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Estimating maximum running speeds using evolutionary robotics


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Maximum running speed is an important locomotor parameter for many animals-predators as well as prey-and is thus of interest to palaeobiologists wishing to reconstruct the behavioural ecology of extinct species. A variety of approaches have been tried in the past including anatomical comparisons, bone scaling and strength, safety factors and ground reaction force analyses. However, these approaches are all indirect and an alternative approach is to create a musculoskeletal model of the animal and see how fast it can run. The major advantage of this approach is that all assumptions about the animal's morphology and physiology are directly addressed, whereas the exact same assumptions are hidden in the indirect approaches. In this paper, we present simple musculoskeletal models of three extant and five extinct bipedal species. The models predict top speed in the extant species with reasonably good agreement with accepted values, so we conclude that the values presented for the five extinct species are reasonable predictions given the modelling assumptions made. Improved musculoskeletal models and better estimates of soft tissue parameters will produce more accurate values. Limited sensitivity analysis is performed on key muscle parameters but there is considerable scope for extending this in the future.
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Estimating dinosaur maximum running speeds
using evolutionary robotics
William Irvin Sellers
and Phillip Lars Manning
Lecturer in Integrative Vertebrate Biology, Faculty of Life Sciences, University of Manchester,
Jackson’s Mill, PO Box 88, Sackville Street, Manchester M60 1QD, UK
Lecturer in Palaeontology, School of Earth, Atmospheric and Environmental Sciences,
University of Manchester, Manchester M13 9PL, UK
Maximum running speed is an important locomotor parameter for many animals—predators as well as
prey—and is thus of interest to palaeobiologists wishing to reconstruct the behavioural ecology of extinct
species. A variety of approaches have been tried in the past including anatomical comparisons, bone scaling
and strength, safety factors and ground reaction force analyses. However, these approaches are all indirect
and an alternative approach is to create a musculoskeletal model of the animal and see how fast it can run.
The major advantage of this approach is that all assumptions about the animal’s morphology and
physiology are directly addressed, whereas the exact same assumptions are hidden in the indirect
approaches. In this paper, we present simple musculoskeletal models of three extant and five extinct
bipedal species. The models predict top speed in the extant species with reasonably good agreement with
accepted values, so we conclude that the values presented for the five extinct species are reasonable
predictions given the modelling assumptions made. Improved musculoskeletal models and better estimates
of soft tissue parameters will produce more accurate values. Limited sensitivity analysis is performed on key
muscle parameters but there is considerable scope for extending this in the future.
Keywords: locomotion; computer simulation; bipedalism; running
Chasing down prey is a vital factor in the lives of extant
predators, as is the avoidance of being captured for prey
animals. It is therefore of little surprise that speed
estimation is of such interest to palaeobiologists who
study dinosaurs. The range of predicted speeds is as
variable as the methods chosen with some authors
favouring high speeds (Paul 1988, 1998) while others
prefer moderate (Farlow et al. 1995) or low speeds
(Alexander 1989; Hutchinson & Garcia 2002). Current
analysis techniques are based on anatomical comparisons,
bone scaling and strength, risk factors and ground reaction
forces, and a recent review (Hutchinson & Gatesy 2006)
summarizes the current state of the art and concludes,
among other things, that a ‘rigorous dynamic simulation
of a moving dinosaur, one encompassing all motions and
forces, cannot yet plausibly be done’. However, such an
approach is clearly the best option because it both
explicitly requires a complete set of modelling assump-
tions and is conceptually simple. It requires a musculos-
keletal model to be constructed necessitating assumptions
about skeletal geometry, body mass and mass distribution,
together with muscle and tendon properties. These
properties all have a considerable effect on locomotor
performance and all that happens in any quantitative
technique that does not make explicit assumptions about
their values is that they will be implicitly scaled from
whatever reference species are employed. This is likely to
be suboptimal given that some of these values can often be
inferred from fossil evidence directly, and unknown values
need to be clearly identified so that their importance to the
final result can be assessed.
It is now possible to produce highly detailed muscu-
loskeletal models and these can be used for fossil
locomotor reconstruction ( Nagano et al. 2005) and such
could be constructed for dinosaur species. However, such
complex models require a great deal of work to construct
and good predictive results can be obtained from rather
simpler models ( Ya m a z a k i et al. 1996; Ogihara &
Yamazaki 2001; Sellers et al. 2003, 2004, 2005). These
latter models have the great advantage of requiring no
knowledge of locomotor kinematics and allow the
generation of a range of gaits de novo, which maximize
or minimize some global optimization parameter such as
speed or energy consumption. These models use an evolu-
tionary robotics approach where so-called evolutionary
algorithms are used to find muscle activation patterns
(Nolfi & Floreano 2000). However, such models are still
computationally demanding. It is perfectly possible to
solve the mechanical constraints of the system (internal
forces generated by muscles and the spring recoil of
tendons, segment movement constraints imposed by
joints, external forces generated by gravity and ground
reaction through contacts with the environment) in more
or less real time on a modern computer using freely
available software. However, finding the activation pattern
of the muscles that produces high-quality gait is extremely
challenging. Even a simple model such as ours with 12
muscles and 5 activation levels per step (half a gait cycle)
leads to 61 dimensions in the search space, which is
Proc. R. Soc. B (2007) 274, 2711–2716
Published online 21 August 2007
Electronic supplementary material is available at
1098/rspb.2007.0846 or via
* Author for correspondence (
Received 23 June 2007
Accepted 24 July 2007
2711 This journal is q 2007 The Royal Society
consequently far too large to search exhaustively. For-
tunately, using a parallel implementation of a suitable non-
exhaustive, evolutionary search procedure such as a
genetic algorithm means that even this is a tractable
problem that can be solved in days or weeks on a modern
It is important that any model attempting to predict the
behaviour of extinct species be tested on extant animals.
Thus, a model attempting to predict the top speeds of a
range of fossil bipedal dinosaurs should also be tested using
equivalent data from living bipeds. However, there is
remarkably little high-quality top-speed data for any living
species other than those actively involved in racing, such as
humans, horses and greyhounds (Alexander 1989) and
even elephants (Hutchinson et al. 2006). The values used
for comparison in this paper (Alexander et al. 1979; Patak &
Baldwin 1998) are based on anecdotal observations and
need to be treated with some caution since there is no way of
knowing whether these animals were actually running as
fast as they could. The anatomy, posture and gait of bipedal
dinosaurs is unique, with no equivalent modern analogue
available for the comparison of locomotor abilities. The
successful testing and validation of the computational
approach using extant species indicates that it is possible to
generate a robust model applicable to extinct species.
