consumption (Riedman and Estes
1990). All in-lever and out-lever measurements were taken from
photographs of the lateral view of the mandible in ImageJ v. 1.48
(Schneider et al. 2012).
Statistical Analyses
We performed all statistical analyses in R 3.2.3 (R Core Team
2015). We natural log transformed (ln) all variables to reduce
skewness and heteroscedasticity across values of all variables
and ensure that traits exhibited linear relationships with each
other. To determine which cranial dimension (condylobasal
length, zygomatic breadth, cranial height) and body size met-
ric (body mass, body length) were the best predictors of bite
force, we performed separate sex-specific multiple regression
analyses. In each analysis, we used theoretical bite force as the
dependent variable and cranial dimensions and body size as
the independent variables. Following Baliga and Mehta (2014),
we estimated the R
2
decomposition of each model (Zuber and
Strimmer 2011) by computing correlations between the response
and the Mahalanobis-decorrelated predictors (CAR scores) us-
ing the R package relaimpo (Grömping 2006). Comparing these
scores allowed us to assess the relative importance of each pre-
dictor, enabling us to identify which measurement most strongly
predicted each sex’s ontogenetic bite force trajectory.
We used the R package smatr (Warton et al. 2011) to simul-
taneously (1) examine scaling patterns between/within the body
size, cranial dimensions, theoretical bite forces, and components
of our bite force model and (2) assess whether these scaling pat-
terns differed between the sexes. To examine scaling among body
size and cranial dimensions, we performed standardized major
axis (SMA) regressions with cranial dimensions as dependent
variables, body mass and body length as independent variables,
and sex as the main factor. Similarly, to examine scaling of bite
force generation, we performed SMA regressions with theoret-
ical bite forces, model components (in-levers, out-levers, jaw mus-
cle masses, and muscle fiber lengths), mechanical advantage, and
muscle PCSAs as dependent variables, body size and cranial di-
mensions as the independent variables, and sex as the main fac-
tor. In each independent analysis, we first tested the null hy-
pothesis that the mean SMA regression slopes and elevation did
not significantly differ between the sexes. Because we found non-
significant differences between slopes in all of our analyses (see
“Results”), we pooled the male and female data sets for sub-
sequent scaling analyses. Scaling relationships between all SMA
regression slopes were compared with null predictions of isometry
(linear measurements p1.0; areas and forces p2.0; masses p
3.0), based on Euclidean geometry (Hill 1950; Schmidt-Nielsen
1984; Emerson and Bramble 1993). Using modified t-tests, we
tested whether each slope significantly deviated from isometry
(i.e., allometry). Predicted slopes significantly greater or less than
the 95% confidence intervals of the observed SMA regression
slopes were interpreted as positive or negative allometry, respec-
tively. We adjusted all Pvalues using a Benjamini-Hochberg
correction to reduce the type I error probability across multiple
comparisons (Benjamini and Hochberg 1995). We then ran a
second set of sex-specific multiple regression analyses and cal-
culated CAR scores to assess which component of the bite force
model contributed the most to theoretical bite forces in each sex.
In these analyses, we used theoretical bite force as the dependent
variable and model components (out-levers, in-levers, jaw mus-
cle masses, and jaw fiber length) as the independent variables.
Last, we used ANOVAs to test for sexual size differences of
each trait and theoretical bite force in the adult specimens. We
used only adults because differential dietary specialization be-
tween the sexes has been examined only in adult southern sea
otters. We did not use natural log–transformed values for these
ANOVA tests.
Table 1: Scaling of cranial dimensions against body mass and body length
Sex effects
Scaling relationships
Intercept PR
2
Slope (95% CI) P
Isometric
prediction
Scaling
patterns
A. Cranial dimensions against BM:
CBL F 4.35, M 4.35 .679 .89 .17 (.15–.19) !.001 .33 NA
ZB F 4.02, M 4.05 .959 .9 .18 (.17–.20) !.001 .33 NA
CH F 3.81, M 3.74 .929 .65 .12 (.09–.13) !.001 .33 NA
B. Cranial dimensions against BL:
CBL F 2.48, M 2.57 .051 .91 .53 (.49–.58) !.001 1NA
ZB F 1.86, M 2.11 .195 .91 .57 (.52–.63) !.001 1NA
CH F 2.72, M 2.43 .621 .57 .36 (.30–.42) !.001 1NA
Note. Cranial dimensions served as dependent variables, while body mass (BM; pt. A) and body length (BL; pt. B) served as independent variables. Pvalues
from tests of sex effects reflect differences in elevation between the sexes, and Pvalues from tests of isometry reflect differences from isometric predictions. All P
values are reported as Benjamini-Hochberg-corrected values. Bold Pvalues indicate significance (ap0.05). See table A3 for tests in difference of slopes. CI p
confidence interval. For scaling patterns, NA pnegative allometry. CBL pcondylobasal length; CH pcranial height; F pfemale; M pmale; ZB pzygomatic
breadth.
350 C. J. Law, C. Young, and R. S. Mehta
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
Results
Mean slopes between the sexes were not significantly different
in all SMA analyses (table A3), indicating that scaling patterns
of cranial morphology and biting ability do not differ between
females and males.
Scaling of Cranial Morphometrics
Condylobasal length, zygomatic breadth, and cranial height all
scaled with negative allometry relative to body mass and body
length (table 1; fig. 2A). Among cranial traits, zygomatic breadth
scaled isometrically to condylobasal length (bp1, Pp0.153),
whereas cranial height scaled with negative allometry (b!1, P!
0.001). These trends were observed in both males and females.
Scaling of Biting Biomechanics
Theoretical bite force at the canine and molar showed positive
allometric relationships with body and cranial dimensions (ta-
ble 2; fig. 2B,2C). CAR scores indicated that ln condylobasal
length and ln body mass were the greatest head and body pre-
dictors of theoretical bite force in both sexes (table 3).
All bite force model components, mechanical advantage at
the canine, and muscle PCSA displayed positive allometry relative
to ln condylobasal length (all P≤0.001–0.012; table 4; figs. 3, 4).
However, we found no relationship between ln condylobasal
length and mechanical advantage at the molar for both jaw mus-
cles (table 4).
Conversely, disparate scaling patterns emerged when we ex-
amined the ontogeny of the bite force model components against
ln body mass (table A4, pt. A). Ln lengths of the out-levers and
temporalis in-lever scaled with negative allometry relative to ln
body mass (b!0.33, P≤0.001–0.041), whereas ln masseter in-
lever length scaled isometrically (bp0.33, Pp0.408). Masses
of the jaw adductor muscles also differed in allometric scaling:
ln temporalis mass scaled with positive allometry relative to ln
body mass (b11, Pp0.041), and ln masseter mass scaled with
negative allometry relative to ln body mass (b!1, Pp0.047).
Last, ln fiber lengths for both jaw adductor muscles scaled iso-
metrically relative to ln body mass (bp0.33, Pp0.183–0.578).
Examination of mechanical advantage and PCSA against ln
body mass also revealed disparate scaling patterns (table A4,
pt. B, C). Ln temporalis and masseter mechanical advantage at
the canine scaled with positive allometry (b10, both P!0.001;
table A4, pt. B). In contrast, there was no significant relationship
between ln body mass and ln mechanical advantage at the mo-
lar for both jaw muscles (R
2
p0.00–0.10, Pp0.067–0.561).
