## SUMMARY

It has been observed that the relationship between locomotor performance
and body mass in terrestrial mammals does not follow a single linear trend
when the entire range of body mass is considered. Large taxa tend to show
different scaling exponents compared to those of small taxa, suggesting that
there would be a differential scaling between small and large mammals. This
pattern, noted previously for several morphological traits in mammals, has
been explained to occur as a result of mechanical constraints over bones due
to the differential effect of gravity on small and large-sized forms. The
relationship between maximum relative running speed (body length
s^{-1}) and body mass was analysed in 142 species of terrestrial
mammals, in order to evaluate whether the relative locomotor performance shows
a differential scaling depending on the range of mass analysed, and whether
the scaling pattern is consistent with the idea of mechanical constraints on
locomotor performance. The scaling of relative locomotor performance proved to
be non-linear when the entire range of body masses was considered and showed a
differential scaling between small and large mammals. Among the small species,
a negative, although nearly independent, relationship with body mass was
noted. In contrast, maximum relative running speed in large mammals showed a
strong negative relationship with body mass. This reduction in locomotor
performance was correlated with a decrease in the ability to withstand the
forces applied on bones and may be understood as a necessary stress reduction
mechanism for assuring the structural integrity of the limb skeleton in large
species.

## Introduction

Locomotor performance has been widely studied and quantified in a variety of organisms. Among terrestrial vertebrates, these studies have focused mainly on reptiles (for example, Garland, 1984; Losos, 1990a; Bauwens et al., 1995; Farley, 1997; Bonine and Garland, 1999; Irschick and Jayne, 1999; Miles et al., 2000). In contrast, information on locomotor performance among mammals is much less common (Garland, 1983; Djawdan and Garland, 1988; Garland et al., 1988; Djawdan, 1993).

Based on geometric similarity models, maximum running speed has been
predicted to be independent of body size
(Hill, 1950;
McMahon, 1975a). Other
similarity models (i.e. elastic, static stress and dynamic similarity) predict
that running speed must increase in larger animals (see
Garland, 1983). Alternatively,
it has been proposed that the relationship between body mass
(*M*_{b}) and running speed is simpler and more intuitive than
these similarity models imply. Biomechanical models predict a positive
relationship between limb length and body size (see
Losos, 1990b), which has been
observed empirically in lizards (Garland
and Losos, 1994 and references therein). However, in a study on
mammal running speeds, Garland
(1983) showed that the
relationship between maximum running speed and *M*_{b} was
curvilinear rather than linear. After analysing the relationship within
taxonomic groups, he found that orders containing the largest animals (i.e.
Artiodactyla and Carnivora) showed negative or mass-independent scaling
exponents, while orders of small animals (i.e. Rodentia, Lagomorpha) had
mass-independent or positive relationships. A similar pattern was found in
skeletal allometry of the limb long bones in mammals, where small and large
body-sized groups yielded different scaling exponents
(McMahon, 1975b;
Alexander, 1977; Alexander et
al., 1977,
1979;
Biewener, 1983a). Economos
(1983) and Bou and Casinos
(1985) suggested that the
different results could be explained by a differential scaling of the long
bones of large *versus* small-sized mammals owing to the greater
effects of gravity on the larger animals
(Biewener, 1990). Differential
scaling of morphological characters, including bone length and width
(Bertram and Biewener, 1990;
Christiansen, 1999), bone
curvature (Bertram and Biewener,
1992) and body length
(Economos, 1983), and of
ecological characteristics (e.g. Silva and
Downing, 1995; Marquet and
Taper, 1998), have been described previously.