Our previous models (Sellers et al. 2003, 2004, 2005) used the
YNAMECHS simulation library ( McMillan et al. 1995).
However, this system has very limited support for contacts
between the simulation and the environment so, for this
model, we switched to using the open dynamics engine (ODE; to provide the physics simulation. This is
again a CCC library so we were able to modify our existing
AITSYM code to use the new simulator. The models
themselves were specified in a custom XML format that
defined the necessary segments, joints, muscles, tendons and
contacts. To perform the optimization, we modified our
existing distributed genetic algorithm system to support the
new format. While it is difficult to compare the results using the
two systems, it is certainly our impression that ODE is both
faster and more numerically stable than D
YNAMECHS in this
application. Communication between the optimization code
and the simulation code was performed using sockets via the
PTypes abstraction library (
to allow easy portability over the variety of computer systems
available to us, and to allow the code to take advantage of
multiple, remote computer clusters, using over 300 processor
cores when available. Graphical display and user interaction
used the GLUI OpenGL widget library (http://glui. to again allow easy portability. The muscle
model was derived from Minetti & Alexander (1997) to
generate both eccentric and concentric velocity-dependent
force characteristics extended with the addition of Hill-style
linear serial and parallel elastic elements (Hill 1938). The
combined musculotendinous unit is solved analytically and
exported as a standard C function using M
ATHEMATICA (http:// that greatly aids numerical stability. A
cylindrical wrapping operator was used where necessary to
maintain the muscle and tendon path around joints.
A set of three extant and five extinct bipeds were modelled.
These are two-dimensional models with a rigid trunk, and left
and right thigh, shank and composite foot segments. These
segments are linked using three hinge joints per limb. The
segment properties are based on published data (Hutchinson
2004a,b) with the single composite foot segment combining
the metatarsus and foot with all floor contact occurring at the
distal end of the metatarsus. The species were chosen to cover a
reasonable size range and are listed in table 1. The published
dataset does not include moments of inertia so these were
calculated by modelling the segments as geometric shapes
chosen to match the published lengths, masses and centres of
mass. Conic segments were used for the limb segments and
back-to-back circular cones were used for the trunk. Muscle
fibre lengths, physiological cross-section areas (PCSAs) and
moment arms were available for limb extensors (Hutchinson
2004a,b), and these were used to create appropriate muscle
paths on the model. Cylindrical wrapping operators were used
for the knee and ankle extensors. Limb flexors were assumed to
have the same properties, but only 59% of the mass was based
on human proportions ( Pierrynowski 1995) but not dissimilar
from the values found in other species (Alexander et al. 1979;
Maloiy et al. 1979; Bennett 1996).
The extensor muscle mass was limited to 5% of the body
mass per joint (Hutchinson 2004b) and all muscles were
considered to act over a single joint, with each joint having a
single flexor and extensor. Muscle volume was calculated
using the standard value of 1056 kg m
for muscle density
(Winter 1990) and PCSA was calculated by dividing this
volume by the fibre length. Force per unit area was chosen to
be 300 000 N m
(Hutchinson 2004b), but there are other
values in the literature: Umberger et al. (2003) use
250 000 N m
, and Alexander (2003) reports an in vitro
maximum value of 360 000 N m
for frog and
330 000 N m
for cat for parallel-fibred leg muscles.
Zheng et al. (1998) recommend a value of 400 000 N m
for human quadriceps and Pierrynowski (1995) suggests
350 000 N m
. There is a similarly large range for
maximum contraction speed. Winter (1990) suggests values
from 6 to 10 times the muscle’s resting length per second for
humans. This value is clearly highly dependent on both the
Table 1. Data for the species used in the study and key simulator outputs.
mass (kg) speed (m s
) cycle time (s) stride length (m) leg length (m) l/hu
Dromaius 27.2 13.3 0.441 5.865 0.864 6.79 20.89
Struthio 65.3 15.4 0.370 5.688 1.086 5.24 22.23
Homo 71 7.9 0.475 3.732 0.994 3.75 6.33
Compsognathus 3 17.8 0.106 1.894 0.179 10.58 180.43
Velociraptor 20 10.8 0.284 3.058 0.489 6.25 24.18
Dilophosaurus 430 10.5 0.579 6.092 1.350 4.51 8.36
Allosaurus 1400 9.4 0.615 5.795 1.750 3.31 5.17
Tyrannosaurus 6000 8.0 1.199 9.559 3.089 3.09 2.10
2712 W. I. Sellers & P. L. Manning Dinosaur running
Proc. R. Soc. B (2007)
fibre-type composition of the muscle and the temperature.
Westneat (2003) reports a range of values for fishes from 3 to
10 s
for different fibre types and Umberger et al. (2003)
recommend values of 12 s
for fast twitch and 4.8 s
slow twitch. A value of 8 s
was chosen to represent a mixed-
fibred muscle. Joint limits were set to extreme values for all
species since these limits are not generally available and the
range of motion permitted by the muscle and tendon lengths
specified should be sufficient to limit joint excursion. Serial
and parallel elastic constants were set so that the serial
element strain was 6% at the maximum isometric contraction
and parallel element strain was 60% for the same force as
used in a previous model (Sellers et al. 2005), and the lengths
of the tendons were scaled based on average human
1995). Muscle attachment points were arranged so that the
muscle plus tendon was at its resting length in the published
mid-stance positions (Hutchinson 2004a,b), so that the
moment arm was approximately correct. This procedure
was performed automaticallyusingacustomM
program ( The full specifi-
cation for each of the models is included as human-readable
XML files as electronic supplementary material.
Gait is generated using a distributed genetic algorithm
optimization system using a genome that represents the gait
cycle duration and the muscle activation levels at 10 time
periods through the gait cycle. The genome contains 61
parameters representing the cycle time and the 5 activation
levels for 12 muscles for half a gait cycle. The left–right
activation levels are simply swapped for the other half of the
gait cycle. This is implemented as a client–server architecture
with the simulators running on multiple client machines and a
central server that gathers the results from the multiple
simulations. The starting conditions used published mid-
stance positions with a trunk forward velocity giving a Froude
number of approximately 1.5 (which equates to a medium
running speed) using the formula velocityZ1.5!(9.81!