Overall ln PCSA of the temporalis and of the masseter scaled
with positive allometry (b10.67, P!0.001) and isometry (bp
0.67, Pp0.198), respectively (table A4, pt. C).
Figure 2. Scaling of condylobasal length (CBL) on body mass (BM)
for female and male southern sea otters (A), bite force at the molar
(BF
M
) on condylobasal length (B), and bite force at the molar on body
mass (C). Circles indicate female otters, and triangles indicate male
otters. Dark gray and light gray solid lines represent standardized
major axis regressions for females and males, respectively. Dotted
lines indicate line of isometry. An asterisk indicates that the slope is
significantly different from isometry. See tables 1, 2, and A3 for more
details. A color version of this figure is available online.
Ontogeny of Sea Otter Bite Forces 351
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
CAR scores revealed that out of the seven components in
ourbiteforcemodel,thetemporalismusclemasswasthegreat-
est contributor to theoretical bite force in both sexes (table 5). A
second CAR score analysis also found that temporalis muscle
mass contributed to the bite force model more than mechanical
advantage (table A5).
Effects of Sexual Dimorphism on the
Ontogeny of Biting Biomechanics
Mean slopes between the sexes were not significantly different
in all SMA analyses (table A3). In addition, we did not find sig-
nificant elevation effects between the sexes in our SMA regres-
sions of cranial dimensions against body size metrics (table 1;
fig. 2A) or theoretical bite forces against body size and cranial
dimensions (table 2; fig. 2B,2C). However, SMA regressions of
the bite force model components against body mass and con-
dylobasal length revealed significant elevation effects in some
model components (tables 4, A4; fig. 4). These analyses sug-
gested that for a given condylobasal length or body mass, female
sea otters exhibit relatively longer temporalis and masseter in-
levers but shorter molar out-levers (tables 4A, A4, pt. A; fig. 4).
In addition, overall temporalis and masseter mechanical advan-
tage to the canine was relatively higher in females than in males
(tables 4, pt. B; A3).
Adult Characteristics
Males were significantly larger than females for absolute values
of body size and cranial dimensions (Pp0.001–0.013; table 6).
Table 2: Scaling of estimated bite forces against body and cranial dimensions
Sex effects
Scaling relationships
Intercept PR
2
Slope (95% CI) P
Isometric
prediction
Scaling
pattern
A. BF
C
against body and
cranial dimensions:
BM F 3.03, M 2.71 .996 .88 .92 (.84–1.01) !.001 .67 PA
BL F 26.40, M 27.62 .297 .88 2.89 (2.63–3.18) !.001 2PA
CBL F 218.90, M 222.49 .621 .9 5.47 (5.02–5.96) !.001 2PA
ZB F 214.54, M 218.87 .959 .9 4.98 (4.56–5.44) !.001 2PA
CH F 229.85, M 226.69 .929 .61 8.06 (6.79–9.57) !.001 2PA
B. BF
M
against body and
cranial dimensions:
BM F 3.77, M 3.55 .831 .89 .86 (.78–.95) !.001 .67 PA
BL F 25.15, M 25.94 .130 .87 2.61 (2.33–2.91) !.001 2PA
CBL F 216.97, M 219.61 .929 .89 5.12 (4.368–5.59) !.001 2PA
ZB F 212.85, M 216.29 .929 .89 4.66 (4.25–5.11) !.001 2PA
CH F 227.33, M 223.48 .996 .62 7.46 (6.30–8.84) !.001 2PA
Note. Bite force at the canine (BF
C
; pt. A) and molar (BF
M
; pt. B) served as dependent variables, while body and cranial dimensions served as independent
variables. Pvalues from tests of sex effect reflect differences in elevation between the sexes, and Pvalues from tests of isometry reflect differences from isometric
predictions. All Pvalues are reported as Benjamini-Hochberg-corrected values. Bold Pvalues indicate significance (ap0.05). See table A3 for tests in difference of
slopes. For scaling patterns, PA ppositive allometry. BM pbody mass; BL pbody length; CBL pcondylobasal length; CH pcranial height; F pfemale; M p
male; ZB pzygomatic breadth.
Table 3: Multiple regression analyses of morphological predictors of estimated bite force
CAR scores for BF
C
BM BL CBL ZB CH Adjusted R
2
Fratio df P
Female .301 .260 .217 .143 .026 .93 54.32 5, 25 !.001
Male .283 .147 .296 .119 .097 .93 55.75 5, 18 !.001
CAR scores for BF
M
BM BL CBL ZB CH
Female .299 .273 .212 .132 .021 .92 44.5 5, 25 !.001
Male .281 .160 .276 .108 .110 .92 48.41 5, 18 !.001
Note. Bold correlation-adjusted correlation (CAR) scores represent the best body and cranial predictors of estimated bite force at the canine (BF
C
)andatthe
molar (BF
M
). Bold Pvalues indicate significance (ap0.05). BM pbody mass; BL pbody length; CBL pcondylobasal length; CH pcranial height; ZB p
zygomatic breadth.
352 C. J. Law, C. Young, and R. S. Mehta
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
Males also exhibited significantly greater theoretical bite forces
(P!0.001) and larger jaw adductor muscle masses (P!0.001).
Despite differences in bite force, we found no significant size
differences in out-lever lengths, in-lever lengths, mechanical ad-
vantage, and muscle fiber lengths (Pp0.053–0.766; table 6).
Discussion
Scaling of Craniomuscular Traits and Bite Force
Our study focused on measurements of body size (body mass
and length), cranial measurements, and muscular traits (tem-
poralis and master mass, fiber lengths, pennation angle, and
insertion points) to understand scaling patterns in male and
female southern sea otters. Our bite force model relied on the
derivations of these measurements and other variables such as
muscle tissue density, peak muscle stress, and gape angle for
which values were taken from the literature and not directly
measured.
The negative allometric relationship between body mass and
condylobasal length suggests that sea otters have shorter heads in
relation to their body. While this pattern is intuitive, closer
examination of the scaling patterns of out-lever lengths indicates
that shorter jaws may also contribute to allometric increases in
theoretical bite force. The out-levers exhibit less of a positive
allometric relationship compared to all the components of the
bite force model. Furthermore, this allometric pattern reverses
when examining the scaling relationship between out-levers
and body mass; out-lever lengths are highly negatively allo-
metric compared to all other bite force model components.
Thus, these patterns strongly suggest that bite force may be
partly driven by the disproportionate decreases in out-lever
lengths. Theoretical bite force in southern sea otters scaled
with positive allometry relative to cranial dimensions and body
size through ontogeny. Studies across a broad range of taxa dem-
onstrate that allometric increases in bite force can be attributed
to allometric increase in PCSA of the jaw muscles (Pfaller et al.
2011; Kolmann et al. 2015), mechanical advantage (Grubich
2005; Huber et al. 2008), or a combination of both (Hernandez
and Motta 1997; Huber et al. 2006; Kolmann and Huber 2009).
