zoological Journal of the Linnean SocieQ (1993), 108: 179-196. With 9 figures
Femoral ontogeny and locomotor biomechanics
of Dryosaurus lettowvorbecki (Dinosauria,
Iguanodontia)
RONALD E. HEINRICH, CHRISTOPHER B. R U F F AND
DAVID B. WEISHAMPEL
Department of Cell Biology and Anatomy, Johns Hopkins University, School of
Medicine, Baltimore, Maryland 21205
Received October 1991, revised manuscript accepted for publication J U !1992
~
Femoral ontogeny in the iguanodontian dinosaur DTyosaurus lettowvorbccki (Late Jurassic, Tanzania)
is analysed biornechanically using principles of beam theory. Statistically significant differences in
cross-sectional properties are found between animals of differing size, reflecting alterations to both
the relative amount and distribution of cortical bone during growth. Two explanations are
suggested to account for these modifications in bone architecture: ( 1 ) increasing mechanical loads
related to increasing body size, and (2) changes in the orientation of these loadings associated with a
caudal shift of the centre of gravity. It is argued that D. lettowvorbecki hatchlings were not bipedal as
generally presumed but obligate quadrupeds. Based on avian growth rates, the transition from
quadrupedality to habitual bipedalisrn is estimated to have occurred within several months of
hatching. The biomechanical approach employed here contributes new insight into ontogeny of
locomotion in D. lettowuorbccki and provides additional ways of analysing ontogenetic processes
among extinct and living species.
ADDITIONAL KEY WORDS:-Cross-sectional
geometry
-
development
-
bipedalism
CONTENTS
Introduction . . . . . . . .
Methods and materials
. . . . .
Results . . . . . . . . .
Weight estimates . . . . . .
Cross-sectional properties . . . .
Discussion
. . . . . . . .
Size transitions . . . . . .
Femoral ontogeny and locomotion
.
A quadrupedal-bipedal locomotor shift
Summary.
. . . . . . . .
Acknowledgements . . . . . .
References
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179
182
185
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195
INTRODUCTION
Bones involved in load-bearing are capable of responding to changes in
mechanical strain in a precise and systematic manner (Alexander et al., 1984;
Lanyon, 1984). As a result, the basic form of limb elements can be profoundly
0024-4082/93/060179+
18 S08.00/0
179
0 1993 The Linnean Society of London
I80
R. E. HEINRICH E l AL.
Figure 1. Cladogram depicting the phylogenetic relationships of Dryosaurur to other ornithopodan
taxa.
altered when subjected to abnormal loadings (Goodship, Lanyon & McFie,
1979; Lanyon et al., 1982; Rubin & Lanyon, 1985). Less well investigated are the
changes in skeletal morphology that accompany normal postnatal ontogeny. If
long bone growth proceeded isometrically, body mass would increase more
rapidly than bone cross-sectional area (A a M2/3)resulting in greater strain
magnitude and reduced safety factors with increasing size. This, however, does
not occur. Analysing the tibiotarsus of chicks, Biewener, Swartz & Bertram
(1986, see also Goodship et al., 1979) demonstrated that strain magnitude at
homologous positions along the bone remained constant throughout ontogeny.
This uniformity of strain magnitude can be attributed to alterations in the
mechanical properties of bone that occur during the course of normal
development (Brear, Currey & Pond, 1990 and references cited therein).
Mechanical properties may be modified in one or both of the following ways:
(1) by altering the material properties of bone (e.g. altering mineral content) or
(2) by changing the amount and distribution of bone. The latter constitutes
changes in size and shape or, more generally, changes in bone architecture.
While changes in material properties of bone certainly occur throughout
ontogeny (Brear et al., 1990),it is the changes in bone architecture which are
thought to be the primary mechanism by which bone responds to increased
loadings (Woo et al., 1981; Lanyon & Rubin, 1985).
An ontogenetic sample of femora attributed to the basal iguanodontian
dinosaur Dryosaurus lettowvorbecki was analysed to assess quantitatively the
importance of architectural changes during development of this particular
species. Iguanodontians were ornithopods (Fig. 1; Sereno, 1986; Sues &
Norman, 1990; Weishampel & Heinrich, 1992), the group of dinosaurs which
became the dominant herbivores in the latter half of the Cretaceous Period
(97-65 million years ago). Two species of Dryosaurus are currently recognized,
D.altus from the Morrison Formation of the western interior of the United
LOCOMOTOR BIOMECHANICS OF DRTOSAURUS
181
States, and D.lettowvorbecki from the Tendaguru Beds of Tanzania (Janensch,
1955; Galton, 1981; Sues & Norman, 1990). These deposits date to roughly 150
million years ago. Both species reached lengths of 6.5 m, over half of which
comprised the tail, and fully mature animals are estimated to have weighed
approximately 70 kg. (Weight estimates are discussed in detail in Methods and
materials.) Hindlimb proportions indicate cursorial specializations in these
bipedal animals (Galton, 1971, 1974; Coombs, 1978), and Thulborn ( 1982)
estimated their top running speed to be in excess of 40 km h-', the fastest of all
ornithischian dinosaurs analysed to date. Overall similarities to Hypsilophodon
(Galton, 1974), one of the best studied of all small euornithopodan taxa, suggests
that Dryosaurus was a habitual biped.