Several studies have shown that bone properties are extremely conservative
regardless of phylogenetic and mass considerations
(Biewener, 1990 and references
therein). Among mammals, compressive failure strength ranges from 180 to 220
MPa (Biewener, 1990), and
ultimate bending strength ranges from 170 to 300 MPa
(Biewener, 1982). If mammals
were designed according to geometric similarity, the static pressure stress
(force per area) should increase in proportion to
*M*_{b}^{0.28} (see
Biewener, 1982), indicating
that the ratio of failure stress (i.e. mechanical strength) to static stress
should decrease as *M*_{b} increases. If we assume that peak
locomotor forces exerted on the ground are constant multiples of
*M*_{b}, then peak locomotor stresses should scale with
*M*_{b} in the same way as static stress. However, *in
vivo* measurements of bone strain
(Biewener and Taylor, 1986;
Biewener et al., 1988;
Rubin and Lanyon, 1984;
Taylor, 1985), and
calculations of bone stress from force platforms using high speed cameras
(Alexander and Vernon, 1975;
Alexander et al., 1984;
Biewener, 1983b;
Biewener and Blickhan, 1988),
in different sized terrestrial species during strenuous activities, such as
running or jumping, indicate that, rather than increasing with
*M*_{b}, peak bone stress is mass-independent. Thus, the ratio
of peak locomotor bone stress and static bone stress, defined as stress scope,
which indicates how much stress can be resisted by a loaded bone, would
decrease in proportion to *M*_{b}^{-0.28} and
*M*_{b}^{-0.27}, for compressive and bending stress,
respectively. Experimental measurements of limb bone stress in a variety of
mammals during locomotion have shown that, within each gait, the forces
applied over bones increase proportionally with speed
(Biewener, 1983b;
Biewener and Taylor, 1986;
Biewener et al., 1988). Farley
and Taylor (1991) showed that
the transition from trot to gallop in horses occurs at the same level of peak
stress on muscles and tendons, suggesting that the gait transition might be
triggered when musculoskeletal forces reach a critical level as a mechanism to
reduce the chance of injury. It has been shown that maximum running speed
recorded during gallop reaches similar peak bone stress values to those
observed during the trot-gallop transition
(Biewener and Taylor, 1986),
indicating that those animals with greater stress scope values should be able
to attain greater speeds than animals with a lower stress scope.

Locomotor performance has been considered an `ecologically relevant' trait
because of its effect on an animal's ability to escape from predators or to
catch prey (Huey and Stevenson,
1979). However, when we wish to compare locomotor performance
among organisms of different body size we are confronted with the problem of
scale because body size affects nearly all physiological functions
(Schmidt-Nielsen, 1984).
Therefore, because (1) the amount that an animal's muscle shortens, and (2)
the distance travelled with one step, both vary directly with body length, a
body length-dependent scale (relative running speed) might be more appropriate
when characterising the performance of animals
(Jones and Lindstedt, 1993).
Accordingly, through a computer simulation, Van Damme and Van Dooren
(1999) showed that animals
with higher relative speeds (in body length s^{-1}) would be less
likely to be caught than relatively slower animals, and that the relationship
between running speed and catchability might be size dependent. Therefore, a
relative measurement of performance might be an important factor that would
predict the outcome of a predator-prey interaction.

In this paper, I analysed the effect of body weight on a length-dependent
measurement of maximum locomotor performance in terrestrial mammals. Based on
the geometric similarity model, the relative running speed should scale as
*M*_{b}^{-0.33}. Alternatively, if relative speed
scales with limb length according to biomechanical predictions, the
relationship should be mass independent. It is hypothesised that gravity would
be playing a differential role on locomotor performance across different size
ranges, and large species would be more affected than small ones. Therefore,
it is expected that small mammals would show an allometric exponent similar to
that predicted by either geometric similarity or biomechanical analysis. In
contrast, if locomotor performance in large mammals is constrained by the
ability of musculoskeletal structures to withstand forces during activity, it
is expected that absolute maximum running speed would be proportional to
stress scope and therefore would scale according to
*M*_{b}^{-0.27}. Consequently, a length-based
measurement of performance would scale in proportion to
*M*_{b}^{-0.60}. On the other hand, if locomotor
performance was not constrained by body weight, a monotonic relationship
between maximum relative speed and body mass should be observed in all ranges
of body mass. In order to test this hypothesis, I worked with a sample
spanning a wide range of body sizes as well as taxonomic groups, analysing the
differences in patterns observed between large and small-sized mammals.

