Leg morphology and locomotion in birds: requirements for force and speed during ankle flexion
Göteborg University, Department of Zoology, Zoomorphology, Box 463, SE 405 30 Göteborg, Sweden
* Author for correspondence (e-mail: a.zeffer{at}zool.gu.se)
Accepted 23 December 2002
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Summary |
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The investigation included 67 bird species divided into six groups according to differences in their hind limb movements and requirements of force and speed. These were birds that walk/run/hop (WH), climb (C) or hang (H), birds of prey (BOP), fast swimmers (FS) and slow swimmers (SS). Predictions for each group correlating their requirements for force and speed are made, based on biomechanical and ecological factors, and the lengths of the moment arms are calculated. The results show that the means for the groups could largely be separated from the norm (i.e. zero), and in many cases the predictions are fulfilled. d is significantly larger than average in species affected by strong forces, for example, gravity (BOP and C), but shorter in species affected only by drag (WH, FS and SS). No differences associated with drag due to differences in medium density were seen. Furthermore, the tarsometatarsus is longer than average only in the BOP species, and shorter in the SS species. Discriminant analysis reveals that using our predictions there is a 53.7% chance of placing a species in the correct group, compared with the 17% chance expected if the species are randomly placed in a group.
Key words: bird, locomotion, force, speed, ankle flexion, leg adaptation, musculus tibialis cranialis, tarsometatarsus
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Introduction |
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Several authors have demonstrated that there are biomechanically meaningful
differences in the lengths of the moment arms in species with different
locomotion patterns (e.g. Palmgren,
1932; Spring,
1965
; Norberg,
1979
; Moreno and Carrascal,
1993
; Carrascal et al.,
1990
,
1994
). Short legs bring a
tree-trunk climber closer to the substrate, which reduces the moments around
the leg joints and thus reduces the muscle force required for maintaining a
vertical posture (Winkler and Bock,
1976
). For hanging species, reduction of the length of the
tarsometatarsus is more important in these respects than shortening of the
other bone elements (Palmgren,
1932
).
Long legs are generally associated with increased speed of movement in
running animals because long legs increase maximum stride length
(Alexander, 1977;
Bennett, 1996
). In a
geometrical analysis, Norberg
(1979
) showed that, in
climbing species, the tarsometatarsus affects stride length the most, followed
by the femur and finally the tibiotarsus. Some aerially feeding birds (such as
swifts, Apus sp.), which do not use their legs during foraging, have
reduced legs. They thereby benefit from a reduction of energy expenditure
needed for building and maintaining long legs, and their short legs may also
reduce parasite drag during flight
(Pennycuick, 1989
;
Barbosa and Moreno, 1995
;
Pennycuick et al., 1996
).
Short legs, particularly short tarsometatarsi, may increase stability in birds
perching on slender and unstable branches by keeping the center of mass close
to the perch (Grant, 1966
;
Schulenberg, 1983
). These
studies thus indicate that the length of the tarsometatarsus is correlated
with the use of the legs.
The major function for the musculus tibialis cranialis (synonymous with m.
tibialis anticus) is to flex the ankle
(Raikow, 1985). The distance
between the point of muscle insertion and the fulcrum (the point of rotation
of the ankle) can be taken as an index of the muscle moment arm, and it has
been measured (e.g. Palmgren,
1932
; Norberg,
1979
; Moreno and Carrascal,
1993
; Carrascal et al.,
1994
). It was found that clinging and climbing species tend to
have a more distally located muscle insertion than species that prefer to hop
on top of the branches. The moment arm is assumed to be long in birds that
need to produce large forces but can forego speed of flexion, as is the case
with hanging and clinging birds (other muscle characteristics being taken as
similar). As the moment arm becomes longer (in an evolutionary perspective),
however, the speed of flexion slows down because the sweep angle per unit of
muscle contraction is reduced. Furthermore, assuming that a muscle's
contracting distance is fixed, an increased moment arm would reduce the
maximum possible sweep angle for the tarsometatarsus.