In turn, allometric increases in PCSA and mechanical advan-
tage can be achieved by changes in the underlying components:
Table 4: Scaling of bite force model components (pt. A), mechanical advantage (pt. B), and physiological cross-sectional area
against condylobasal length (CBL; pt. C)
Sex effects
Scaling relationships
Intercept PR
2
Slope (95% CI) P
Isometric
prediction
Scaling
patterns
A. BF components
against CBL:
O
C
F23.75, M 23.21 .057 .94 1.09 (1.02–1.16) .012 1PA
O
M
F26.37, M 26.47 .000 .93 1.58 (1.45–1.72) !.001 1PA
MAT F 28.14, M 27.59 .000 .89 1.74 (1.59–1.91) !.001 1PA
MAM F 28.09, M 29.39 .000 .67 1.87 (1.59–2.18) !.001 1PA
m
TEM
F225.89, M 230.85 .959 .92 6.81 (6.31–7.36) !.001 3PA
m
MAS
F222.18, M 225.36 .228 .88 5.33 (4.83–5.86) !.001 3PA
f
TEM
F210.10, M 28.85 .610 .64 2.15 (1.83–2.54) !.001 1PA
f
MAS
F28.65, M 28.15 .056 .4 1.83 (1.48–2.26) !.001 1PA
B. MA against CBL:
temMA
C
F24.93, M 24.98 .002 .56 .77 (.64–.92) !.001 0PA
temMA
M
NS
masMA
C
F26.40, M 27.33 .000 .17 1.05 (.79–1.39) !.001 0PA
masMA
M
NS
C. PCSA against CBL:
PCSA
TEM
F220.13, M 223.58 .996 .89 5.11 (4.66–5.60) !.001 2PA
PCSA
MAS
F222.18, M 225.36 .228 .88 5.35 (4.84–5.86) .001 2PA
Note. Bite force (BF) components, mechanical advantage, and physiological cross-sectional area (PCSA) served as dependent variables, while body mass served
as the independent variable. Pvalues from tests of sex effect reflect differences in elevation between the sexes, and Pvalues from tests of isometry reflect
differences from isometric predictions. All Pvalues are reported as Benjamini-Hochberg-corrected values. Bold Pvalues indicate significance (ap0.05). NS p
nonsignificant relationship (R
2
p0.00–0.08, Pp0.067–0.680). See table A3 for tests in difference of slopes. For scaling patterns, I pisometry, PA ppositive
allometry, and NA pnegative allometry. f
MAS
pmasseter fiber length; f
TEM
ptemporalis fiber length; M pmale; m
MAS
pmasseter mass; m
TEM
ptemporalis
mass; MAM pmasseter in-lever; MAT ptemporalis in-lever; masMA
C
pmasseter mechanical advantage to the canine; masMA
M
pmasseter mechanical
advantage to the molar; O
C
pout-lever to canine; O
M
pout-lever to molar; PCSA
MAS
pphysiological cross-sectional area of masseter; PCSA
TEM
p
physiological cross-sectional area of temporalis; temMA
C
ptemporalis mechanical advantage to the canine; temMA
M
ptemporalis mechanical advantage to the
molar.
Ontogeny of Sea Otter Bite Forces 353
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
scaling patterns in muscle PCSA can be altered by changes in
jaw muscle mass, muscle fiber lengths, and/or pennation angle
(Pfaller et al. 2011; Kolmann et al. 2015), and scaling patterns of
mechanical advantage can be altered by changes in in-lever and
out-lever lengths (Grubich 2005; Huber et al. 2008). In sea
otters, we found that positive allometry of theoretical bite force
is the product of allometric increases in both muscle PCSA and
mechanical advantage relative to condylobasal length. Exam-
ination of the bite force model components revealed that out-
lever lengths, in-lever lengths, jaw muscle masses, and jaw muscle
fiber lengths all scaled with positive allometry with respect to
condylobasal length, suggesting that all these components con-
tribute to the allometric increase in bite force. Nevertheless, CAR
scores show that temporalis mass is the most important con-
tributor to bite force estimation, indicating that ontogenetic
changesintemporalismasscontributedmorestronglytothe
ontogenetic patterns in bite force than did lever lengths or
muscle fiber lengths. This is corroborated by the fact that tem-
poralis mass was the only model component to exhibit strong
positive allometry relative to body mass, suggesting that the
disproportionate increase in theoretical bite force with respect to
body mass is driven by the disproportionate increase in tem-
poralis mass.
Our finding that the temporalis mass is the most important
contributor to theoretical bite force is not surprising. It is well
documented that the temporalis is the dominant jaw adductor
muscle in carnivores (Scapino 1968; Turnbull 1970). In mus-
telids, the temporalis (deep and superficial) can comprise up
to 80% of the jaw adductor mass (Turnbull 1970; Riley 1985;
Timm 2013; Davis 2014). Large temporalis muscles are used to
generate the high bite forces at large gape angles necessary to
capture and kill prey (Turnbull 1970). In addition, the tem-
poralis helps to resist dislocation of the condyle during force-
ful posterior biting (Maynard Smith and Savage 1959). In the
durophagous southern sea otter, hard-shelled prey are often
crushed with molars (carnassial position) where bite forces are
greatest. Therefore, large temporalis muscles are essential in
generating the high bite forces at large gape angles that are nec-
essary to break open these heavily armored invertebrate prey
(Timm 2013).
Patterns of Sexual Dimorphism
Our data indicated that adult males exhibited significantly larger
cranial dimensions, bigger jaw musculature, and greater theoret-
ical bite forces than adult females. Our finding of larger cranial
traits is consistent with previous findings (Scheffer 1951; Roest
1985; Wilson et al. 1991; Law et al., forthcoming). Sexual se-
lection may drive male sea otters to have greater biting ability
than females, as they use that ability to fight with other males to
defend territories (Garshelis et al. 1984) and for copulating with
females, during which they grasp a female’s nose with their teeth
(Fisher 1939). However, a difference in absolute theoretical bite
force between the sexes also is consistent with the niche di-
vergence hypothesis, which suggests that intersexual differences
in traits related to feeding are linked to dietary partitioning
between the sexes (Darwin 1871; Hedrick and Temeles 1989;
Shine 1989). Law et al. (forthcoming) attributed the morpho-
logical differences in the sea otter feeding apparatus as an in-
dication of niche divergence, which also aids in the maintenance
of sexual dimorphism. Southern sea otter foraging and habitat
use patterns may corroborate the niche divergence hypothesis.
Male sea otters utilize larger home ranges than females (Smith
et al. 2015) and often are the first to explore and occupy new
areas (Garshelis et al. 1984), facilitating range expansion. In ad-
dition, sea otter foraging studies in California have indicated a
strong pattern of dietary specialization (Estes et al. 2003; Tinker
et al. 2007), particularly in food-limited areas (Tinker et al.
2008), with females showing a greater degree of specialization
(Smith et al. 2015). Generalists are typically better equipped to
use a broader array of habitats and prey types (Bolnick et al.
2007; Darimont et al. 2009).Therefore, in southern sea otters,
greater biting ability may benefit males as they move through
and establish new territories, which may host larger or novel
prey items that require greater bite force to obtain, whereas
female sea otter prey diversity is constrained by their relatively
small home ranges and their tendency to specialize on a few
prey items. This difference may allow male sea otters to take
advantage of different foraging opportunities than females and
may be explained by the niche divergence hypothesis.