The position of the centre of gravity and the kinematics of locomotion have
obvious and important implications for understanding the magnitude and
orientation of mechanical loadings acting on the femur. Comparison of grounddwelling bird kinematics with what can be inferred of locomotion in adult
Dryosaurus illustrates this point. The centre of gravity in all bipedal dinosaurs is
reconstructed as near the hip joint, with the long, heavy tail acting to
counterbalance the presacral region of the body during locomotion (Alexander,
1985). Gatesy (1990) has shown that parasagittal limb motion in theropod
dinosaurs involved considerable retraction of the femur and movement of the
feet symmetrically beneath the pelvis. This was presumably the case in bipedal
ornithopods such as Dryosaurus as well (Galton, 1974). In contrast, the
parasagittal gait kinematics of birds differs substantially from that of non-avian
archosaurs, owing in large part to the loss of the counterbalancing tail. T o
support a centre of gravity in front of the hip, birds have adopted a
subhorizontal femoral orientation which positions the foot directly under the
centre of gravity. Rather than retracting the femur, as do bipedal dinosaurs and
other non-avian archosaurs, ground-dwelling birds rely predominantly on
flexion at the knee to move the foot under the centre of gravity (Gatesy, 1990).
Along with the kinematic differences found in these two groups of bipeds there
are structural differences in the hindlimb; bipedal dinosaurs have proportions
more characteristic of quadrupedal cursorial mammals than of birds (Coombs,
1978; Anderson et al., 1985).
The level of strain, or strain magnitude, acting on a load-bearing element is
the product of (1) the mechanical properties of bone, as defined above, and
(2) the size and orientation of the mechanical loadings acting on it (Lanyon &
Rubin, 1985). The resultant cross-sectional morphology of a load-bearing
element reflects this unique interaction. Cross-sectional geometries, then, can be
used to reconstruct the mechanical loadings that acted on long bones in vivo
(Ruff & Hayes, 1983), and an ontogenetic series of cross-sections provides a
means of reconstructing the pattern of loadings that accompanied growth and
development. If young animals maintain similar weight distributions and utilize
the same locomotory gaits as mature animals, then we might expect crosssectional properties of bone to demonstrate unidirectional changes as body
weight increases. Although rates of change may vary during different stages of
growth, the direction of change, if any, should remain constant-an assumption
supported by data collected from the South American bipedal ratite, Rhea
americana (Table 1). Conversely, if the pattern of change in cross-sectional
morphology deviates significantly from unidirectional trends, factors other than
R. E. HEINRICH ET AL.
182
TABLE
1. Cross-sectional properties of an ontogenetic sequence ot'
Rhea amen'cana femora. See Methods and materials section for a
discussion of the cross-sectional properties listed in the Table.
Abbreviation: AMNH, American Museum of Natural History.
Specimen AMNH 1474 was collected from Southern Brazil,
specimens AMNH 6470 and 6471 from Uruguay
Specimen No.
Length
yo Cortical area
AMNH 6471
AMNH 6470
AMNH 1474
I25
195
210
55.1
50.6
54.2
I,,/I,,
1.499
1.579
1.858
increasing size are probably affecting femoral loadings and modifications to bone
architecture.
METHODS AND MATERIALS
Long bone diaphyses modelled as hollow beams can be analysed using
standard engineering beam theory principles (Timoshenko & Gere, 1972; Ruff
& Hayes, 1983 and references cited therein). Stresses resulting from the loading
of hollow beams are expressed by the equations
where
and
6, is
compressive stress; Fa is axial loading; and A is cross-sectional area;
Mbc
bb= -
I
where ob is compressive or tensile stress; M b is the externally applied bending
moment about a given axis; c is the distance from neutral plane of bending to the
beam's surface; and I is the second moment of area about the neutral axis in the
plane of bending.
The amount and distribution of bone a t a given cross-section is reflected in the
cross-sectional area (A) and the second moment of area ( I ) respectively. To
compare the relative amount of cortical bone in cross-sections of varying size,
percentage cortical area (cortical area/total subperiosteal area) was calculated.
Comparisons of bone distribution involved calculations of the second moments of
area about the craniocaudal (I,)and mediolateral ( I y )axes of the femur, as well
second moments of area of the
as the maximum (Imax)and minimum (Imin)
section. The angle 8,measured counterclockwise from the M-L axis of greatest
bending strength, provides information on the general orientation of bone
distribution. These cross-sectional properties are presented in Fig. 2.
Cross-sectional shape can be compared using the ratios I,/Z or Imax/Zmin
which in
turn provide information about relative resistance to bending loadings in
different planes of the femur.