(thigh lengthCshank lengthCmetatarsus length)) following
Alexander (2003) but using leg length as a proxy for hip
height. Forward velocities for the support leg segments
decreased to zero depending on the height of the segment
from the ground, and the velocities of the swing-leg segments
increased to double the trunk forward velocity again
depending on height. The fitness criterion used for the
genetic algorithm optimization was the maximum forward
distance achieved in a fixed time (3 s for most species but 5 s
for the Allosaurus and Tyrannosaurus to allow a reasonable
number of complete gait cycles). Thus, runs where the animal
fell over scored very badly and the runs with the highest
average speed would score the highest. The population was
1000 and up to 1000 generations were allowed in each run
unless a steady maximum average forward velocity was
achieved earlier. This procedure was repeated at least five
times until a good quality run was obtained. Runs were
judged to be good quality when the animal did not fall over
within the time limit and managed at least 15 m forward
1.5 (a)
( f )
2.0 2.5
2.5 3.0 3.5 4.0 4.5 5.0
3.0 3.5 4.0 4.5
1.0 1.5 2.0 2.5 3.0
4 6 8 10121416
Figure 1. Overlay images of the simulated gaits. All scales are in metres and 10 images are generated per gait cycle. (a) Dromaius;
(b) Struthio ;(c) Homo;(d ) Compsognathus;(e) Velociraptor;(f ) Dilophosaurus; ( g) Allosaurus;(h) Tyrannosaurus.
Dinosaur running W. I. Sellers & P. L. Manning 2713
Proc. R. Soc. B (2007)
movement. The best run was then used as the basis for a gait
morphing procedure (Sellers et al. 2004), where the best
results for a previous run were used to generate the starting
conditions for subsequent runs. This procedure was repeated
at least 20 times to obtain the highest speed estimate for each
species. An individual simulation ran in approximately real
time but at least 1 000 000 repeats were needed to generate
the optimized running gait for each species.
All the models generated high-quality running gaits that
were stable over the whole simulation period as shown in
figure 1. This figure shows a series of snapshots of the
generated gaits at 1/10 cycle time intervals. The lines
connect the joint centres, except for the foot line that is
drawn between the ankle joint and the contact point on
the metatarsal head and the trunk line that is drawn from
the hip joint to the position of the centre of mass of the
trunk segment.
The top speeds achieved for each species are shown in
table 1 and there is reasonably good correspondence for
the extant species between the speeds generated by the
model and those cited in the literature: Dromaius 14 m s
(Patak & Baldwin 1998); Struthio 17 m s
et al. 1979); and Homo 10 m s
(Alexander 1989). To
investigate whether mass alone is a good predictor of top
speed, we plotted the top speed against body mass in
figure 2, which shows a monotonic reduction in speed for
the extinct bipeds but not for the extant species. The
extinct species have a consistent 15% of body mass as
muscle mass for each limb, whereas the value for Dromaius
is 15.5%, for Struthio is 12.2% and for Homo is 10.6%, so
this alone does not explain the speed differences seen in
the extant species.
Similarly, there is a well-known empirical relationship
between speed, leg length and stride length based on
Froude numbers that is often used for trackway analysis:
, where l is the stride length; h is a
characteristic length (in this case, leg length); u is the
forward velocity and g is the acceleration due to gravity
(Alexander 1976). This information is shown in table 1
where the characteristic length used is leg length (the sum
of thigh, shank and metatarsus lengths). Figure 3 shows a
plot of l/h against u
/gh for the models to compare the
simulations against the empirical relationship demonstrat-
ing extremely good agreement.
A key area of uncertainty in our model is the choice of
muscle parameters, so a simple sensitivity analysis was
performed. The maximum force available per muscle is
directionally proportional to the mass of muscle (F
dM/rl, where d is the force per unit area; M is the muscle
mass; r is the muscle density and l is the muscle fibre
length). Of these the greatest uncertainty is likely to be the
value of muscle mass (Hutchinson & Garcia 2002); hence,
this was varied over a range of 2.5–7.5% per joint, which
should encompass the probable variation. Similarly, V
known to vary widely and it may scale negatively with body
mass (Medler 2002), although there is little information
about contraction velocities in large animals. Values
between 4 and 12 s
were tested to both encompass
the probable range and give the same degree of variation
(G50%) as used for muscle mass. The results of the
sensitivity analysis on the Tyrannosaurus rex model are
shown in figure 4. Both parameters have an approximately
linear effect over this range, and the effect of muscle mass is
approximately double the effect of contraction velocity.
However, the model was unable to sustain locomotion
when the muscle mass was reduced to 2.5% per joint.
Multibody dynamic simulations using evolutionary
robotic optimization approaches appear to provide reliable
estimates for the maximum running speeds of extant
animals. Multiple simulations with small changes in both
starting conditions and muscle activation patterns pro-
duced highly consistent estimates. Maximum running
speed is a highly variable character and difficult to estimate
in any animal. The observed speed is always a lower bound
estimate of maximum speed since the animal might not be
running as fast as it can. In addition, many quoted values
for running speed are based on observations made in less
than ideal conditions, which may lead to considerable
10 000
body mass (kg)
max s
eed (m s
Figure 2. Graph showing the body mass and top speeds of the
1 10 100 1000
l /h
Figure 3. Graph showing the Froude number, stride length
relationship for the simulations and also the empirical
relationship (Alexander 1976).
2714 W. I. Sellers & P. L. Manning Dinosaur running
Proc. R. Soc. B (2007)
errors (Garland 1983; Alexander 1989). Even for humans,
the situation is not straightforward: while 200 m sprint
averages are in excess of 10 m s
, the peak speed reached
can be in excess of 12 m s
(Brown et al. 2004), and these
are values for elite athletes who have considerably greater
leg muscle mass than the average values used in our
simulations. Tests on more general female athletes from
other sports give typical speeds of approximately 6 m s
with short bursts of less than 8 m s
(Brown et al. 2004).
Our estimates are broadly in line with other biomechanical
estimation techniques, which predict 18 m s
for ostrich
and 13 m s
for emu (Blanco & Jones 2005). It is self-
evident (and has been demonstrated in various models;
Hutchinson & Garcia 2002; Sellers & Paul 2005) that
changes in muscle mass will affect maximum speed and
this is a major source of uncertainty in these predictions.
However, we would propose that limits can be set using
functional bracketing to set minimum and maximum values.