The aim of this investigation was to determine whether the sizes of the force-lever arms for in- and out-forces alone could be used to trace adaptations to different movement patterns in different groups of birds. Here, we have focused on ankle flexion, and for this purpose we calculated indices for the in-force and out-force lever arms. However, the mass and the length of the toes also greatly influence the moments that the flexor muscle must produce during a swinging movement. The present study is based on measurements of skeletized material and the length of the tarsometatarsus has been taken to represent the out-force lever arm. This simplification excludes the effect of the mass of the toes, which limits our conclusions. But if we can show that there are correlations between the lengths of the tarsometatarsus and muscle moment arm for the ankle flexor and movement patterns, by using simple biomechanics on lever action, we can show that it is likely that lever action does indeed play a role in the evolution of the morphology of bird limbs.
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Materials and methods |
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Morphometrics
We used freshly frozen birds and measurements were completed using dry
skeletal material. Values for mean body mass (M) for each species
were taken from the literature (Cramp and
Simmons, 1980; Cramp,
1985
). Two lengths were measured: the total length of the
tarsometatarsus (tmt) and the distance between the ankle joint and
the insertion of m. tibialis cranialis (d). This muscle originates
deep in the dorsal surface of crista patellaris and on the distal end of the
femur, and inserts on the tuberositas m. tibialis cranialis on the dorsal
surface of the proximal part of the tarsometatarsus
(Fig. 1; nomenclature taken
from Baumel et al., 1979
). The
fulcrum is considered to be at the top of the eminentia intercondylaris.
Because the out-force is taken to be perpendicular to the long axis of the
tarsometatarsus, tmt here equals the out-force lever arm. Distance
d is a function of the in-force lever arm, and the insertion point is
clearly visible on the bare bones. The true lengths of the moment arms differ,
however, during a stride (see below). The measurements were taken with a slide
caliper to the nearest 0.01 mm.
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The ratio of the length of the in-force moment arm to the length of the out-force lever arm (d/tmt) has often been used as an indication of the magnitude of the force output, but this may be correct only for geometrically similar birds. If the ratio d/tmt is in fact size dependent, its use would be limited. The relationship between the tarsometatarsus length and the body mass introduces an unknown factor for which is difficult to properly account. Plots of the ratio d/tmt against body mass revealed that there is such a correlation (see Results). Therefore, in order to compare the sizes of d and tmt (and their ratio) between the groups, d should be made independent of body mass and tmt (since d makes up a proportion of tmt), and tmt should be made independent of body mass, as described below.
To avoid problems associated with colinearity between body mass and
tarsometatarsus length (which affects the confidence interval for the
regression), a principal components analysis (PCA) was conducted (on the
natural logarithms for body mass and tmt) by rotating these data sets
using the correlation matrix. This procedure first standardizes the variables
by subtracting the mean for all species and then dividing the variables by the
standard deviation (S.D.) before the analysis is conducted. The scores for
PC1 and PC2 were then used as independent variables in a
multiple linear regression where loged was treated as the
dependent variable, so that:
![]() | (1) |
Furthermore, the residuals (2) from a linear regression of
logetmt against logeM were used as
size (M)-independent measurements of tarsometatarsus length
(henceforth called tmtindex), where:
![]() | (2) |
Statistical analyses
For each group, the means of the residuals for each index were tested for
deviation from zero by the use of a t-test (when the residuals had a
normal distribution). In two cases (tmtindex for the H and
SS groups) the distribution was non-normal, so a Wilcoxon signed-rank test was
used instead. Furthermore, the means of the indices were compared between some
groups of interest using analysis of variance (ANOVA) followed by a
Games-Howell post hoc test.
To calculate the maximum separation of the groups based on tmtindex and dindex, we performed a discriminant analysis using Mahalanobi's distances. This method measures the validity of the groups and presents discriminant functions (DF) describing the orthogonal vectors that maximally separate the groups. The means of the DF scores for the groups were calculated along with the 95% confidence intervals of the means. All analyses were conducted with SPSS 10.0, except for the PCA and the Wilcoxon signed-rank test, which were performed according to SAS procedures (version 8.0).