Body mass is obviously an important parameter in any analysis of mechanical
loading of limb elements. For purposes here weight estimates of D . lettowvorbecki
at different stages of ontogeny are of particular interest. Estimates of body mass
in dinosaurs have generally applied a technique of volume displacement using
LOCOMOTOR BIOMECHANICS OF DRYOSAURUS
I83
Subperiosteal area = 395 mm2
Cortical area = 273 mm2
l x = 13345 mm4
ly = 9937 mm'
I,, = 13484 mm'
lmin= 9798mm'
e = 79.00
Figure 2. Proximal cross-section of medium-sized femur (UT 1495/ 14) demonstrating the crosssectional properties; total area, cortical area, 0, and the second moment of areas I,, Iy,I,,,, I,,,$",
analysed in this study. Y-Axis indicates craniocaudal orientation, x-axis mediolateral.
isometrically scaled models of specific species and density estimates obtained
from living reptiles (Colbert, 1962; Alexander, 1985). Anderson, Hall-Martin &
Russell ( 1985), however, have presented a regression for calculating weight of
bipedal dinosaurs from femoral circumference,
W = 0.16 G.73
(3)
where W is body weight and C,is midshaft circumference. The exponent is based
on a regression of 23 species of quadrupedal mammals, and the proportionality
constant from mass estimates of Troodon (Stenonychosaurus discussed by Anderson et
al., 1985, is a junior synonym of Troodon; Currie, 1987). Anderson et al. (1985)
justify the mammalian exponent on the basis of ( 1 ) similarities in limb
proportions between quadrupedal mammals and bipedal dinosaurs, and (2)
similarities between the 2.73 exponent calculated for mammals and exponents
previously calculated for femoral circumference of three bipedal dinosaurs. Since
it could be argued that a quadrupedal based regression might overestimate body
mass in bipeds, weight estimates for D. lettowvorbecki are calculated using both
equation (3) and the equation,
W = 1.08
c.28
(4)
184
R. E. HEINRICH E l AL.
calculated by Anderson et al. (1985) from 72 species of birds. In this way we can
be reasonably confident that we have bracketed the actual weight of
D. lettowvorbecki, assuming that the modern analogues on which the regression
equations are based accurately reflect allometric proportions of cross-sectional
area to body weight in the femora of small bipedal dinosaurs.
All remains referred to D . lettowvorbecki come from a single locality in the
Tendaguru Hills, Quarry IG, c. 75 km west of the Tanzanian port city of Lind
(Janensch, 1914). Quarry IG represents a monospecific mass death assemblage
where animals of all sizes are thought to have perished during widespread
drought conditions (Russell et al., 1980). All material is highly disarticulated and
disassociated and most elements are fragmentary (Janensch, 1914; G. Maier,
personal communication). Among the available specimens, however, are five
complete and undistorted femora ranging in length from 120 to 276 mm. These
were used to calculate regressions of greater trochanter and medial condyle
length, and total condylar width against total length (Fig. 3, Table 2). Lengths
of incomplete femora were then estimated using these regressions. If both medial
condyle length and condylar width could be measured for a given specimen, the
regression of medial condyle against length was used because of its higher
correlation coefficient (Table 2). Using this method the resulting range of
femoral lengths was calculated to be 109 to 330 mm. For purposes of this study,
femora were assigned to one of three sizes classes based on length: small
(109-146 mm), medium (180-234 mm), and large (282-330 mm). These classes
presumably reflect relative age groups.
Geometric data were obtained from 27 femora with naturally broken crosssections. The location of these cross-sections was between c. 50% and 30% of
femoral length from the distal end of the bone (all percentages are given from the
distal end of the bone). Break position was categorized as either proximal (those
breaks occurring between 41% and 50%) or distal (those between 30% and
39%). Since inaccurate length estimates may affect the accuracy of the break
location, comparisons of external femoral morphology provided a means of
verifying the categorization of each cross-section. O n the basis of femoral length
and location of break, each specimen was assigned to one of six groups: smalldistal, small-proximal, medium-distal, medium-proximal, large-distal and largeproximal. The cross-sections at these breaks were photographed and the
endosteal and periosteal perimeters manually digitized. Cross-sectional area,
and 8, were calculated using a modified version of
cortical area, I,, I,, I,,,,,,Imin
the program SLICE (Nagurka & Hayes, 1980). These dimensions were then
ratios. Statistical
used to calculate percentage cortical area and I,/Z, and Imax/Imin
analyses were carried out using the multiple comparison Tukey test (Systat
version 5.1 ; Wilkinson, 1988).
TABLE
2. Regression equations for estimating femoral length (mm)
in D . lettowvorbecki. Abbreviations: N , sample size; ?, coefficient of
determination; SE, standard error of estimate
Character
N
Slope
y-int.
?