## Materials and methods

### Morphological and running speed data

Data on running speed and *M*_{b} of 142 terrestrial
mammals, spanning a wide range of *M*_{b} (from 9 g to 6 tons)
and belonging to the orders Proboscidae (*N*=2), Perissodactyla
(*N*=7), Artiodactyla (*N*=37), Primata (*N*=3),
Carnivora (*N*=21), Rodentia (*N*=50), Lagomorpha (*N*=8)
and Marsupialia (*N*=14), were gathered from the literature
(Garland, 1983;
Djawdan and Garland, 1988;
Garland et al., 1988;
Garland and Janis, 1993)
(Table 1). Maximum running
speeds have been obtained using a wide variety of methodologies that are of
highly variable quality (see Garland,
1983). There are potentially some errors associated with the
analyses due to the fact that some values have been estimated or measured with
poor-precision methods (e.g. car chasing for absolute speed). The magnitude of
these errors will be dependent on the range analysed (larger errors in small
allometric ranges of *M*_{b} than in large ranges). Most
recompiled data were included, necessarily sacrificing precision for
completeness. Assuming there is no systematic bias in measurements, the
analyses would underestimate the real relationships between relative speed and
*M*_{b}. When more than one value had been reported for the
same species, the single fastest running speed documented was chosen in an
attempt to reduce the effect of differences in procedure and/or motivation
among studies (Garland, 1983;
Garland et al., 1988). Species
with highly specialised habits and limb morphologies, such as arboreal and
fully fossorial species, were excluded from the analysis (i.e. *Erithizon,
Didelphis, Bradypus, Talpa* and *Scalopus*).

Data on body length (*L*_{b}), measured as the length of the
head and body (excluding tail length), were obtained mainly from Eisenberg
(1981) and Nowak
(1999). Data reported
correspond to mean values for adult individuals. If mean values were
unavailable, the midpoint of ranges was used. Where specific values were
unavailable, values were obtained from Silva's
(1998) allometric equation for
terrestrial non-flying mammals *L*_{b}=0.330
*M*_{b}^{0.334} (*r*^{2}=0.98).

An estimation of bending stress scope for mammals analysed in this study
was obtained using the equation
1
calculated using an arbitrary stress scope value of 1 for *Loxodonta*
(*M*_{b}=6000 kg).

### Statistical analysis

The relationship between *M*_{b} and maximum relative speed
(*V*_{max}/*L*_{b}) was obtained through linear
regression on log-transformed data to yield estimates of the parameters of the
allometric equation
2
where *y* is *V*_{max}/*L*_{b} in body
length s^{-1}, and *x* is *M*_{b} in kg. Scaling
equation parameters were obtained through ordinary least-squares regression
analysis (OLS). As neither relative maximum running speed nor
*M*_{b} can be considered errorless, a model II regression
(reduced major axis, RMA) is more appropriate for estimating parameters
(LaBarbera, 1989;
Swartz and Biewener, 1992). In
this study, both OLS and RMA are shown, but analyses and discussions are
mainly based on OLS estimations in order to be able to compare exponent values
with previously existing data reported in the literature, and also for the
purposes of comparing linear with non-linear regression results.

Non-linearity in the relationship between maximum relative running speed
and *M*_{b} was suggested by the LOWESS method (robust
*lo*cally *we*ighted *s*catterplot *s*moother;
Cleveland, 1979), a
non-parametric technique of sequential smoothing that does not attempt to fit
a simple model over the entire range of data, but fits a series of local
regression curves using restricted sets of data near the area of interest
(Efron and Tibshirani, 1991).
This procedure is used for revealing distribution patterns that are difficult
to identify in a scatterplot (Ellison,
1993). I used polynomial regression analysis to test for
statistical significance of non-linearity indicated by LOWESS. Differential
scaling can be modelled by a continuous linear relationship with different
slopes on either side of a critical point (*k*), generating a broken
line. If there is only one critical point, there will be two domains with
their own linear regressions (bilinear model). If there are two critical
points, three domains will appear (trilinear model). Comparisons between
regression models were conducted by comparing the resulting Error Mean Squares
under the different models (polynomial, bilinear, and trilinear) to calculate
the *F*-statistic from their ratio and applying the sequential
Bonferroni test using the
Dunn—S̆idák method to avoid
inflating the type I error (Sokal and
Rohlf, 1995). This approach was used rather than comparing
coefficients of determination because it considers the reduction in degree of
freedom by fitting additional parameters to the regression model.