The 15% value used here is similar to that found in large
extant bipeds and as our sensitivity analysis shows, an
appreciably smaller value does not even allow the animal
to walk. An upper limit would be harder to estimate but
one approach that is possible (even if computationally
expensive) is to calculate the bone loading during high-
speed locomotion and compare the safety factors with
those known for extant animals (Alexander 1997). For
these models, the general decrease in top speed as body
size increases is certainly in line with predictions made
elsewhere (Hutchinson 2004b) and the predicted top
speeds, with the possible exception of 17.8 m s
Compsognathus, are not exceptional. However, we would
expect that the actual top speeds are likely to be somewhat
higher than those given here since it is probable that
improvements could be made by altering the distribution
of the leg muscle and optimizing the fibre and tendon
lengths. In addition, all the models are relatively simplistic
and lack multiple-joint muscles and accessory elastic
storage structures, which when combined should increase
the maximum speed. Our initial sensitivity analysis shows
that changing our assumptions about the muscles has a
considerable effect on our estimates. A 50% increase in
muscle mass leads to a 60% increase in top speed and a
50% decrease stops the model working at all. Similarly, a
50% increase in maximum contraction velocity leads to
a 30% increase in top speed with a 50% decrease leading
to a 20% decrease. However, there is considerable scope
for further sensitivity analyses such as variation in muscle
attachment points (Sellers & Crompton 2004) and the
effects of perturbation ( Wilson et al. in press).
The kinematics generated by the models show a wide
range of variation. It is very hard to judge the probable
accuracy of these values without subject-specific kinematic
matching, and in any case with such simple models it may
be optimistic to expect high-quality kinematics. In
particular, we would expect better estimates of muscle
and tendon lengths (and to a lesser extent joint limits) to
have a considerable effect on kinematics. However, as
shown in figure 3, the mechanical accuracy of the
simulations is high. The models represent a wide range
of Froude numbers and follow the predicted stride length
relationship very closely indeed. Overall, simulations such
as ours illustrate how an animal could have moved given its
physiological and morphological constraints, and perhaps
also indicate probable movement patterns, but we are still
some way off saying that this is how it must have moved.
There are a number of possible future developments in
animal gait simulation. Our models already allow us to
calculate the energetic costs of gaits in some detail. This
includes estimates of metabolic and mechanical power,
including active contraction and passive elasticity contri-
butions on a muscle by muscle basis. However, these
predictions need better validation and this can be achieved
using a combination of species-specific modelling and
in vivo physiological measurement. As computers get
faster and cheaper, it would be useful to increase the
biofidelity of the models by adding more muscles,
including the forelimb in the simulation, and having
considerably greater detail in the feet and the interactions
with the substrate. In addition, reconstruction improve-
ments such as new estimates of inertial parameters
(Hutchinson et al. 2007) and better comparative ana-
tomical and physiological data will certainly help. In
particular, very little comparative data are available on the
elastic properties of muscles. Similarly, the addition of a
feedback-based control system will increase the range of
locomotor activities that can be encompassed and allow
this technology to look at non-continuous activities, such
as starting, stopping, cornering and complex movements
such as sitting and standing up.
We would like to thank Prof. Robin Crompton for allowing
access to his Beowulf Cluster to perform the required
simulations; Cliff Addison for arranging access to the
NW-Grid; funding from BBSRC, NERC and the Leverhulme
Trust; and two anonymous referees for their helpful
comments on the original draft of the manuscript.
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2716 W. I. Sellers & P. L. Manning Dinosaur running
Proc. R. Soc. B (2007)
... This study made use of a FPUA value of 300,000 N m À2 . In the literature, this value has been applied to dinosaurian models of varying sizes and inferred locomotor modes including a sauropod (Sellers et al., 2013), and large and small theropod Sellers et al., 2017;Sellers & Manning, 2007) however it is clear that a case can be made for a range of both considerably lower and higher values (for discussion see Alexander, 2003). ...
... Following the initial set of simulations, intended to explore gait repertoire before further constraints were imposed, both bipedal and quadrupedal gaits were recovered. The fact that the model did not exclusively produce bipedal gaits in spite of its relatively caudal COM at the very least capable of reaching 6.5 ms À1 (Bishop, Falisse, et al., 2021, p. 202) and 10.5 ms À1 (Sellers & Manning, 2007), respectively, which would exceed what our model suggests Scutellosaurus was capable of as a quadruped. Similarly, the calculated balance metric shows no advantage of the quadrupedal gait with higher values found for the bipedal gaits. ...
... As well as potentially enhancing the model's quadrupedal ability, the muscle mass distribution used may also have limited bipedal ability by allotting too little power to the hindlimbs. Previous simulations have attempted to quantify the effect that changing muscle mass has on achievable top speed (Bates et al., 2010;Sellers & Manning, 2007), and ideally, this type of sensitivity analysis needs to be repeated with dinosaur models of different sizes and locomotor modes. ...
A reversion to secondary quadrupedality is exceptionally rare in nature, yet the convergent re-evolution of this locomotor style occurred at least four separate times within Dinosauria. Facultative quadrupedality, an intermediate state between obligate bipedality and obligate quadrupedality, may have been an important transitional step in this locomotor shift, and is proposed for a range of basal ornithischians and sauropodomorphs. Advances in virtual biomechanical modeling and simulation have allowed for the investigation of limb anatomy and function in a range of extinct dinosaurian species, yet this technique has not been widely applied to explore facultatively quadrupedal gait generation. This study places its focus on Scutellosaurus, a basal thyreophoran that has previously been described as both an obligate biped and a facultative quadruped. The functional anatomy of the musculoskeletal system (myology, mass properties, and joint ranges of motion) has been reconstructed using extant phylogenetic bracketing and comparative anatomical datasets. This information was used to create a multi-body dynamic locomotor simulation that demonstrates that whil quadrupedal gaits were physically possible, they did not outperform bipedal gaits is any tested metric. Scutellosaurus cannot therefore be described as an obligate biped, but we would predict its use of quadrupedality would be very rare, and perhaps restricted to specific activities such as foraging. This finding suggests that basal thyreophorans are still overwhelmingly bipedal but is perhaps indicative of an adaptive pathway for later evolution of quadrupedality.