SE
Greater trochanter
Medial condyle
Condylar width
5
5
5
6.015
4.077
3.810
-7.86
28.55
17.60
0.977
0.992
0.982
3.415
5.624
8.130
LOCOMOTOR BIOMECHANICS OF DRYOSAURUS
r
I85
Cranial
t
Medial
Medial
4
Cranial
D
B
A
Figure 3. Schematic diagram of a D. leftozuvorbecki femur in (A) cranial, (B) lateral, (C) proximal
and (D) distal views. Length estimates are based on regressions derived from the three
measurements shown; greater trochanter, medial condyle, and condyle width. Abbreviations: L,
length; GT, greater trochanter; MD, medial condyle; CW, condylar width. Scale bar = 4 cm.
RESULTS
Weight estimates
Eight weight estimates calculated from femora spanning the ontogenetic size
range of our sample are given in Table 3. Since none of the 100 or so
fragmentary femora available for study is recognizably larger than no. 8, this
specimen probably represents a mature animal. Using the regression derived for
quadrupedal mammals as suggested by Anderson et al. (1985), this animal is
estimated to have had a mass of 70 kg. T h e only other estimate of body weight
for Dryosaurus of which we are aware is 120 kg, given by Thulborn (1982). His
method of calculation, however, is not given and therefore we are unable to
critically compare Thulborn's estimate with those derived here.
TABLE
3. Weight estimates (in kg) for D . lettowvorbecki based on
femoral midshaft circumferences (Circ. in mm).
~
Specimen
Length
Circ.
Weightb
Weight'
109"
120
143
175"
204
276
299"
3304
37.0
46.0
55.0
69.5
76.0
108.0
111.5
116.5
4.1
6.7
10.0
17.1
21.0
46.7
50.3
55.6
3.1
5.5
9.0
17.1
21.8
56.9
62.1
70.0
"Femoral length is estimated; 'weight estimates based on the bipedal
regression equation W = 1.08GzBof Anderson et al. (1985, see text for
discussion); 'weight estimates based on the quadrupedal regresion equation
W = 0.16G 73 of Anderson el al. (1985, see text for discussion)
R. E. HEINRICH E l AL.
I86
7o
70
t-
$ld
A
no
A
"t
".-
30
0
0
O
I
I
I
Figure 4. Relationship between percentage cortical area of a cross-section and femoral length (given
in mm). Femoral size: 0 , small; A, medium; 0 , large.
TABLE
4. Comparisons of percentage cortical area: data for proximal and distal
sections of D. lettowvorbecki femora pooled. Abbreviations: N , sample size; SD,
standard deviation; SE, standard error of estimate;
not significantly different
at P = 0.10
~
~~
Size
Small
Medium
Large
~
~~
Jv
Mean
SD
SE
Range
11
52.30
5.295
1.596
38.940.6
9
68.34
2.954
0.985
61.7-71.7
8
67.09
3.295
1.165
60.9-71.2
Sign.
o.ool
~
Cross-sectional properties
Cross-sectional data collected for D. lettowvorbecki femora are summarized in
Figs 4-7 and accompanying Tables 4-7. Since we are interested in the
architectural differences that exist between successive stages of ontogeny, the
statistical results of Tukey test comparisons between small-medium and mediumlarge femora are also presented in Tables 4-7.
Percentage cortical area
Comparisons of proximal and distal locations within size classes revealed no
statistically significant differences in percentage cortical area between the two
regions. Therefore, these data were combined to provide more robust
comparisons between size classes. Statistically significant differences in
percentage cortical area do occur between small and medium sized animals
( P < 0.001) but not between medium and large animals (Fig. 4, Table 4).
Ratio of I, lo Iu
Statistically significant differences in the second moment of area ratio, I x / I y ,
LOCOMOTOR BIOMECHANICS OF DRYOSAURUS
A
0
0
A
A
0
0
O 0
0.4
I
100
187
I
I
200
300
Femoral length
I
.,
Figure 5. Relationship between the second moment of area ratio, Ix/Iy,and femoral length (given in
mm). Femoral size and break position noted by symbols: 0 , small-proximal; 0 , small-distal;
A, medium-proximal; A,medium-distal; 0 , large-proximal;
large-distal.
TABLE
5. Comparisons of I x / I yvalues between size classes and at two locations along the femoral
shaft. Abbreviations: as in Table 4.
Location
Distal
Proximal
Jv
Mean
SD
SE
Small
7
0.826
0.080
0.030
0.705-0.921
Medium
6
0.780
0.027
0.01 I
0.750-0.821
Large
5
0.794
0.117
0.052
0.597-0.890
Small
4
1.208
0.1 10
0.055
1.0941.324
Medium
3
1.307
0.039
0.022
1.266-1.307
Large
3
1.016
0.216
0.125
0.771-1.180
Size
Range
Sign
-~
~
= o.082
are found only at P < 0.10 (Fig. 5 , Table 5 ) . Proximal ZJZY ratios of medium
and large femora (discussed further under 0) differ at P = 0.083.