In contrast, when the morphological and functional traits are
size corrected with either condylobasal length or body mass, we
found that ontogenetic scaling patterns of cranial dimensions
and theoretical bite forces do not significantly differ between the
sexes, suggesting that for a given condylobasal length or body
Figure 3. Scaling of temporalis (m
TEM
) and masseter (m
MAS
)muscle
masses on condylobasal length (CBL). Circles indicate female otters,
and triangles indicate male otters. Dark gray and light gray solid lines
represent standardized major axis regressions for females and males,
respectively. Dotted lines indicate line of isometry. An asterisk in-
dicates that the slope is significantly different from isometry. See ta-
ble 4 for more details. A color version of this figure is available online.
354 C. J. Law, C. Young, and R. S. Mehta
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
mass, males and females do not differ in cranial features related
to biting or theoretical bite force. Similarly, the majority of the
muscular components of our model exhibited no significant dif-
ferences between the sexes when corrected for size. These results
indicate that male southern sea otters exhibit greater theoretical
bite forces because of their larger crania and greater jaw muscle
sizes rather than differences in scaling patterns.
Despite not finding size-corrected differences in theoretical
bite force between the sexes, we observed size-corrected differ-
ences in the mechanical advantage at the canine, with females
exhibiting relatively higher mechanical advantage compared to
males. These differences in jaw mechanics can be traced back to
relative differences in lever lengths between the sexes; females
exhibited relatively longer in-levers for both the temporalis and
masseter muscles, whereas females and males did not exhibit
relatively different canine out-lever lengths. Intersexual differ-
ences in size-corrected in-lever lengths but not size-corrected
out-lever lengths are consistent with recent work based on linear
measurements of 112 adult southern sea otter skulls (Law et al.,
forthcoming). Because higher mechanical advantage is typically
associated with increased force-modified jaws (Kardong 2014),
it is surprising that females exhibited relatively higher mechani-
cal advantage than males yet did not exhibit relatively higher
theoretical bite forces. A possible explanation for this observed
pattern is the role of temporalis muscle mass—a trait that did
not exhibit size-controlled intersexual differences—in biting
performance. As the greatest contributor to bite force, temporalis
muscle mass may have simply masked the signal of intersexual
Figure 4. Scaling of out-levers and in-levers on condylobasal length. Circles indicate female otters, and triangles indicate male otters. Dark gray
and light gray solid lines represent standardized major axis regressions for females and males, respectively. Dotted lines indicate line of
isometry. An asterisk indicates that the slope is significantly different from isometry. See table 4 for more details. A color version of this figure
is available online.
Ontogeny of Sea Otter Bite Forces 355
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
differences from mechanical advantage in our overall estimation
of bite force.
Modeling Biting Ability
Our study is one of the few ontogenetic scaling studies ex-
amining the underlying muscular and skeletal components
that contribute to biting ability in a single mammalian species.
While the focus of our article is on the ontogenetic pattern of
bite force development, our model came with two caveats.
First,wewereunabletoempiricallytestourbiteforcemodel
with measured bite forces from live sea otters. Southern sea
otters are protected under the US Marine Mammal Protection
Act as well as the US Endangered Species Act, making in vivo
Table 5: Multiple regression analyses of model components that contribute to estimated bite force
CAR scores for BF
C
components
O
C
MAT MAM m
TEM
m
MAS
f
TEM
f
MAS
Adjusted R
2
Fratio df P
Female .084 .209 .073 .392 .210 .000 .032 1 79,730 7, 16 !.001
Male .117 .168 .109 .349 .179 .035 .042 .99 50,240 7, 23 !.001
CAR scores for BF
M
components
O
M
MAT MAM m
TEM
m
MAS
f
TEM
f
MAS
Female .095 .210 .090 .359 .205 .000 .040 1 47,000 7, 13 !.001
Male .111 .184 .103 .351 .193 .027 .032 .99 36,140 7, 15 !.001
Note. Correlation-adjusted correlation (CAR) scores representing relative contribution of model components to estimated bite force at the canine (BF
C
)andat
the molar (BF
M
). Bold CAR scores represent the best model component predictor. Bold Pvalues indicate significance (ap0.05). f
MAS
pmasseter fiber length;
f
TEM
ptemporalis fiber length; m
TEM
ptemporalis mass; m
MAS
pmasseter mass; MAM pmasseter in-lever; MAT ptemporalis in-lever; O
C
pout-lever to
canine; O
M
pout-lever to molar.
Table 6: Summary statistics for raw morphological and estimated bite-force data and results of ANOVAs
to assess sexual differences in each craniodental trait
Traits
Adult females
(np7; mean 5SE)
Adult males
(np12; mean 5SE) F
1, 17
P
BM (kg) 17.09 51.07 24.75 51.31 15.0901 .002
BL (cm) 89.17 5.99 97.27 5.96 28.9562 !.001
CBL (cm) 123.70 5.83 130.97 5.97 24.3057 !.001
ZB (cm) 96.75 5.63 101.79 51.00 11.9562 .004
CH (cm) 59.30 5.63 62.60 5.63 11.2042 .005
BF
C
(N) 227.73 56.40 318.53 512.04 27.465 !.001
BF
M
(N) 420.48 511.70 582.16 519.12 33.7689 !.001
O
C
(cm) 7.77 5.11 8.11 5.07 8.2809 .013
O
M
(cm) 4.21 5.07 4.43 5.06 4.9634 .053
MAT (cm) 3.13 5.05 3.21 5.06 .848 .452
MAM (cm) 2.19 5.07 2.33 5.05 2.7134 .158
temMA
C
.40 5.00 .40 5.01 .7653 .455
temMA
M
.74 5.01 .73 5.01 1.9873 .225
masMA
C
.28 5.01 .29 5.01 .2967 .653
masMA
M
.52 5.01 .53 5.01 .1195 .766
m
TEM
(g) 37.32 51.03 60.64 53.05 29.4098 !.001
m
MAS
(g) 8.15 5.34 10.93 5.37 23.3904 !.001
f
TEM
(cm) 4.18 5.05 4.75 5.13 9.295 .010
f
MAS
(cm) 3.34 5.10 3.40 5.12 .0909 .766
PCSA
TEM
(cm
2
)8.425.21 12.00 5.45 31.5618 !.001
PCSA
MAS
(cm
2
)2.315.10 3.07 5.11 21.4458 !.001
Note. All Pvalues are reported as Benjamini-Hochberg-corrected values. Bold Pvalues indicate significance (ap0.05). BF
C
pbite force at
canine; BF
M
pbite force at molar; BL pbody length; BM pbody mass; CBL pcondylobasal length; CH pcranial height; f
MAS
pmasseter
fiber length; f
TEM
ptemporalis fiber length; m
MAS
pmasseter mass; m
TEM
ptemporalis mass; MAM pmasseter in-lever; MAT ptemporalis
in-lever; O
C
pout-lever to canine; O
M
pout-lever to molar; PCSA
MAS
pphysiological cross-sectional area of masseter; PCSA
TEM
pphysiological
cross-sectional area of temporalis; temMA
C
ptemporalis mechanical advantage to the canine; temMA
M
ptemporalis mechanical advantage to the
masseter; ZB pzygomatic breadth.