... Biomechanical analyses were used to discuss the predatory capabilities of large theropods in speculative scenarios (Krauss & Robinson, 2013;Henderson & Nichols, 2015;Blanco et al., 2018). The running ability of Tyrannosaurus rex Osborn, 1905 and other large theropods has been debated intensely (Alexander, 1985;Bakker, 1986;Farlow et al., 1995;Paul, 1998Paul, , 2010Blanco & Mazzetta, 2001;Hutchinson & García, 2002;Sellers & Manning, 2007;Sellers et al., 2009). Several biomechanical analyses concluded that adult large theropods, such as Tyrannosaurus rex, could not run, and their top speed was probably 10 m/s at most (Hutchinson & García, 2002;Hutchinson, 2004;Hutchinson et al., 2005;Gatesy et al., 2009;Sellers et al., 2017;Hutchinson, 2021). ...
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Biomechanical analyses suggest that adult large theropods, such as Tyrannosaurus rex, could not run, and its top speed probably was at most 10 m/s. This probably implied a speed disadvantage of adult T. rex compared with some smaller potential prey. Living predators at a disadvantage owing to speed or manoeuvrability sometimes use the environment or special techniques to minimize those differences. Here, I made a theoretical analysis of the possibility that adult large theropods, such as T. rex, could occasionally pursue prey in water to take advantage of their body size. There are arguments based on scaling laws to support this hypothesis. To give an example, I applied a biomechanical model to estimate the speed in a shallow-water environment of adult T. rex and two smaller dinosaurs, a juvenile Edmontosaurus annectens and Struthiomimus sedens. I conclude that by wading or swimming, the adult T. rex would have been faster than smaller prey in water. I also suggest that in water, adult large theropods, such as T. rex, were able to use a running gait that was probably precluded on land. Finally, I propose a near-shore hunting scenario for adult T. rex and other full-grown large theropods.
... As a result, measuring distances between tracks and track length has been a crucial component of characterizing track sites (e.g., Farlow, 1981;Kozu et al., 2017;Moreno et al., 2012;Navarro-Lorbés et al., 2021). More recently, evolutionary robotics and biomechanical modeling approaches have been employed with body fossils to assess both gait and running speed (Bates et al., 2012;Hutchinson, 2004;Sellers & Manning, 2007). Such methods complement direct evidence from trackways, which may be problematic in predicting locomotor speed and gait when used singularly (Marmol-Guijarro et al., 2020), granting paleobiologists an unprecedented view into nonavian dinosaur locomotor behavior. ...
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Using morphometrics to study nonavian dinosaur fossils is a practice that predates the origin of the word "dinosaur." By the 1970s, linear morphometrics had become established as a valuable tool for analyzing intra- and interspecific variation in nonavian dinosaurs. With the advent of more recent techniques such as geometric morphometrics and more advanced statistical approaches, morphometric analyses of nonavian dinosaurs have proliferated, granting unprecedented insight into many aspects of their biology and evolution. I outline the past, present, and future of morphometrics as applied to the study of nonavian dinosaurs zeroing in on five aspects of nonavian dinosaur paleobiology where morphometrics has been widely utilized to advance our knowledge: systematics, sexual dimorphism, locomotion, macroevolution, and trackways. Morphometric methods are especially susceptible to taphonomic distortion. As such, the impact of taphonomic distortion on original fossil shape is discussed as are current and future methods for quantifying and accounting for distortion with the goal of reducing the taphonomic noise to biological signal ratio. Finally, the future of morphometrics in nonavian dinosaur paleobiology is discussed as paleobiologists move into a "virtual paleobiology" framework, whereby digital renditions of fossils are captured via methods such as photogrammetry and computed tomography. These primary data form the basis for three-dimensional (3D) geometric morphometric analyses along with a slew of other forms of analyses. These 3D specimen data form part of the extended specimen and help to democratize paleobiology, unlocking the specimen from the physical museum and making the specimen available to researchers across the world.
... Tracks are a record of dinosaurs moving, with the space of the print and relative stride length making it possible to estimate how fast the dinosaurs moved and their geographical distribution. In addition, ichnology enhances the paleo-ecosystems and demographic knowledge of the area (Lockley and Hunt 1995;Lockley and Meyer 2000;Sellers, and Manning 2007). A quantitative assessment reveals high scientific value, high educational value, and moderate touristic value due to its easy accessibility and uniqueness (Tables 1, 2, 3). ...
The Hin Lat Pa Chad geosite represents the diversity of dinosaurs. Located in the Khon Kaen National Geopark (Northeastern Thailand) and part of the Khorat Plateau, this geosite displays the footprints of small theropods Carmelopodus isp. and orni-thischians Neoanomoepus isp. in the Phra Wihan Formation, deposited during the Early Cretaceous (Berriasian-Barremian) epoch. This study aims at assessing the scientific, educational, and touristic value of these footprints as well as the risk of degradation. In addition, researchers have proposed a conservation plan to protect the dinosaur footprints at the Hin Lat Pa Chad geosite. According to the evaluation, the Hin Lat Pa Chad geosite is of high scientific, moderate educational, and touristic value while being at high risk of deterioration. When considering the surrounding environment, the most apparent factors affecting deterioration were found to be climatic conditions (humid subtropical climate), stream patterns, road construction, and anthropic activities. The geoconservation approach is adopted in this study to change the flow direction to bypass the channel out of the geosite and remove the construction sediment from the surrounding area while constantly monitoring and enhancing geoeducation development.
... Fundamentally, all qualitative and quantitative inferences about how extinct archosaurs moved to depend upon some understanding of the magnitude of forces their limbs might have generated. Recent approaches have tried abstracting 'antigravity' and other muscles acting around joints to general masses, pennation angles and fascicle lengths scaled from extant taxa (e.g. Bates et al., 2010;Gatesy et al., 2009;Hutchinson, 2004aHutchinson, , 2004bHutchinson & Garcia, 2002;Sellers & Manning, 2007;Sellers et al., 2013) or even partitioning total muscle masses into individual muscle masses or other parameters Sellers, Pond, et al. 2017). Snively et al. (2019 estimated hip muscle areas in theropod dinosaurs for approximating moment-generating capacity useful in turning, assuming that PCSA and AA were consistently related across muscles and taxa. ...