Ratio of I,,,
to
I,,,
At both proximal and distal femoral locations, differences in the ratio of
Zmax/Zmin
are statistically significant at the P < 0.10 level. I n each case increases
from small to medium-sized femora are followed by decreases from medium to
large (Fig. 6, Table 6). This is particularly noticeable proximally where,
although large Zmax/Zmin
ranges exist, no overlap in Zmax/Zminratios occurs between
either small-medium or medium-large groups (Table 7). Although small sample
sizes limit the degree of statistical significance, distinct differences in relative
maximum/minimum bending strength between femora of differing size are
strongly suggested.
R. E. HEINRICH ET AL.
188
.
.
..
I
A
A
A
A
A
A4
A
0
0
0 .
1.0I
100
I
200
Femoral length
Figure 6. Relationship between the second moment of area ratio I,,/I,,
in mm). Symbols for femoral size and break position as in Fig. 5.
I
300
and femoral length (given
TABLE
6. Comparisons of Imax/Imin
values between D.lettowvorbecki size classes and at two locations
along the femoral shaft. Abbreviations: as in Table 4.
Location
Distal
Proximal
Size
N
Mean
SD
SE
Range
Small
7
1.276
0.129
0.049
1.09&1.450
= o.087
Medium
6
1.47 I
0.148
0.060
1.326-1.678
__
Large
5
I .402
0.188
0.084
1.1841.690
Small
4
1.269
0.102
0.051
1.127-1.369 p = o.072
Medium
3
1.444
0.081
0.047
1,3761,534
Large
3
1.241
0.059
0.034
1.181-1.299
Sign.
= o,053
The angle 0
Distally, 8 is oriented almost mediolaterally, i.e. approximately 180", in
animals of all sizes, while proximally the orientation is closer to being
craniocaudal, i.e. 90" ( = 270"). The regional differences in the orientation of the
axis of maximum bending strength are statistically significant in all
proximodistal comparisons within a size class, while no significant differences are
found between proximal or distal locations across size classes (Fig. 7, Table 7).
The 0 value of one large-proximal cross-section is much smaller than is found
in proximal specimens of any size class (Fig. 7). This specimen also has an IJI,,
ratio significantly smaller than both of the other large-proximal specimens
ratio of the three femora (Fig. 6). All of these
(Fig. 5) and the largest Imax/lmin
cross-sectional properties suggest that this particular specimen may be better
interpreted as a distal rather than proximal cross-section, although the
calculated position of the break is 45%. (The other two large-proximal sections
LOCOMOTOR BIOMECHANICS OF DRYOSAURUS
I89
A
A
0
240
A
0
220
.
rn
A
0.
180
A
160
A
'
rn
A
200
100
300
Femoral length
Figure 7 . Relationship of the axis of greatest bending strength in proximal and distal cross-sections
for femora of differing length. Symbols for femoral size and break position as in Fig. 5.
TABLE
7 . Comparisons of the orientation of axes of greatest bending strength (degrees) in
D.lettowvorbecki femoral cross sections. Abbreviations: as in Table 4.
Location
Size
N
Mean
SD
SE
Range
Sign.
Small
7
171.9
13.87
5.24 I
159.6- 198.3
Medium
6
162.7
17.03
6.953
149.0-195.4
Large
5
182.8
24.65
11.02
151.9-215.7
Small
4
251.8
8.638
4.319
240.7-260.1
__
Medium
3
250.4
8.502
4.908
242.0-259.0
__
Large
3
228.8
~~
Distal
~
Proximal
43.45
25.09
181.7-267.3
are 48y0.)Two possible explanations may account for this: either the break
location has been inaccurately estimated, or the morphology of large femora
simply differs appreciably from that of small and medium sized elements. Since
all shape properties (second moment of area ratios) of the proximal cross-sections
are smaller in large than in medium sized femora (Figs 5, 6), the ZJZY and 8
deviations of the one large specimen may not be as incongruent as they first
appear. These differences are, however, larger than would be predicted on the
basis of the remainder of the data and it may be that the cross-sectional break is
less than the 45% position calculated, although it is unlikely to be distal
(30-39y0) as defined here.
DISCUSSION
Femoral growth in Dryosaurus lettowvorbecki is accompanied by adjustments in
both the relative amount and distribution of bone. While it is known that
190
R. E. HEINRICH ET AL.
material properties of bone change during development, particularly early
ontogeny (Torzilli et al., 1981; Currey & Pond, 1989; Brear el al., 1990),
architectural modifications in load-bearing elements are generally attributed to
a process of remodelling in response to strain (Lanyon et al., 1982; Lanyon,
1984; Rubin, 1984). Consequently, cross-sectional geometry is a reflection of,
and can be used to reconstruct, the mechanical loadings which acted on the
load-bearing element in vivo (Ruff & Hayes, 1983). By analysing the crosssectional morphology at various stages of ontogeny (small-medium-large) in
D. lettowvorbecki, a pattern of mechanical loadings accompanying normal growth
and development of the femur is reconstructed. This pattern is then used to make
locomotor inferences.