356 C. J. Law, C. Young, and R. S. Mehta
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
studies challenging. Regardless, in vivo studies would be in-
valuable in providing cranial and bite force measurements
needed to validate our model. However, we found that our
theoretical bite forces of just the adult specimens (mean adult
BF
C
p270.4 N; mean adult BF
M
p482.2 N) are comparable
to theoretical bite forces using the dry skull method (mean
BF
C
p281.0 N; mean BF
M
p394.2 N), which uses photo-
graphs of dorsoposterior and ventral views of the cranium to
estimate muscle cross-sectional area (Christiansen and Wroe
2007). In addition, our estimations of adult temporalis muscle
force (310.7 N) and mass (52.6 g) and adult masseter muscle
force (84.3 N) and mass (10.0 g) were similar to muscle force
estimations in Alaskan sea otters (temporalis force, 313.0 N;
temporalis mass, 53.6 g; and masseter force, 59.4 N; masseter
mass, 7.9 g; Timm 2013). Despite our lack of in vivo bite forces,
our study primarily focuses on the ontogenetic scaling of bite
force generation rather than absolute values.
Second, our model does not account the force generated by
the medial pterygoid, which can contribute to biting ability.
However, the medial pterygoid is greatly reduced in mustelids,
making up approximately 3.3% of the jaw adductor muscle
volume in Alaskan sea otters (Enhydra lutris kenyoni;Timm
2013), 4% in ferrets (Mustela putorius furo; Davis 2014), and
4.2% in Eurasian otters (Lutra lutra; Turnbull 1970). Because
of its relatively small size, the medial pterygoid is a weak
adductor and more likely serves in stabilizing the jaws during
biting in mustelids (Davis 2014). Estimation of medial pter-
ygoid force generation (19.5 N) accounted for just 4.9% of
total jaw muscle force generation in Alaskan sea otters (Timm
2013). Therefore, the medial pterygoid is unlikely to signifi-
cantly contribute to biting ability.
Conclusion
We found that in southern sea otters, allometric increases of
PCSA for the major jaw adductor muscle and mechanical
advantage underlie the pattern of positive allometry for the-
oretical bite force. Although all the components of our model
scaled with positive allometry relative to condylobasal length,
CAR scores indicated that temporalis muscle mass was the
greatest contributor to theoretical bite force. This is corrob-
orated by the fact that temporalis mass was the only model
component out of eight variables to exhibit positive allometry
relative to body mass. Alternatively, allometric decreases in
out-lever lengths also contribute to allometric increases in
theoretical bite force. In our analysis of sexual dimorphism, we
found no differences in scaling patterns of bite force and mor-
phological traits between the sexesthrough ontogeny.Although we
did not find size-corrected differences in theoretical bite forces,
muscle PCSA, and the majority of cranial traits between the
sexes, we found that for a given condylobasal length or body
mass, female sea otters exhibit relatively longer temporalis and
masseter in-levers but shorter molar out-levers. We postulate
that as the greatest contributor to theoretical bite force, tem-
poralis muscle mass may have masked the signal of sex effects
from lever lengths in our overall estimation of bite force. In
adults, we found that adult male sea otters can generate greater
bite forces than adult female sea otters, and these intersexual
differences are a result of differences in overall size (in which
males are larger) rather than differences in scaling patterns. Our
results demonstrating a difference in absolute theoretical bite
force between the sexes are consistent with the niche divergence
hypothesis. Nevertheless, additional field studies in sea otter
foraging ecology will further validate the role of the niche
divergence hypothesis in the maintenance of sexual dimor-
phism in sea otters.
Acknowledgments
We are grateful to Erin Dodd (California Department of Fish
and Wildlife [CDFW]), Francesca Batac (CDFW), and Sue
Pemberton (California Academy of Sciences) for helping clean
out the skulls; Lilian Carswell (US Fish and Wildlife Service)
for permitting logistics; Tim Tinker (US Geological Survey)
for helpful discussions on sea otter life history; Sharlene San-
tana (University of Washington) for providing PDFs of rare
references; and Vikram Baliga (University of California–Santa
Cruz) for guidance with the statistical analyses. We also thank
Vikram Baliga, Ben Higgins, Jacob Harrison, and two anony-
mous reviewers for helpful comments and discussions on var-
ious versions of this manuscript. Funding was provided partly
by a Grant-in-Aid of Research from the American Society of
Mammalogists, a Lerner-Gray Fund through the American Mu-
seum of Natural History, a Rebecca and Steve Sooy Graduate
Research Fellowship for Marine Mammals, and a National Sci-
ence Foundation Graduate Research Fellowship (all awarded to
C.J.L.).
Ontogeny of Sea Otter Bite Forces 357
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
APPENDIX
Supplementary Tables
Table A1: Specimens used in this study
Female Male
CDFW specimen no. Body mass (kg) Body length (cm) CDFW specimen no. Body mass (kg) Body length (cm)
6859-13 22.5 88.5 6857-13 27.1 99
6977-13 7 73.5 6914-13 20.5 95
7039-14 11.8 82 6919-13 24.1 93
7075-14 12.8 80 7022-14 20 98
7138-14 20.6 92.5 7078-14 18.8 92
7157-14 6.465 64.5 7136-14 6.175 58
7171-14 13.2 89.5 7207-14 33.4 102.5
7205-14 12.6 89 7216-14 32.8 101
7232-14 16.2 85 7272-14 14 83
7248-14 4.64 56 7294-14 17.1 100
7268-14 5.5 60.5 7301-14 16.9 87
7276-14 15.6 80 7302-14 16.1 88.5
7285-14 7 72 7310-14 6.36 63
7382-14 14.1 80.5 7318-14 21 91
7634-15 8.8 67 7322-14 22.2 100
7637-15 16.9 93 7342-14 25.7 98.6
7645-15 10.9 77 7391-14 8.2 71.5
7657-15 8.7 73 7405-15 16 81.5
7666-15 16.2 92 7415-15 6 59.5
7668-15 17.1 88 7503-15 13.34 77.5
7744-15 11.2 75 7529-15 31 94
7749-15 19.1 88 7626-15 29.7 92
7774-15 16.5 85 7665-15 9.4 71
7777-16 8.5 74 7743-15 9.9 68
7752-15 24.6 98
7755-15 13.3 99
7758-15 6 65
7763-15 20.6 96
7764-15 20.1 96
7773-15 24.9 98
7789-16 30.8 104
Note. CDFW pCalifornia Department of Fish and Wildlife.
Table A2: Age classes of the southern sea otter and the skull sample size per age class used in this study
Age class Age Skull sample size Total body length (cm) Skull characteristics
Pup 2.5–6 mo F 2, M 1 40–90 All sutures open; all teeth deciduous
Immature 6 mo–1yr F5,M6 80–105 Exoccipital-basioccipital suture closed; some teeth
deciduous, some permanent
Subadult 1–4yr F8,M7 F95–115, M 100–125 Basioccipital-basisphenoid suture open; all teeth
permanent; no tooth wear evident
Adult 4–9yr F9,M17 F1105, M 1115 All sutures closed; lambdoidal and sagittal crests
starting to develop; slight to obvious tooth wear
Note. Age classes were defined based on the total body length and skull characteristics following California Department of Fish and Wildlife protocol (Hatfield
2006). F pfemale; M pmale.