Comparisons of estimated slopes with slopes obtained from the literature
were made by *t*-test. Analysis of covariance (ANCOVA) was used to test
the equality of slopes of different taxa or size ranges. When more than two
slopes were compared, multiple comparisons of slopes were carried out through
a Bonferroni test (Zar, 1996).
All analyses were made with α=0.05.

## Results

Overall, maximum relative running speed was found to decrease with
increasing *M*_{b} (Fig.
1). A scaling exponent of -0.17 was obtained through linear
regression on the complete sample of mammals
(Table 2). The heteromyid
rodent *Dipodomys merriami* proved to be the mammalian species with the
fastest relative running speed. LOWESS analysis suggested that the
relationship between relative running speed and *M*_{b} was
non-linear (Fig. 1) with
polynomial regression yielding higher coefficient of determination
(*r*^{2}=0.798) and fit than simple linear regression, as
indicated by a significant quadratic coefficient (*P*<0.001). Three
body mass ranges over which allometric exponents differed were identified
using LOWESS analysis, giving rise to a trilinear model
(*r*^{2}=0.813): below 10 kg, between 10 and 100 kg, and over
100 kg, with scaling exponents of -0.09±0.04 (mean ± 95%
confidence interval), -0.34±0.20 and -0.51±0.10, respectively.
Allometric slopes differed significantly among these size groups (ANCOVA,
*P*<0.001), being significantly different in small *vesus*
large-sized mammals (Bonferroni test, *P*<0.05). Intermediate-sized
mammals did not differ from large (Bonferroni test, *P*>0.05,
power=0.96) or small mammals (Bonferroni test, *P*>0.05,
power=1.00). This pattern of differential scaling may also be modelled through
a bilinear model. The critical body mass breakpoint, where the change in slope
between small and large mammals occurs, was positioned at
*M*_{b}=30 kg, around the interception between linear
regressions for mammals below 10 kg and above 100 kg (see
Fig. 1). The scaling exponent
of small mammals (below 30 kg) differed significantly from that of larger
mammals (Table 2). However,
despite the fact this bilinear model presents the highest coefficient of
determination (*r*^{2}=0.815), there were no significant
differences in the fit between the models (Bonferroni test,
*P*>0.05).

When plotted against stress scope, maximum relative speed showed a similar
pattern to that observed against body mass. The group of small-sized mammals
showed a significant positive correlation between these traits
(*r*=0.548; *P*<0.01; Fig.
2A), and the group of large mammals showed an even stronger
correlation (*r*=0.803; *P*<0.001;
Fig. 2B).

Separate analyses on taxonomic groups for which adequate data sets were
available (*N*≥7) suggested more negative scaling exponents in large
body-sized orders of mammals than in small body-sized ones (see
Table 3). There were
differences in allometric exponents among the best represented taxonomic
groups: Artiodactyla, Carnivora and Rodentia (ANCOVA, *P*<0.01). The
slope of Artiodactyla differed significantly from that of Rodentia (Bonferroni
test, *P*<0.05). Consistently, the allometric exponent of Carnivora,
an intermediate body sized group (2.5-265 kg), was intermediate between that
of Artiodactyla and Rodentia, and did not differ significantly from them
(Bonferroni test, *P*>0.05; Table
3; power, 0.870 and 0.369, respectively). The only slope that did
not differ significantly from zero was that of lagomorphs, while the scaling
exponents of rodents and marsupials proved to be slightly less than zero.

## Discussion

Body mass seems to be more highly correlated with maximum relative speed
(*r*^{2}=0.69, this study) than with maximum absolute running
speed (*r*^{2}=0.44, from
Garland, 1983). This higher
correlation might be a simple consequence that some body-length data were
obtained from a single allometric equation. However, when analyses were
carried using Silva's (1998)
equation only, the correlation was not significantly improved, indicating that
the way as data were expressed would not have a significant effect on the
results. The scaling exponent found for all pooled mammals does not differ
from that predicted by the dynamic similarity hypothesis
(*M*_{b}^{-0.16};
Alexander and Jayes, 1983).
However, this result must be taken cautiously as geometric similarity in
general morphology is an implicit assumption in dynamic similarity models
(Alexander and Jayes, 1983),
which is not true for all mammals (McMahon,
1975a,b;
Bou et al., 1987;
Christiansen, 1999).
Furthermore, the non-linear relationship between body mass and maximum running
speed was evident, both in terms of absolute as well as relative speed. In the
case of relative speed, the relationship between *M*_{b} and
running speed behaved differently over different ranges of body mass.