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In vertebrates, active movement is driven by muscle forces acting on bones, either directly or through tendinous insertions. There has been much debate over how muscle size and force are reflected by the muscular attachment areas (AAs). Here we investigate the relationship between the physiological cross-sectional area (PCSA), a proxy for the force production of the muscle, and the AA of hindlimb muscles in Nile crocodiles and five bird species. The limbs were held in a fixed position whilst blunt dissection was carried out to isolate the individual muscles. AAs were digitised using a point digitiser, before the muscle was removed from the bone. Muscles were then further dissected and fibre architecture was measured, and PCSA calculated. The raw measures, as well as the ratio of PCSA to AA, were studied and compared for intra-observer error as well as intra- and interspecies differences. We found large variations in the ratio between AAs and PCSA both within and across species, but muscle fascicle lengths are conserved within individual species, whether this was Nile crocodiles or tinamou. Whilst a discriminant analysis was able to separate crocodylian and avian muscle data, the ratios for AA to cross-sectional area for all species and most muscles can be represented by a single equation. The remaining muscles have specific equations to represent their scaling, but equations often have a relatively high success at predicting the ratio of muscle AA to PCSA. We then digitised the muscle AAs of Coelophysis bauri, a dinosaur, to estimate the PCSAs and therefore maximal isometric muscle forces. The results are somewhat consistent with other methods for estimating force production, and suggest that, at least for some archosaurian muscles, that it is possible to use muscle AA to estimate muscle sizes. This method is complementary to other methods such as digital volumetric modelling.
... Its use in paleontology has grown over the last 25 years, particularly in paleoanthropology with the first models attempting to generate movements based on fossil morphology appearing in the late 1990s (Crompton et al., 1998;Kramer, 1999) followed by muscle driven models in the early 2000s (Sellers et al., 2004(Sellers et al., , 2005Nagano et al., 2005;Ogihara and Yamazaki, 2006). Other vertebrates have also been simulated, starting with very simple 2D dinosaur models (Sellers and Manning, 2007) which were rapidly extended to 3D , with increasing sophistication in terms of anatomical realism and including additional mechanical modalities to reduce the uncertainty of the predictions (Sellers et al., 2017). Whilst there are plenty of non-locomotor studies using MDA [for review see Lautenschlager (2020)], there are far fewer on locomotion. ...
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Multibody dynamic analysis (MDA) has become part of the standard toolkit used to reconstruct the biomechanics of extinct animals. However, its use is currently almost exclusively limited to steady state activities such as walking and running at constant velocity. If we want to reconstruct the full range of activities that a given morphology can achieve then we must be able to reconstruct non-steady-state activities such as starting, stopping, and turning. In this paper we demonstrate how we can borrow techniques from the robotics literature to produce gait controllers that allow us to generate non-steady-state gaits in a biologically realistic quadrupedal simulation of a chimpanzee. We use a novel proportional-derivative (PD) reach controller that can accommodate both the non-linear contraction dynamics of Hill-type muscles and the large numbers of both single-joint and two-joint muscles to allow us to define the trajectory of the distal limb segment. With defined autopodial trajectories we can then use tegotae style locomotor controllers that use decentralized reaction force feedback to control the trajectory speed in order to produce quadrupedal gait. This combination of controllers can generate starting, stopping, and turning kinematics, something that we believe has never before been achieved in a simulation that uses both physiologically realistic muscles and a high level of anatomical fidelity. The gait quality is currently relatively low compared to the more commonly used feedforward control methods, but this can almost certainly be improved in future by using more biologically based foot trajectories and increasing the complexity of the underlying model and controllers. Understanding these more complex gaits is essential, particularly in fields such as paleoanthropology where the transition from an ancestral hominoid with a diversified repertoire to a bipedal hominin is of such fundamental importance, and this approach illustrates one possible avenue for further research in this area.
... Para calcular el índice de velocidad, se utilizaron varios estimadores para poder comparar los valores aproximados, y que se calcula como: = √ • ℎ • Donde V es la velocidad en m/s; Fr es el número de Froude (n.b., número adimensional que permite eliminar el tamaño relativo de los cálculos de velocidad; ver Dececchi et al., 2020); h es la altura hasta la cadera, que es el producto de la longitud total del miembro posterior por 0,8 (n.b., que corresponde al índice de flexión que se da en las aves terrestres modernas y valores similares en terópodos); y g, que corresponde a la gravedad. Para aquellos taxones con una masa corporal menor a 1000 kg, se calcula un rango de valores de Froude que va desde 0,25 a 15 con el objetivo de documentar un amplio rango de comportamientos que van desde una marcha lenta hasta la velocidad máxima alcanzada en terópodos (Cottam et al., 1942;Hutchinson y Garcia, 2002;Sellers y Manning, 2007;Kim y Huh, 2010;Kim et al., 2018;Dececchi et al., 2020). Para taxones con una masa corporal superior a los 1000 kg, el número máximo de Froude alcanzado por estos terópodos sería equivalente a 5 (Pontzer et al., 2009). ...