Size transitions
The cross-sectional properties of medium sized femora differ most noticeably
from those of small femora in two ways. First, they possess a relatively greater
amount of cortical bone (Fig. 4, Table 4), and second, they are characterized by
a larger Zmax/Zmin
ratio (Fig. 6, Table 6). The roughly 33% increase in percentage
cortical area corresponds to femoral lengthening from c. 150 to 180 mm and an
increase in weight of roughly 7 or 8 kg (Table 3, and discussed further below).
Interestingly this increase is not preceded by a recognizable trend towards
increasing percent cortical area among small femora (Fig. 4). The second
difference found between small and medium sized femora, both proximally and
distally, is in relative maximum to minimum bending strength. Again, small
femora do not demonstrate any clear trend towards increasing relative
maximum bending strength over their size range (Fig. 6). The angle 8 remains
the same at both locations over the small-medium size transition (Table 7).
Differences in cross-sectional properties between femora of medium and large
size are restricted to proximal cross-sections and, in general, are less distinctive
than those between small and medium femora. Percentage cortical area remains
constant (Fig. 4, Table 4) over almost a doubling in femoral length and an
approximate 50 kg increase in body weight (Table 3). The IJZY and
ratios of large femora, however, are distinctly smaller than
particularily Imax/Zmin
those of medium femora, indicating a relative reduction in maximum to
minimum bending stress (Tables 5 and 6).
Except for the changes in percentage cortical area, the morphology of distal
cross-sections is relatively similar in femora of all sizes. More significant
architectural changes occur proximally, as demonstrated in Fig. 8 using
representative cross-sections of each size class. Increases in both relative amount
and distribution of bone occur over the first size transition, while only changes in
the distribution of bone occur over the medium-large transition. In the light of
these alterations in bone distribution it is interesting that the axis of maximum
bending strength remains (with the one large specimen exception discussed
previously) constant both proximally and distally. The result of these
architectural differences is reflected in cross-sectional shape, which is more
elliptical in femora of medium size than in either small or large femora.
Femoral ontogeny and locomotion
Over the size range exhibited by our sample the most conspicuous alterations
in cross-sectional morphology are manifested during what appears to be a very
LOCOMOTOR BIOMECHANICS OF DRYOSAURUS
191
1
Cranial
Medial
SMALL
MEDIUM
LARGE
Figure 8. Proximal cross-sections representing each of the three size classes: small (uncatalogued),
medium (U?' 1495/14), and large (WJ 10000). Scale bar = I cm.
short period of time, a period arbitrarily defined here as the small-medium size
transition. Increases in both the relative amount and the maximum bending
strength of bone over this period suggest that loadings on the femur had
increased significantly. If increasing body mass alone accounted for these
changes in architecture, then we would expect the trends documented over the
first size transition to continue, albeit possibly at modified rates, as animals got
larger (Table 1 : ZmaX/lmin).The predicted unidirectional trends, however, are not
found in any of the comparisons made. Percentage cortical area increases
dramatically in relatively small animals, while subsequent increases of over
3000/, in body mass (20-70 kg, Table 3) produce no increases in the relative
amount of bone. Proximal and distal Zmax/Zminand proximal Zx/Iyratios exhibit a
more parabolic than linear pattern of change (Fig. 6), suggesting that relative
bending loads do not continue to increase with increasing size. Instead an
apparent initial increase in bending stresses is followed by a relative reduction.
Increasing body size alone, therefore, seems an unlikely explanation for the
observed architectural changes in cross-sectional morphology.
If increasing body size is insufficient to account for the ontogenetic pattern
documented, then differences in the orientation of those loadings must also be
important. Recent fossil evidence supports this conjecture. Horner &
Weishampel (1988) described embryonic and juvenile remains of two
euorni thopodans, Orodromeus makelai and Maiasaura peeblesorum. These animals
had large heads and small tails relative to body size, proportions unlike those of
fully grown individuals. Although no embryonic material of D . lettowvorbecki
exists, a large head-to-body size ratio can be inferred for D . lettowvorbecki
hatchlings given that the condition occurs in 0. makelai (a hypsilophodontid)
and M . peeblesorum (a hadrosaurid), two taxa which phylogenetically bracket
Dryosaurus (Fig. 1: Sereno, 1986; Weishampel & Heinrich, 1992). O n this basis
we hypothesize that the body centre of gravity in D . lettowvorbecki hatchlings was
cranial to the hip, and that this position shifted caudally during development.