358 C. J. Law, C. Young, and R. S. Mehta
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
Table A3: Comparison of the mean slopes between the sexes
Dependent variable Mean slopes tdf P
Cranial dimensions against BM:
CBL F .17, M .17 2.85E-05 1 .996
ZB F .19, M .18 .352 1 .553
CH F .10, M .12 1.28 1 .258
Cranial dimensions against BL:
CBL F .52, M .50 .147 1 .701
ZB F .60, M .55 1.116 1 .291
CH F .30, M .38 .8802 1 .348
BF
C
against body and cranial dimensions:
BM F .84, M .96 1.624 1 .203
BL F 2.63, M 2.92 .976 1 .323
CBL F 5.05, M 5.79 1.709 1 .204
ZB F 4.37, M 5.33 3.945 1 .052
CH F 8.63, M 7.85 .198 1 .635
BF
M
against body and cranial dimensions:
BM F .79, M .88 1.055 1 .304
BL F 22.49, M 22.69 .5526 1 .457
CBL F 4.77, M 5.32 1.002 1 .317
ZB F 4.13, M 4.90 2.649 1 .104
CH F 8.17, M 7.22 .3348 1 .563
BF components against CBL:
O
C
F 1.20, M 1.09 2.006 1 .157
O
M
F 1.62, M 1.63 .008438 1 .927
MAT F 1.93, M 1.80 .6233 1 .430
MAM F 1.85, M 2.10 .661 1 .416
m
TEM
F 12.24, M 14.32 2.786 1 .095
m
MAS
F 5.04, M 5.69 1.143 1 .285
f
TEM
F 2.40, M 2.13 .3868 1 .534
f
MAS
F 2.05, M 1.93 .08146 1 .775
MA against CBL:
temMA
C
F .83, M .83 2.66E-06 1 .999
temMA
M
masMA
C
F 1.08, M 1.25 .3395 1 .560
masMA
M
PCSA against CBL:
PCSA
TEM
F 4.62, M 5.34 1.762 1 .184
PCSA
MAS
F25.04, M 25.69 1.143 1 .285
BF components against BM:
O
C
F .20, M .18 .7311 1 .393
O
M
F .27, M .27 .003539 1 .953
MAT F .32, M .30 .3245 1 .569
MAM F .31, M .35 .4502 1 .502
m
TEM
F 1.02, M 1.19 2.276 1 .131
m
MAS
F .84, M .95 .8881 1 .346
f
TEM
F .40, M .35 .352 1 .553
f
MAS
F .34, M .32 .0793 1 .778
MA against BM:
temMA
C
F .14, M .14 2.17E-05 1 .996
temMA
M
masMA
C
F .18, M .21 .2424 1 .623
masMA
M
PCSA against BM:
PCSA
TEM
F .77, M .89 1.827 1 .177
PCSA
MAS
F .84, M .95 .8881 1 .431
Note. The trait listed in each row indicates the dependent variable used in sex-specific standardized major axis regressions. Pvalues are reported as Benjamini-
Hochberg-corrected values. Significance level p0.05. BL pbody length; BM pbody mass; CBL pcondylobasal length; CH pcranial height; F pfemale; f
MAS
p
masseter fiber length; f
TEM
ptemporalis fiber length; M pmale; m
MAS
pmasseter mass; m
TEM
ptemporalis mass; MAM pmasseter in-lever; MAT ptemporalis in-
lever; O
C
pout-lever to canine; O
M
pout-lever to molar; PCSA
TEM
pphysiological cross-sectional area of temporalis; PCSA
MAS
pphysiological cross-sectional area of
masseter; temMA
C
ptemporalis mechanical advantage to the canine; temMA
M
ptemporalis mechanical advantage to the masseter; ZB pzygomatic breadth.
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
Table A4: Scaling of bite force model components (pt. A), mechanical advantage (pt. B), and physiological cross-sectional area
(pt. C) against body mass
Sex effects
Scaling relationships
Intercept PR
2
Slope (95% CI) P
Isometric
prediction
Scaling
patterns
A. BF components against BM:
O
C
F 1.49, M 1.53 .515 .86 .18 (.17–.21) !.001 .33 NA
O
M
F.69,M.64 .047 .82 .26 (.24–.3) .001 .33 NA
MAT F .23, M .24 .040 .81 .29 (.26–.33) .041 .33 NA
MAM F 2.05, M 2.25 .004 .63 .31 (.26–.37) .408 .33 I
m
TEM
F .71, M .30 .761 .9 1.15 (1.05–1.25) .041 1PA
m
MAS
F2.25, M 2.58 .663 .84 .9 (.8–.99) .047 1NA
f
TEM
F .35, M .44 .774 .62 .38 (.31–.46) .183 .33 I
f
MAS
F .26, M .23 .089 .36 .31 (.24–.4) .578 .33 I
B. MA against BM:
temMA
C
F21.31, M 21.35 .009 .53 .13 (.10–.15) !.001 0PA
temMA
M
NS
masMA
C
F21.71, M 21.88 .001 .19 .18 (.13–.23) !.001 0PA
masMA
M
NS
C. PCSA against BM:
PCSA
TEM
F2.07, M 2.34 .663 .88 .86 (.78–.95) !.001 .67 PA
PCSA
MAS
F2.25, M 2.57 .663 .84 .9 (.80–1.00) .198 .67 I
Note. Bite force components, mechanical advantage, and physiological cross-sectional area served as dependent variables, while body mass served asthe
independent variable. Pvalues from tests of sex effect reflect differences in elevation between the sexes, and Pvalues from tests of isometry reflect differences
from isometric predictions. All Pvalues are reported as Benjamini-Hochberg-corrected values. Bold Pvalues indicate significance (ap0.05). NS p
nonsignificant relationship (R
2
p0.00–0.10, Pp0.067–0.561). See table A3 for tests in difference of slopes. CI pconfidence interval. For scaling patterns, I p
isometry, NA pnegative allometry, and PA ppositive allometry. F pfemale; f
MAS
pmasseter fiber length; f
TEM
ptemporalis fiber length; M pmale; m
MAS
p
masseter mass; m
TEM
ptemporalis mass; MAM pmasseter in-lever; masMA
C
pmasseter mechanical advantage to the canine; masMA
M
pmasseter mechanical
advantage to the molar; MAT ptemporalis in-lever; O
C
pout-lever to canine; O
M
pout-lever to molar; PCSA
MAS
pphysiological cross-sectional area of masseter;
PCSA
TEM
pphysiological cross-sectional area of temporalis; temMA
C
ptemporalis mechanical advantage to the canine; temMA
M
ptemporalis mechanical advantage
to the molar.
Table A5: Multiple regression analyses of model components that contribute to estimated bite force
CAR scores for BF
C
components
temMA
C
masMA
C
m
TEM
m
MAS
f
TEM
f
MAS
Adjusted R
2
Fratio df P
Female .215 .024 .469 .264 .000 .026 1 10,960 6, 17 !.001
Male .127 .070 .428 .254 .064 .058 1 51,660 6, 24 !.001
CAR scores for BF
M
components
temMA
M
masMA
M
m
TEM
m
MAS
f
TEM
f
MAS
Female .078 .001 .557 .328 .000 .035 1 9,277 6, 17 !.001
Male .018 .016 .517 .308 .077 .064 1 41,240 6, 24 !.001
Note. Correlation-adjusted correlation (CAR) scores representing relative contribution of model components to estimated bite force at the canine (BF
C
)andat
the molar (BF
M
). Bold CAR scores represent the best model component predictor. Bold Pvalues indicate significance (ap0.05). f
MAS
masseter fiber length;
f
TEM
ptemporalis fiber length; m
MAS
pmasseter mass; m
TEM
ptemporalis mass; temMA
C
ptemporalis mechanical advantage to the canine; temMA
M
p
temporalis mechanical advantage to the masseter.