During the last decade, the effect of phylogeny on comparative studies has
been fully recognized (e.g. Felsenstein,
1985; Cheverud et al.,
1985
; Harvey and Pagel,
1991
; Martins and Hansen,
1996
). It is possible that the groups identified in this work
coincide with phylogenetic groups, consequently the species should not be
considered as statistically independent units
(Felsenstein, 1985
;
Harvey and Pagel, 1991
).
Several methods have been developed to allow for the phylogenetic effect (for
a review, see Martins and Hansen,
1996
), but they all have some limitations. The main problem with
these methods is that they depend on a good estimate of the phylogeny,
including estimates of branch lengths as well as interpretations of excluded
branches. Other problems are also present in the underlying assumptions of
these methods, most of which assume that a change in character state is the
only indicator of selection, and ignore stabilizing selection, which is
probably an important factor in adaptations
(Hansen, 1997
). For these
reasons, and difficulty in finding a method to deal with a combination of
continuous and categorical variables (with more than 2-3 categories), we were
unable to take the phylogeny into consideration.
Biomechanics and predictions
The force that a muscle can develop and its speed of movement depend on
several things, including the length of the bone and the muscle moment. The
true, instantaneous length d' of the moment arm of the muscle
force changes during the course of leg movement. When the tarsometatarsus and
the tibiotarsus form a given angle with each other, d' can be
expressed as a function of d and the angle between the line
of action of the muscle's tendon and tmt:
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![]() | (4) |
![]() | (5) |
The drag from the surrounding media during movements in air and water may
also affect the length of the tarsometatarsus and the ankle flexor moment arm.
Drag D is given by the equation:
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Thus selective pressures on the lengths of the moment arms required for
large force production and high speed of movement are contradictory, and the
ability to produce a large force may sometimes be relinquished in order to
accommodate speed of movement. To cope with this problem, several swimming
birds have streamlined legs to reduce drag (e.g.
Lovvorn, 1991), and the feet
are also flexed during the recovery stroke. Increased acceleration due to
large force production may also add to increasing speed.
Inertial forces (involved in oscillation of the legs) are of great
importance during leg swinging and are dependent on the mass distribution of
the limbs, leg (+foot) length, and angular velocity of the legs during a
stroke (e.g. Norberg, 1990).
Rotational inertia is a function of the radius of gyration squared, so the
toes, whose mass are farthest out from the axis of rotation in the ankle, may
have greater influence on the length of the out-force lever arm than does the
tarsometatarsus. The mass of the air or water stuck to the legs during
oscillation also must be added, and this added mass is 800 times greater for
water than for air. It is therefore particularly important for swimming birds
to reduce inertial forces. To do so, the legs and feet should be short and
light.
Certainly, movements other than those accounted for may affect the parameters in question (discussed below). If, however, we can find correlations between certain behaviours (i.e. movement modes) and lengths of moment arms, and if these coincide with predictions based on biomechanics, the indication would be that the requirements of force output and speed can partly be met by biomechanical arrangements. Based on the facts that a high index means a long tmt or d, and a low index means a short tmt or d, and assuming that different out-forces (Fig. 1B) are required for different movement modes but that muscle performance is equal for all species, we can make the following predictions for the different groups of birds.
(1) WH group. Birds protracting the legs in air experience almost no drag forces on the legs, because of the low density of the medium (see above). We predict that birds in this group are more dependent on speed of flexion than on force produced during flexion. Therefore, dindex should be lower than expected from the norm (0). The tmtindex is predicted to be high to maximize step length (and hence travelling speed) and to facilitate locomotion among vegetation on ground.
(2) BOP group. The legs of birds of prey must be kept flexed, and the m.
tibialis cranialis thus has to work against the force of gravity on the prey.