What effect would a centre of gravity in front of the hip have on femoral
loadings and hatchling locomotion? This problem is illustrated schematically in
Fig. 9 and can be quantified by the expression
M=FxD
(5)
192
R. E. HEINRICH E T AL.
\
Moment = F x D
\
Figure 9. A schematic representation of D.lcttowvorbccki demonstrating the biomechanical effect of
the position of the centre of gravity on the bending stresses incurred by the femur. Given that the
forces exerted by muscles are identical, a centre of gravity well cranial to the hip (left) would
produce a larger moment acting about the femoral midshaft, resulting in larger bending stresses
than a centre of gravity positioned near the hip (right).
where M is the moment being generated about the femur; F is the mechanical
load approximated here by body weight; and D is the perpendicular distance
between the femoral midshaft and the mechanical load acting at the centre of
gravity. Although calculating actual bending moments about the femur would
require knowledge of the forces exerted by the appropriate muscles, Fig. 9
demonstrates the biomechanical importance of the position of the centre of
gravity for an animal locomoting on two legs. For a bipedal dinosaur then, the
greater the distance from the hip joint to the centre of gravity, the larger the
moment acting about the femur and the greater the bending stress on the
element. Since the centre of gravity was most cranial in the smallest animals, i.e.
hatchlings, and assuming they were bipedal, bending loads should have been
relatively greater in these animals than at any other stage of ontogeny. However,
none of the cross-sectional properties analysed here support this supposition. The
ratios found in femora of
increased percentage cortical area and larger Zmax/lmin
medium size both suggest that the relatively greatest femoral bending stresses
occurred in animals associated with medium size. How might this be accounted
for?
A centre of gravity positioned well in front of the hip may have made habitual
bipedality difficult, if not impossible for hatchlings. We suggest instead that
D. lettowvorbecki hatchlings were constrained by the position of their centre of
gravity to a quadrupedal stance during early neonatal life. It is postulated that,
as these animals grew to some threshold size, the combination of increasing body
and tail size effectively shifted the centre of gravity to a position more near the
LOCOMOTOR BIOMECHANICS OF DRYOSAURUS
I93
hip. That is, the tail became an adequate counter balance. At that time a
habitual bipedal posture would have been assumed.
Shifting from quadrupedal locomotion, where the body centre of gravity was
supported by four limbs, to bipedality, where body mass was distributed over
only two, would essentially double the mechanical loadings on the hindlimb.
Bending and compressional stresses would increase significantly, requiring
structural compensation to maintain acceptable safety factors. Over the smallmedium size transition, distinct and relatively dramatic architectural
modifications have been identified. These are ( 1 ) an increase in relative bone
mass and (2) an increase in the relative magnitude of greatest bending strength.
Since neither of these cross-sectional parameters increases with increasing length
among small femora, the abruptness of these changes in cross-sectional properties
fits a hypothesis of novel mechanical loadings acting on the femur at a specific
body size.
Modifications in femoral architecture that occur after the small-medium size
transition involve some changes in the distribution but not the relative amount
of bone. We suggest that given a quadrupedal-bipedal transition and a shifting
centre of gravity, craniocaudal bending stresses in femora of medium size were
relatively larger than at any other time during the life of a D . lettowvorbecki
individual. As these animals continued to increase in body size and the centre of
gravity moved closer to the hip, a relative reduction in the bending moments
acting about the femur resulted. Consequently relative craniocaudal bending
stress was reduced in the largest animals.
A quadrupedal-bipedal locomotor shqt
Assuming that D . lettowvorbecki hatchlings were obligate quadrupeds, it is of
some interest to decipher the amount of time that elapsed between hatching and
the onset of bipedalism. Estimating age from femoral length requires
ascertaining a rate of development in these animals, a problem made more
difficult because of the uncertainty as to whether dinosaurs were warm or coldblooded. We have attempted to encompass the range of possible growth rates for
D . lettowvorbecki by utilizing rates compiled for modern ecto- and endothermic
animals (Case, 1978). For phylogenetic reasons, growth rates of reptiles,
precocial and altricial birds have been considered. T o determine a speciesspecific growth rate for D . lettowvorbecki from the regressions presented by Case
(1978), adult body weight estimates of 56 and 70 kg were used (Table 3). The
growth rates calculated in this manner are provided in Table 8. If the femur
used to calculate these body weights is not that of a mature animal, or if the
method of calculation underestimates actual adult body weight, then the growth
rates presented in Table 8 constitute minimal values.
Since the architectural modifications of the small-medium size transition
coincide with femoral lengthening from c. 150 to 180 mm, estimating body
weights at these lengths enables age to be assessed using the formula:
Age =
Postnatal growth
Growth rate
where age is in days; postnatal growth is the difference between body weight at a
given femoral length minus weight at hatching (estimated to have been c. 0.5 kg
I94
R. E. HEINRICH ET AL.
TABLE8. Growth rates (gms day-') and associated weight (kg)-age (days) estimates for
D.lettowvorbecki. Abbreviation: Sm-Med Trans, small-medium transitional period (days)
Growth
rate
Weight
150 mm
Age
150 m m
Weight
180 m m
Age
180 m m
Sm-Med
Trans
Reptilian"
Precocial Bird"
Altricial Bird"
6.8
79.2
552.3
12.4
12.4
12.4
I750
150
22
19.8
19.8
19.8
2838
244
35
1088
94
13
Reptilianb
Precocial Birdb
Altricial Birdb
7.9
91.4
648.9
12.3
12.3
12.3
1494
I29
18
21.4
21.4
21.4
2709
234
33
1215
105
15
Model
"Growth rate based on estimated adult body weight of 56.6 kg; bgrowthrate based on estimated adult body
weight of 70.0 kg.