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
Literature Cited
Anderson R.A., L.D. McBrayer, and A. Herrel. 2008. Bite force
in vertebrates: opportunities and caveats for use of a non-
pareil whole-animal performance measure. Biol J Linn Soc
93:709–720.
BaligaV.B.andR.S.Mehta.2014.Scalingpatternsinform
ontogenetic transitions away from cleaning in Thalassoma
wrasses. J Exp Biol 217:3597–3606.
Benjamini Y. and Y. Hochberg. 1995. Controlling the false
discovery rate: a practical and powerful approach to mul-
tiple testing. J R Stat Soc B 57:289–300.
Biewener A.A. and R.J. Full. 1992. Force platform and kine-
matic analysis. Pp. 45–73 in A.A. Biewener, ed. Biomechanics
structures and systems: a practical approach. Oxford Univer-
sity Press, New York.
Binder W.J. and B. Valkenburgh. 2000. Development of bite
strength and feeding behaviour in juvenile spotted hyenas
(Crocuta crocuta). J Zool 252:273–283.
Bolnick D.I., P. Amarasekare, M.S. Araújo, R. Bürger, J.M.
Levine,M.Novak,V.H.W.Rudolf,etal.2011.Whyintra-
specific trait variation matters in community ecology. Trends
Ecol Evol 26:183–192.
Bolnick D.I., R. Svanbäck, M.S. Araújo, and L. Persson. 2007.
Comparative support for the niche variation hypothesis that
more generalized populations also are more heterogeneous.
Proc Natl Acad Sci USA 104:10075–10079.
Bulté G., D.J. Irschick, and G. Blouin-Demers. 2008. The re-
productive role hypothesis explains trophic morphology di-
morphism in the northern map turtle. Funct Ecol 22:824–830.
Camilleri C. and R. Shine. 1990. Sexual dimorphism and die-
tary divergence: differences in trophic morphology between
male and female snakes. Copeia 1990:649–658.
Christiansen P. and S. Wroe. 2007. Bite forces and evolution-
ary adaptations to feeding ecology in carnivores. Ecology 88:
347–358.
Clutton-Brock T. 2007. Sexual selection in males and females.
Science 318:1882–1885.
Collar D.C., J.S. Reece, M.E. Alfaro, and P.C. Wainwright.
2014. Imperfect morphological convergence: variable changes
in cranial structures underlie transitions to durophagy in moray
eels. Am Nat 183:E168–E184. doi:10.1086/675810.
Constantino P.J., J.J.W. Lee, D. Morris, P.W. Lucas, A.
Hartstone-Rose, W.-K. Lee, N.J. Dominy, et al. 2011. Adap-
tation to hard-object feeding in sea otters and hominins.
JHumEvol61:89–96.
DarimontC.T.,P.C.Paquet,andT.E.Reimchen.2009.Land-
scape heterogeneity and marine subsidy generate extensive
intrapopulation niche diversity in a large terrestrial verte-
brate. J Anim Ecol 78:126–133.
Darwin C. 1871. The descent of man and selection in relation
to sex. J. Murray, London.
Davis J.L., S.E. Santana, E.R. Dumont, and I.R. Grosse. 2010.
Predicting bite force in mammals: two-dimensional versus
three-dimensional lever models. J Exp Biol 213:1844–1851.
Davis J.S. 2014. Functional morphology of mastication in
musteloid carnivorans. PhD diss. Ohio State University, Co-
lumbus.
Emerson S.B. and D.M. Bramble. 1993. Scaling, allometry, and
skull design. Pp. 384–421 in J. Hanken and B.K. Hall, eds.
The skull. Vol. 3. Functional and evolutionary mechanisms.
University of Chicago Press, Chicago.
EricksonG.M.,A.K.Lappin,andK.A.Vliet.2003.Theontog-
eny of bite-force performance in American alligator (Alli-
gator mississippiensis). J Zool 260:317–327.
Estes J.A., M.L. Riedman, M.M. Staedler, M.T. Tinker, and B.E.
Lyon. 2003. Individual variation in prey selection by sea otters:
patterns, causes and implications. J Anim Ecol 72:144–155.
Fisher E.M. 1939. Habits of the southern sea otter. J Mammal
20:21.
———. 1941. Notes on the teeth of the sea otter. J Mammal
22:428.
Garshelis D.L. and A.M. Johnson. 1984. Social organization of
sea otters in Prince William Sound, Alaska. Can J Zool 62:
2648–2658.
Grömping U. 2006. Relative importance for linear regression
in R: the package relaimpo. J Stat Softw 17:1–27.
Grubich J.R. 2005. Disparity between feeding performance
and predicted muscle strength in the pharyngeal muscu-
lature of black drum, Pogonias cromis (Sciaenidae). Environ
Biol Fish 74:261–272.
Hatfield B. 2006. Protocol for stranded and dead sea otters.
California Department of Fish and Wildlife, Sacramento.
Hedrick A.V. and E.J. Temeles. 1989. The evolution of sexual
dimorphism in animals: hypotheses and tests. Trends Ecol
Evol 4:136–138.
Hernandez L.P. and P.J. Motta. 1997. Trophic consequences of
differential performance: ontogeny of oral jaw-crushing per-
formance in the sheepshead, Archosargus probatocephalus
(Teleostei, Sparidae). J Zool 243:737–756.
HerrelA.,R.V.Damme,B.Vanhooydonck,andF.D.Vree.
2001. The implications of bite performance for diet in two
species of lacertid lizards. Can J Zool 79:662–670.
Herrel A., A. De Smet, L.F. Aguirre, and P. Aerts. 2008.
Morphological and mechanical determinants of bite force
in bats: do muscles matter? J Exp Biol 211:86–91.
HerrelA.,R.Joachim,B.Vanhooydonck,andD.J.Irschick.
2006. Ecological consequences of ontogenetic changes in
head shape and bite performance in the Jamaican lizard
Anolis lineatopus. Biol J Linn Soc 89:443–454.
HerrelA.,L.D.McBrayer,andP.M.Larson.2007.Functional
basis for sexual differences in bite force in the lizard Anolis
carolinensis.BiolJLinnSoc91:111–119.
HerrelA.,L.Spithoven,R.VanDamme,andF.DeVree.1999.
Sexual dimorphism of head size in Gallotia galloti:testing
the niche divergence hypothesis by functional analyses. Funct
Ecol 13:289–297.
Herzog W. 1994. Muscle. Pp. 154–187 in B.M. Nigg and
W. Herzog, eds. Biomechanics of the musculoskeletal system.
Wiley, Chichester.
Ontogeny of Sea Otter Bite Forces 361
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
Hill A.V. 1950. The dimensions of animals and their muscular
dynamics. Sci Prog 38:209–230.
Huber D.R., M.N. Dean, and A.P. Summers. 2008. Hard prey,
soft jaws and the ontogeny of feeding mechanics in the
spotted ratfish Hydrolagus colliei.JRSocInterface5:941–
952.