Three domains (small, intermediate and large-sized mammals), each with different scaling exponents, were identified through LOWESS analysis. This may be reflecting a pattern of two extreme regimes with different slopes and a transitional zone of gradual exponent change, although it needs to be considered in terms of the taxa that comprise this zone in order to evaluate potentially evolutionary or taxonomic effects (see below). In this particular case, these domains may be modelled by gravitational effect over organisms. For simplification, the data set was modelled as if there were only two domains with one critical or break point distinguishing small and large-sized mammals. This model yielded a similar fit to the two-point change model, but makes interpretations easier. There was no difference between scaling exponents of mammals below 10 and 30 kg, and between mammals above 30 and 100 kg. The power analyses showed very low values (approx. 0.1) for these comparisons, but these should be considered cautiously. The values obtained from retrospective power analysis are dependent on the observed differences between treatments, so if the difference is close to zero, the power of the test will be extremely low. In this case, the differences observed in slope between below 10 and 30 kg groups and above 30 and 100 kg groups and the associated errors are small. Besides, the differences between the large groups and between the small-sized groups using the different models are also small in terms of number of species. For example, the below 30 kg and below 10 kg groups differed in only seven species, yielding, as expected, few differences in the estimated slopes. This would indicate that the distinction between two or three domains would have no effects on parameter estimation.

The scaling exponent of small-sized mammals (below 30 kg) did not differ
from that which would be expected under elastic similarity
(*M*_{b}^{-0.08};
McMahon, 1975a). However, Bou
et al. (1987) reported a
significantly different allometric exponent for the limb bones dimensions
(diameter and length) of rodents and insectivores from those expected under
elastic similarity, mainly due to limb adaptations to their habitat (e.g.
fossorial and arboreal mammals). On the other hand, linear dimensions in large
mammals scale to *M*_{b} in agreement with elastic or static
stress similarity, depending on the range of *M*_{b} analysed
(Prothero and Sereno, 1982;
Bertram and Biewener, 1990;
Biewener, 1990). However, in
this study it was found that the scaling exponent of relative locomotor
performance of large mammals cannot be predicted by any particular similarity
model, although geometric similarity is the model that predicts the closer
exponent (*b*=-0.33).

The discrepancies between morphological and speed scaling, as noted by Günther (1975), show that there is no single criterion that provides a satisfactory explanation for qualitatively different characters such as limb proportions and locomotor performance. Furthermore, the non-correspondence between morphology and performance based on expectations from similarity models might be due to a lack of knowledge of the factors that contribute towards determining maximum locomotor performance. Predictions obtained might be based on erroneous assumptions yielding spurious results. For example, predicted values of scaling exponents from geometric similarity are derived from the assumption that absolute maximum performance is determined by maximum mechanical power developed by limb muscles (for derivation, see McMahon, 1975a). However, among lizards, some evidence has been gathered suggesting that the mechanical power developed by limb muscles is not a determinant of maximum running speed (Farley, 1997). Also, the absence of correlation between power output and running speed might be a mass-dependent phenomenon of this methodology, where larger lizards would be more affected in their performance by mechanical power output, as Farley (1997) pointed out. In addition, other factors could be affecting maximum locomotor performance, such as muscle energetics, neuromuscular coordination, dynamic constraints and efficiency (for a review, see Jones and Lindstedt, 1993). There is some evidence suggesting that mechanical impositions over musculoskeletal structures could be constraining locomotor performance (Biewener, 1990), although this hypothesis has not been tested directly.