on the basis of comparisons to similar sized modern iguanas; Weishampel,
unpublished data); and growth rate values are those determined from the
regressions of Case (1978) as discussed above. Regression equations of weight
against femoral length obtained from the data of Table 3 were used to estimate
body weight of individuals whose femora were 150 and 180 mm in length
(Table 8). Finally, to obtain some idea of the amount of time required to cross
the small-medium transition, the age at femoral length 150 mm is subtracted
from that at 180 mm (Table 8).
Several generalizations can be made on the basis of these calculations. Clearly,
unless D.lettowvorbecki possessed growth rates comparable to those of modern
avian endotherms, any postulated transition from quadrupedality to bipedality
would have been preceded by several years of postnatal development (Table 8).
If D.lettowvorbecki growth did follow a n ectothermic pattern, the apparent
'abrupt' increase in percentage cortical area is merely an artefact of our size
classification scheme. Likewise, changes to the second moment of area properties
analysed would have occurred over a considerably greater period of time than
has been suggested here. Interpreting the biomechanical evidence in terms of an
ectothermic growth rate, however, is equivocal. We can think of no reason for
cross-sectional properties to undergo substantial alterations after several years of
growth. A locomotory shift in the second or third year of life is inconsistent with
functional and behavioural interpretations of D.lettowvorbecki made to date.
Given that dryosaurids were adapted for speed (Coombs, 1978; Galton, 1974,
1981; Thulborn, 1982), it seems unlikely that slower moving quadrupedal
individuals would have been accommodated by the swifter moving adults, yet
the taphonomic evidence at Tendaguru indicates that individuals of all sizes
were living in close approximation, if not herding (Russell et al., 1980). If the
architectural modifications found in the femora of Dryosaurus are related to a
locomotory shift from quadrupedality to bipedality, then growth rates must have
exceeded those of modern reptiles.
If the growth rate of D . lettowvorbecki fell somewhere between modern precocial
and altricial birds, then the initiation of bipedality (femoral length of c. 150 mm)
is estimated to have occurred within five months of hatching and potentially as
early as two and a half weeks. Devoting energy towards growth during early
ontogeny may well have been of selective advantage for a species that appears to
have travelled in large groups. This would also imply that posthatching parental
LOCOMOTOR BIOMECHANICS OF DRYOSAURUS
195
care was important during at least early ontogeny of D . lettowvorbecki, as has been
suggested for both hadrosaurids (Horner, 1984, Horner & Weishampel, 1988)
and hypsilophodontids (Winkler & Murry, 1989). O n the basis of the evidence
presented here, we speculate that growth rates in Ornithopoda were more
similar to modern endotherms than ectotherms and that all femora categorized
in this study as small or medium represent animals in their first year of growth.
Those femora classified as large are thought to represent adult or subadult
members of the species.
SUMMARY
Ontogenetic changes in femoral morphology and locomotion were analysed in
the iguanodontian dinosaur Dryosaurus lettowvorbecki using cross-sectional data
and applying principles of beam theory. The results presented here suggest that
locomotor ontogeny in D . lettowvorbecki was more complicated than has generally
been recognized. The percentage cortical area (a measure of the relative amount
of bone) increases abruptly over a relatively short period during early ontogeny
and then remains uniform during subsequent increases in body size.
Modifications in cross-sectional shape also occur with increasing size, as
demonstrated by differences in second moment of area ratios. The patterns of
change in these properties indicate that the orientation of mechanical loadings
acting on the femur of D . lettowvorbecki differed at various stages of growth and
development. It is suggested that the alterations in femoral architecture
described here reflect a shift from quadrupedality to bipedality early in the
ontogeny of this animal.
ACKNOWLEDGEMENTS
We gratefully acknowledge Frank Westphal (Institut f i r Geologie und
Palaontologie, Universitat Tubingen, Germany) for permission to study the
Dryosaurus specimens and George Barrowclough and Allison Andors (American
Museum of Natural History) for access to rhea femora. L. Witmer and an
anonymous reviewer provided useful comments on a n earlier version of this
manuscript. Funding was provided in part by a Natural Science and
Engineering Research Council of Canada Postgraduate Scholarship and Lucille
B. Markey Scholarship to REH, and NSF grant support (EAR-8719878,
EAR-9004458) and a Visiting Professorship (through Sonderforschungsbereich
230) at the Universitat Tubingen, Germany, to DBW.
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