Huber D.R., C.L. Weggelaar, and P.J. Motta. 2006. Scaling of
bite force in the blacktip shark Carcharhinus limbatus.Zo-
ology 109:109–119.
Kardong K.V. 2014. Vertebrates: comparative anatomy, func-
tion, evolution. McGraw-Hill, Boston.
Kolmann M.A. and D.R. Huber. 2009. Scaling of feeding bio-
mechanics in the horn shark Heterodontus francisci:on-
togenetic constraints on durophagy. Zoology 112:351–361.
Kolmann M.A., D.R. Huber, P.J. Motta, and R.D. Grubbs.
2015. Feeding biomechanics of the cownose ray, Rhinoptera
bonasus, over ontogeny. J Anat 227:341–351.
Law C.J., V. Venkatram, and R.S.Mehta.Forthcoming.Sexual
dimorphism in the craniomandibular morphology of south-
ern sea otters (Enhydra lutris nereis). J Mammal.
MarshallC.D.,A.Guzman,T.Narazaki,K.Sato,E.A.Kane,
and B.D. Sterba-Boatwright. 2012. The ontogenetic scaling
of bite force and head size in loggerhead sea turtles (Caretta
caretta): implications for durophagy in neritic, benthic habi-
tats. J Exp Biol 215:4166–4174.
Marshall C.D., J. Wang, A. Rocha-Olivares, C. Godinez-Reyes,
S. Fisler, T. Narazaki, K. Sato, et al. 2014. Scaling of bite per-
formance with head and carapace morphometrics in green
turtles (Chelonia mydas). J Exp Mar Biol 451:91–97.
Maynard Smith J. and R. Savage. 1959. The mechanics of
mammalian jaws. Sch Sci Rev 141:289–301.
McGee M.D. and P.C. Wainwright. 2013. Sexual dimorphism
in the feeding mechanism of threespine stickleback. J Exp
Biol 216:835–840.
Mendez J. and A. Keys. 1960. Density and composition of
mammalian muscle. Metab Clin Exp 9:184–188.
Pfaller J.B., P.M. Gignac, and G.M. Erickson. 2011. Ontoge-
netic changes in jaw-muscle architecture facilitate durophagy
in the turtle Sternotherus minor. J Exp Biol 214:1655–1667.
R Core Team. 2015. R: a language and environment for sta-
tistical computing. R Foundation for Statistical Computing,
Vienna. http://www.R-project.org/.
Radford A.N. and M.A. Du Plessis. 2003. Bill dimorphism and
foraging niche partitioning in the green woodhoopoe. J Anim
Ecol 72:258–269.
Riedman M. and J.A. Estes. 1990. The sea otter (Enhydra lutris):
behavior, ecology, and natural history. Biol Rep 90:1–117.
Riley M.A. 1985. An analysis of masticatory form and function
in three mustelids (Martes americana, Lutra canadensis,
Enhydra lutris). J Mammal 66:519–528.
Roest A.I. 1985. Determining the sex of sea otters from skulls.
Calif Fish Game 71:179–183.
Sacks R.D. and R.R. Roy. 1982. Architecture of the hind limb
muscles of cats: functional significance. J Morphol 173:185–
195.
Santana S.E., E. Dumont, and J.L. Davis. 2010. Mechanics of
bite force production and its relationship to diet in bats.
Funct Ecol 24:776–784.
Santana S.E. and K.E. Miller. 2016. Extreme postnatal scaling in
bat feeding performance: a view of ecomorphology from on-
togenetic and macroevolutionary perspectives. Integr Comp
Biol. doi:10.1093/icb/icw075.
Scapino R.P. 1968. Biomechanics of feeding in Carnivora. PhD
diss. University of Illinois, Chicago.
Scheffer V.B. 1951. Measurements of sea otters from western
Alaska. J Mammal 32:10–14.
Schmidt-Nielsen K. 1984. Scaling. Cambridge University Press,
Cambridge.
Schneider C.A., W.S. Rasband, and K.W. Eliceiri. 2012. NIH
Image to ImageJ: 25 years of image analysis. Nat Methods 9:
671–675.
Shine R. 1989. Ecological causes for the evolution of sexual di-
morphism: a review of the evidence. Q Rev Biol 64:419–461.
Smith E.A., S.D. Newsome, J.A. Estes, and M.T. Tinker. 2015.
The cost of reproduction: differential resource specializa-
tion in female and male California sea otters. Oecologia 178:
17–29.
Thom M.D. and L.A. Harrington. 2004. Why are American
mink sexually dimorphic? a role for niche separation. Oikos
105:525–535.
ThomasP.,E.Pouydebat,I.Hardy,F.Aujard,C.F.Ross,and
A. Herrel. 2015. Sexual dimorphism in bite force in the grey
mouse lemur. J Zool 296:133–138.
Timm L.L. 2013. Feeding biomechanics and craniodental mor-
phology in otters (Lutrinae). PhD diss. Texas A&M Univer-
sity, College Station.
Timm-Davis L.L., T.J. DeWitt, and C.D. Marshall. 2015. Di-
vergent skull morphology supports two trophic specializa-
tions in otters (Lutrinae). PLoS ONE 10:e0143236.
Tinker M.T., G. Bentall, and J.A. Estes. 2008. Food limitation
leads to behavioral diversification and dietary specialization
in sea otters. Proc Natl Acad Sci USA 105:560–565.
TinkerM.T.,D.P.Costa,J.A.Estes,andN.Wieringa.2007.
Individual dietary specialization and dive behaviour in
the California sea otter: using archival time-depth data to
detect alternative foraging strategies. Deep Sea Res II 54:
330–342.
Turnbull W.D. 1970. Mammalian masticatory apparatus. Field
Museum of Natural History, Chicago.
van der Meij M.A.A. and R.G.Bout. 2006. Seed husking time and
maximal bite force in finches. J Exp Biol 209:3329–3335.
Van Valkenburgh B. 2007. Deja vu: the evolution of feeding
morphologies in the Carnivora. Am Zool 47:147–163.
Verwaijen D., R. Van Damme, and A. Herrel. 2002. Relation-
ships between head size, bite force, prey handling efficiency
and diet in two sympatric lacertid lizards. Funct Ecol 16:
842–850.
Warton D.I., R.A. Duursma, D.S. Falster, and S. Taskinen.
2011. smatr 3: an R package for estimation and inference
about allometric lines. Methods Ecol Evol 3:257–259.
362 C. J. Law, C. Young, and R. S. Mehta
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
WilsonD.E.,M.A.Bogan,R.L.Brownell,A.M.Burdin,and
M.K. Maminov. 1991. Geographic variation in sea otters,
Enhydra lutris. J Mammal 72:22–36.
Ziscovici C., P.W. Lucas, P.J. Constantino, T.G. Bromage, and
A. van Casteren. 2014. Sea otter dental enamel is highly
resistant to chipping due to its microstructure. Biol Lett 10:
20140484.
Zuber V. and K. Strimmer. 2011. High-dimensional regression
and variable selection using CAR scores. Stat Appl Genet
MolBiol10:1–34.
Ontogeny of Sea Otter Bite Forces 363
This content downloaded from 128.114.044.070 on September 12, 2016 15:27:29 PM
All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c).