The steeper reduction in locomotor performance with increasing
*M*_{b} in large mammals observed in this study is consistent
with the hypothesis of differential scaling between large and small-sized
species, and it could be explained to occur as a result of mechanical
constraints imposed on the skeletal structure, as pointed out by Biewener
(1990). If mammals scale
following geometric similarity, bone peak stress would increase faster than
the ability to resist it, making organisms mechanically unviable over
determined *M*_{b}
(Biewener, 1990).
Fariña et al. (1997),
in an allometric study of bending resistance of long bones of birds, mammals
and dinosaurs, showed that the ability of limb bones to withstand forces
decreases with *M*_{b}. This is in agreement with previous
laboratory studies that reported that small mammals can resist more gravity
than large ones (Economos,
1981). Nevertheless, it has been observed that mammals keep
relatively constant values of safety factors (i.e. the ratio between the
bone's failure stress and stress experienced during functional activities;
Alexander, 1981) in a wide
range of *M*_{b} (Biewener,
1990 and references therein). Thus, as *M*_{b}
increases, mammals must carry out several postural, morphologic, and
behavioural modifications in order to keep the structural integrity of the
skeletal support, such as more upright postures (Biewener,
1983a,
1989), more robust skeletons
in larger organisms (Bertram and Biewener,
1990; Christiansen,
1999) and reductions in locomotor performance
(Biewener, 1990). This is
noted in the correlation between relative performance and stress scope, where
very large mammals (i.e. those having very low stress scope values within the
large mammal group) show little variation around the regression line. This
variation, however, increases concomitantly with stress scope, in agreement
with the idea that very large species are more restricted in their performance
by mechanical constraints over support structures than smaller species.
Nevertheless, when the group of small-sized species is analysed, correlation
between stress scope and performance becomes weaker, showing great variation
around the regression line, apparently independent of stress scope, which may
be the product of factors other than *M*_{b}, such as
morphological adaptations to habitat and modes of locomotion
(Bou et al., 1987;
Garland et al., 1988).

Locomotor performance in large mammals is more highly correlated with
*M*_{b} and stress scope than in small ones (see
Fig. 2). The small amount of
variation around the regression line could reflect the fact that almost all
mammals above 10 kg are `cursorial' (*sensu*
Alexander and Jayes, 1983),
which means that they stand and run with the femur and humerus upright and
have conservative locomotor modes (Bertram
and Biewener, 1990). In addition, it has been noted that the
values of speed tend to be independent of locomotor adaptations as
*M*_{b} increases (Bou et
al., 1987). Thus, *M*_{b} alone could be
responsible for the variation in locomotor performance.

In regression analyses within restricted taxonomic groups, Perissodactyla
and Artiodactyla, the largest groups of mammals analysed, showed the highest
allometric exponents (see Table
3). Both exponents were not different from those previously
described for large mammals overall (over 30 kg), suggesting that exponent
estimation does not seem to be affected when phylogenetic relationships among
species included in the analyses are taken into account. The low retrospective
power of these tests (0.168 and 0.418, respectively) seems to be a product of
the small differences in slope estimations between the groups rather than an
actual low power of test, at least in the case of artiodactyls. For
perisodactyls, the slope estimation would not be reliable due to the large
error associate caused by the small sample size (*N*=7). Artiodactyls
possess a greater scaling exponent than the small-sized group Rodentia,
whereas the medium-sized Carnivora have an intermediate exponent, although
this value is not significantly different from that of large and small-sized
taxonomic groups. However, the value of this exponent should be considered
cautiously. The group of carnivores has the smallest sample size and the
greatest error estimates when compared to rodents and artiodactyls, and would
be expected to have the least sensitivity to the differences in slope.
Moreover, Carnivora is the only well-represented group that is present on both
sides of critical point. In residual analysis, the carnivores of the small
mammals group are evenly distributed throughout the regression line
(Fig. 3A), whereas all the
large-sized carnivores (except one, the cheetah) are grouped as negative
residuals (Fig. 3B). This
pattern is explained by the fact that small and large-sized carnivores do not
follow a monotonic relationship with *M*_{b}, but have a
differential scaling as observed in the pooled-sample of all mammals (nearly
mass independent in small species, and strongly negative in large ones).
Therefore, the observed scaling exponent of Carnivora would be spurious.

Lagomorpha is a group of species with fast running speeds and spanning a
narrow body mass range. All species in this group fall above the regression
line of the pooled small-sized mammals
(Fig. 3A), generating a high
leverage over parameter estimation. When lagomorphs are excluded from the
analysis, the regression slope becomes steeper, but still significantly
different from that of rodents (*P*<0.05).