This Doctoral Thesis presents an exhaustive review of the Patagonian alvarezsaurids (Dinosauria, Theropoda). It includes a detailed osteological description of specimens of Patagonykus puertai (Holotype, MCF-PVPH-37), cf. Patagonykus puertai (MCF-PVPH-38), Patagonykinae indet. (MCF-PVPH-102), Alvarezsaurus calvoi (Holotype, MUCPv-54), Achillesaurus manazzonei (Holotype, MACN-PV-RN 1116), Bonapartenykus ultimus (Holotype, MPCA 1290), and cf. Bonapartenykus ultimus (MPCN-PV 738). A phylogenetic analysis and a discussion about the taxonomic validity of the recognized species and the taxonomic assignment of the materials MCF-PVPH-38, MCF-PVPH-102 and MPCN-PV 738 are presented. Different evolutionary and paleobiological studies were carried out in order to elucidate functional and behavioral aspects. Alvarezsaurus calvoi (MUCPv-54), Achillesaurus manazzonei (MACN-PV-RN 1116), Patagonykus puertai (MCF-PVPH-37) and Bonapartenykus ultimus (MPCA 1290) are valid species due to the presence of many autapomorphies. In this sense, the hypothesis proposed by P. Makovicky and collaborators that Achillesaurus manazzonei is a junior synonym of Alvarezsaurus calvoi is rejected. Likewise, certain morphological evidence allows hypothesizing that Alvarezsaurus calvoi represents a growth stage earlier than skeletal maturity. Specimen MCF-PVPH-38 is referable as cf. Patagonykus puertai, while MCF-PVPH-102 is considered an indeterminate Patagonykinae. In turn, MPCN-PV 738 is assigned as cf. Bonapartenykus ultimus based on the little overlapping material with the Bonapartenykus ultimus holotype. The results obtained from the mineralogical characterization through the X-ray diffraction method of specimens MPCN-PV 738 and the holotype of Bonapartenykus ultimus (MPCA 1290), allow to suggest that both specimens come from the same geographical area and stratigraphic level. The phylogenetic analysis, which is based upon the matrix of Gianechini and collaborators of 2018 with the inclusion of proper characters, and the database of Xu and collaborators of 2018, recovered the South American members of Alvarezsauria, such as Alnashetri cerropoliciensis (Candeleros Formation; Cenomanian), Patagonykus puertai (Portezuelo Formation, Turonian-Coniacian), Alvarezsaurus calvoi and Achillesaurus manazzonei (Bajo de La Carpa Formation, Coniacian-Santonian), and Bonapartenykus ultimus (Allen Formation, Campanian-Maastrichtian), nesting within the family Alvarezsauridae. In this sense, the forms that come from the Bajo de La Carpa Formation (Coniacian-Santonian) are recovered at the base of the Alvarezsauridae clade, while Alnashetri cerropoliciensis nests as a non-Patagonykinae alvarezsaurid. Regarding the type specimens of Patagonykus puertai and Bonapartenykus ultimus, they are recovered as members of the Patagonykinae subclade, a group that is recovered as a sister taxon of Parvicursorinae, both nested within the Alvarezsauridae. In addition, the topology obtained allows discerning the pattern, rhythm and time of evolution of the highly strange and derived alvarezsaurian skeleton, concluding in a gradual evolution. The Bremer and Bootstrap supports of the nodes (Haplocheirus + Aorun), [Bannykus + (Tugulusaurus + Xiyunykus)], and Patagonykinae, show indices that represent very robust values for these nodes. Likewise, these values suggest that two endemic clades originated early in Asia, while one endemic clade is observed in Patagonia, i.e., Patagonykinae. The analysis of the directional trends of the Alvarezsauria clade, tested by means of a own database on body masses based on the Christiansen and Fariña method, subsequently calibrated with the group's phylogeny using the R software, shows two independent miniaturization events in the alvarezsaurid evolution, namely the former originating from the base of the Alvarezsauridae (sustained by Alvarezsaurus), and the latter within the Parvicursorinae. Analysis of the Alvarezsauria dentition reveals possible dental synapomorphies for the Alvarezsauria clade that should be tested in an integrative phylogenetic analysis. The general characterization of the forelimb and a partial reconstruction of the myology of alvarezsaurs demonstrate different configurations for Patagonykinae and Parvicursorinae. The multivariate analyzes carried out from the databases of Elissamburu and Vizcaíno, plus that of Cau and collaborators, show that the Patagonykinae would have had ranges of movements greater than those observed in Parvicursorinae, although the latter would have had a greater capacity to carry out more strenuous jobs. The morphometric analysis of the hindlimb and the use of the Snively and collaborators equations, show that the configuration of this element in Alvarezsauria is indicative of a highly cursorial lifestyle, as well as possible particular strategies for more efficient locomotion. The topology obtained in the phylogenetic analysis that was carried out in this Doctoral Thesis, allowed clarifying the ontogenetic changes observed in the ontogenetic series of the manual ungueal element II-2 within the clade Alvarezsauridae. In addition, the multivariate analysis carried out from the manual phalanx II-2 allows us to infer that alvarezsaurs could have performed functions such as hook-and-pull and piercing, where the arm would function as a single unit. The anatomy and myology of the alvarezsaurian tail show that the caudal vertebrae of alvarezsaurians exhibit a combination of derived osteological features that suggests functions unique among theropods, such as considerable dorsal and lateral movements, as well as exceptional abilities to support distal loading of their long tail without compromising stability and/or mobility.
... By applying a modeling technique that uses the morphology of articular cartilage to characterize joint kinematics, we were able to test multiple articular cartilage reconstructions, which in turn improves our reconstructions of this organism that can be used in future studies to better understand broader aspects of its paleobiology (e.g., functional morphology, locomotion). Additionally, identifying and using the minimum magnitude of force to achieve full range of motion (i.e., flexion until the forelimb and humerus come into contact) provides an alternative approach independent of estimates of muscular attributes not preserved in the majority of fossils (such as muscle cross-sectional area, muscle mass, and muscle fiber length [e.g., Sellers and Manning, 2007;Sellers et al., 2013;Snively et al., 2013]). No further speculations are made as to whether this force magnitude was within those used by the animal during locomotion as herein we are not investigating locomotion. ...
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Rarity of soft tissue preservation, including of articular cartilage, in the fossil record hinders creation of biologically-realistic mechanical models. Previous studies of articular cartilage in extant taxa have documented important aspects of cartilage shapes and thicknesses, but these insights remain generalized and have yet to see systematic implementation in biomechanical modeling. Herein, we present a new method for modeling joints that allows for testing of hypotheses about articular cartilage morphology in extinct taxa. Our case study examines the left elbow joint of the sauropod dinosaur Dreadnoughtus schrani using articular cartilage reconstructions constrained by extant phylogenetic bracketing (EPB). EPB investigations of alligator and chicken articular cartilage revealed the presence of a spherical anterior projection of cartilage on the distal humerus which articulates with the radius during flexion. Importantly, this shape does not directly mirror the underlying bone. Using multibody dynamic models created in Adams™ without a priori restrictions on joint degrees of freedom, we simulated the effects of three alternative cartilage reconstructions based on these EPB findings which differ in mediolateral placement of a cartilage sphere and its anteroposterior thickness, encompassing a range of possibilities for the condition in Dreadnoughtus. Bone kinematics and contact area (calculated in Geomagic®) were tracked. Additionally, we modeled the elbow of an alligator and turkey using the same methodology and compared the results to XROMM (X-ray Reconstruction of Moving Morphology) analysis of the same limbs. Each model produced distinct results but were generally similar supporting our modeling methodology. Based on these findings, we predict that Dreadnoughtus, and presumably other extinct archosaurs, had a spherical projection of cartilage on the anterior face of the distal end of the humerus for articulation with the radius. Though many valuable insights have been gained by existing modeling methodologies, we chose a different approach that focused on joint contact surfaces. Moreover, applying our methods within a quantitative hypothesis-testing framework can advance the field of paleobiology by testing hypotheses relating shape and kinematics that are not possible with prescribed joint motions.