The differential scaling observed in mammals would have ecological implications also. Small mammals are commonly prey for animals that use surprise attacks as hunting techniques (e.g. raptors, snakes, and felines). In these cases, the predators are usually bigger and faster (in absolute terms) than the prey, which escape by running to a suitable refuge. In this type of predation technique, where the attacks are quick and discrete, the success of an attack might be dependent of the size of the prey. It is intuitively logical that in a choice between two prey of different size moving at the same absolute speed, the predator has more chance if it chases the larger one, as shown by Van Damme and Van Dooren (1999). Another important factor in predator—prey interactions is the manoeuvrability of the organism. Many animals are able to escape a predator that is, in absolute terms, faster, thanks to the ability to make a tighter turn than predator. This escape strategy, called the `turning gambit' (sensu Howland, 1974), has been observed in different species spanning from small moths to large mammals. The turning gambit has been shown to be a size-dependent characteristic (Webb, 1976; Witter et al., 1994; Domenici, 2001), but few works have evaluated the effect of shape and size of the body on turning performance in terrestrial vertebrates (Eilam, 1994; Carrier et al., 2001; Lee et al., 2001). Turning performance is dependent on the rotational inertia of the body (i.e. the sum of differential elements of mass multiplied by the square of the perpendicular distance from the axis of rotation) and, therefore, larger animals should have a higher rotational inertia and a poorer turning performance than smaller ones. This work shows that the largest species of the small-sized group should be more susceptible to predation because of their reduced relative performance and reduced manoeuvrability. According to this, Hedenström and Rosén (2001) suggested that selection of large-sized prey by sparrowhawks over small-sized ones could be due to the higher manoeuvrability of the latter; it could also be an energy-based decision, because larger prey are more profitable.

On the other hand, large mammals are chased by large predators (e.g. lions)
using maintained persecutions (Emerson et
al., 1994). In this type of hunting, the absolute running speed
seems to be more important in determining the success of an attack. However,
manoeuvrability plays an important role in the escape strategy of prey and as
pointed out above, this depends on body length. The poor performance (absolute
and relative) observed in large mammals indicates that they would be easily
susceptible to individual predation. Thus, the life in groups observed in some
large mammals (e.g. some artiodactyls) has been explained as an antipredation
protective mechanism (Jarman and Jarman, 1979) in order to compensate their
poor running ability. Some morphological adaptations to rapid locomotion in
some large species of mammals have been described
(Taylor et al., 1971;
Lindstedt et al., 1991), but these adaptations might be a secondary
acquisition, where the initial selection would be the reduction in transport
costs and the increase of home range
(Janis and Wilhelm, 1993). The
strong diminution in relative performance as *M*_{b} increases
in large mammals supports the idea that running speed, either absolute or
relative, has not been a selected characteristic in mammalian evolution.

This study showed that an analysis of scaling of maximum locomotor
performance over a broad range of *M*_{b} might yield spurious
results. As observed in several traits, the relationship between maximum
locomotor performance and body size changes depending on the range of
*M*_{b} studied. Locomotor performance of small mammals seems
to be nearly independent of *M*_{b}, which agrees with previous
studies conducted in rodents (Garland,
1983; Djawdan and Garland,
1988; Garland et al.,
1988). However, when large-sized mammal species are analysed, the
relationship between relative locomotor performance and *M*_{b}
becomes more negative. The reduction in locomotor performance in large mammals
is consistent with the hypothesis of mechanical constraints and may be
understood as a stress reduction mechanism. Nevertheless, despite the fact
that this idea had been mentioned previously in the literature
(Garland, 1983;
Biewener, 1990), it has not
been tested.

## ACKNOWLEDGEMENTS

I thank F. Bozinovic and two anonymous reviewers for their helpful comments which significantly improved the manuscript. I am very grateful to E. L. Rezende for his time, patience and help on earlier drafts. This study was partially supported by Dpto. de Postgrado y Postítulo, Universidad de Chile: Beca PG/9/2001 and by the Millennium Center for Advanced Studies in Ecology and Research on Biodiversity, P99-103-F ICM.

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