The natural history of birds is summarized. Account of what contemporary birds are, when and how they came to be what they are, and why and how they evolved exceptional physiognomies are given. The evolution of birds from reptilian stock, their domestication that resulted in some of the species becoming leading food animals and the sociocultural impacts of birds on organizations of many human societies are outlined. The evolution of the lung-air sac system of birds, which among the air-breathing vertebrates is the most structurally complex and efficient gas exchanger, is described. Unique properties, capacities, and activities such as long distant migration, flight under the extremely hypoxic conditions of high altitude, anthropogenic impacts of climate change (global warming) on the ecology and biology of birds, sound production (vocalization), birds as bioindicator animals of environmental health, and the cognitive prowess of birds in exploits such as dropping hard food objects on firm surfaces to break them and that way access otherwise unobtainable food and caching of food in various ways and places and shrewdly accessing it for use during adverse conditions are presented. The biology of birds can only be well understood by considering them from various perspectives that include the habitats they occupy and the lifestyles that they lead.
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Most physics courses begin with one-dimensional kinematics, which is usually restricted to the case of constant acceleration. Here we report a unique exercise for an introductory algebra-based physics course involving the running and non-constant acceleration of the theropod dinosaur Dilophosaurus wetherilli and the world-famous Jamaican sprinter Usain Bolt. Given the interest that most students have about dinosaurs (as well as Usain Bolt), students are excited to examine a hypothetical 100-meter race between Dilophosaurus and Usain Bolt. Since these students have not yet taken calculus, and as part of our effort to build computational skills in our students, numerical methods are used via a spreadsheet to calculate displacements and accelerations numerically from velocity data. This work includes a discussion of uncertainties.
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To understand the evolution of bipedalism among the hominoids in an ecological context we need to be able to estimate the energetic cost of locomotion in fossil forms. Ideally such an estimate would be based entirely on morphology since, except for the rare instances where footprints are preserved, this is the only primary source of evidence available. In this paper we use evolutionary robotics techniques (genetic algorithms, pattern generators and mechanical modeling) to produce a biomimetic simulation of bipedalism based on human body dimensions. The mechanical simulation is a seven-segment, two-dimensional model with motive force provided by tension generators representing the major muscle groups acting around the lower-limb joints. Metabolic energy costs are calculated from the muscle model, and bipedal gait is generated using a finite-state pattern generator whose parameters are produced using a genetic algorithm with locomotor economy (maximum distance for a fixed energy cost) as the fitness criterion. The model is validated by comparing the values it generates with those for modern humans. The result (maximum efficiency of 200 J m–1) is within 15% of the experimentally derived value, which is very encouraging and suggests that this is a useful analytic technique for investigating the locomotor behaviour of fossil forms. Initial work suggests that in the future this technique could be used to estimate other locomotor parameters such as top speed. In addition, the animations produced by this technique are qualitatively very convincing, which suggests that this may also be a useful technique for visualizing bipedal locomotion.
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The purpose of this manuscript is to describe a theoretical paradigm from which to more accurately assess linear sprinting performance. More importantly, the model describes how to interpret test results in order to pinpoint weaknesses in linear sprinting performance and design subsequent training programs. A retrospective, quasi-experimental cross sectional analysis was performed using 86 Division I female soccer and lacrosse players. Linear sprinting performance was assessed using infrared sensors at 9.14, 18.28, 27.42, and 36.58 meter distances. Cumulative (9.14, 18.28, 27.42, and 36.58 meter) and individual (1(st), 2(nd), 3(rd), and 4(th) 9.14 meter) split times were used to illustrate the theoretical paradigm. Sub-groups were identified from the sample and labelled as above average (faster), average, and below average (slower). Statistical analysis showed each sub-group was significantly different from each other (fast < average < slow). From each sub-group select individuals were identified by having a 36.58 meter time within 0.05 seconds of each other (n = 11, 13, and 7, respectively). Three phases of the sprint test were suggested to exist and called initial acceleration (0-9.14 m), middle acceleration (9.14-27.42 m), and metabolic-stiffness transition (27.42-36.58 m). A new model for assessing and interpreting linear sprinting performance was developed. Implementation of this paradigm should assist sport performance professionals identify weaknesses, minimize training errors, and maximize training adaptations. Key PointsAssessment of linear sprinting should include splits for a greater understanding of performance.Individual split times can be used to identify specific areas of weakness.Appropriate training strategies can be developed and used to improve the identified weaknesses.
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The available data on maximal running speeds of mammals are presented, and the relationship between speed and body mass is considered. For all mammals (n= 106), maximal running speed scales as (body mass)0–17; however, the largest mammals are not the fastest, and an optimal size with regards to running ability is suggested ( 119 kg). Maximal running speeds are, on the average, somewhat more than twice maximal aerobic speeds. Within the Artiodactyla, Carnivora or Rodentia, maximal running speed is mass independent, in agreement with theoretical expectations for geometrically similar animals (Thompson, 1917; Hill, 1950). McMahon's (1975b) model for elastic similarity is therefore not supported by the available data on maximal running speeds, and there appears to be no necessary correspondence between scaling of limb bone proportions and running ability.
THE faster an animal walks or runs the longer, in general, are its strides. Many dinosaur tracks have been found from which stride lengths can be measured1 .I have now obtained a relationship between speed, stride length and body size from observations of living animals and applied this to dinosaurs to achieve estimates of their speeds. The estimated speeds are rather low-between 1.0 and 3.6 m s-1.
The musculoskeletal components of the hindlimbs of 20 species of birds, considered non-runners, were examined. Allometry was used to compare these data with previously published information on the limbs of running birds. In non-runners the digital flexor muscle and tendon areas scaled approximately isometrically, in contrast to running birds where tendon areas had a lower exponent. Non-running birds had muscle fibre areas approximately half that of runners of equal mass. In both groups, the muscle:tendon area ratio for m. gastrocnemius increased as M0.13, suggesting factors other than elastic energy storage are important. Runners exhibited relatively longer tibiotarsi and tarsometatarsi and shorter toes. With very few exceptions, the linear dimensions of bones, tendon cross-sectional areas, and muscle masses and fibre areas in the legs of the non-running birds scaled closely according to the requirements for geometric similarity, but the confidence limits are often wide. Deviations from geometric similarity in birds reflect differences in locomotor behaviours and abilities.