Therefore, we predict that birds of prey should have a high
dindex for large force production for ankle flexion. A low
tmtindex would also add to a large force production,
because the tarsometatarsus acts as an index of the out-force lever arm
(prediction BOP1). On the other hand, birds of prey have often been observed
to stretch out the legs laterally to catch prey, either in the air or on the
ground (Newton, 1979), a
situation for which long legs would be beneficial. It would also be
advantageous for these birds to have long legs in order to improve the
acceleration rate at take-off from the ground, in order to cushion a prey
strike in the air or on the ground during rapid attacks, and to improve their
ability to maintain visual contact with the prey at the strike moment without
jeopardizing flight stability. We therefore make a contradictory prediction:
tmtindex should be high in birds of prey for the reasons
explained above (prediction BOP2).
(3) Species in the C group hop upwards on tree trunks during climbing and
should benefit from a short tarsometatarsus to minimize the distance between
the center of mass and the trunk during the vertical climb. They should also
have a large muscle force for flexion to withstand the effect of gravity
during hanging in the climb. On the other hand, the hops need to be rapid; in
the tree creeper Certhia familiaris, each stride takes only 0.14 s,
of which the floating phase (during which the feet are flexed before the bird
lands on the trunk) takes 0.075 s (Norberg, 1985). The tarsometatarsus thus
has to be flexed rapidly during the recovery stroke. We therefore have two
conflicting selection pressures: the need for a long flexor moment arm for
large force production, and the need for a short moment arm for high speed of
flexion (Norberg, 1979). We
predict that these birds should have a low tmtindex, but
it is difficult to estimate the trade-off for the length of the moment arm,
which is why no prediction is made for the dindex.
Furthermore, it is important for these birds to have a low overall body mass
to reduce the gravitational force, and large ankle extensors to produce the
large forces needed for the power stroke during vertical climbing. The
extensor muscles are not, however, studied here.
(4) H group. Both types of H birds are dependent on large force production
(rather than speed of movement) to keep the tarsometatarsus flexed when
exposed to gravity (Palmgren,
1932; Norberg,
1979
). Further, the tarsometatarsus should be short to minimize
the muscle moment needed to maintain the leg bones in fixed positions. Speed
of flexion is not important for this kind of action. Thus, we predict the
dindex to be higher and the tmtindex
to be lower than the norm for all species.
(5,6) Swimming birds. We would expect that the dindex
should be higher in swimming birds than in birds flexing the tarsometatarsus
in air (WH birds) for larger force production. All swimming birds should
benefit from short tarsometatarsi to reduce inertial forces during the foot
stroke. This may be most important for birds with the highest swim-stroke
frequencies. FS birds (5) are considered to be more dependent on higher speed
of movement to be able to catch agile fish than the SS birds (6), and
therefore also on higher stroke frequencies. Diving speeds of approximately
1.2-2 m s-1 have been observed among the FS birds
(Stephenson et al., 1989;
Johansson and Lindhe Norberg,
2001
) and approximately 0.04-0.8 m s-1 in SS birds
(Stephenson et al., 1989
). We
can then make the following predictions for the two swimming groups.
(i) FS group. These species should have a low dindex
for high stride frequencies. Short tarsometatarsi (low
tmtindex) and overall short legs would be preferred to
reduce inertial forces. On the other hand, long legs (and high
tmtindex) would be beneficial to produce high forward
speeds. Birds in this group have various drag-reducing and thrust-increasing
mechanisms for improvement of swimming performance. For example, in several
diving species the tarsometatarsi are laterally flattened (streamlined), which
reduces profile drag (e.g. Lovvorn,
1991). In grebes the toes are asymmetrically lobed and form
multiple slots during the power stroke, which highly improves swimming
performance (Johansson and Lindhe Norberg,
2001
). Therefore, these birds may be allowed to have rather long
legs, although this increases the inertial forces. We therefore predict that
FS birds should have a higher tmtindex than the birds of
the SS group. However, it is difficult to predict the size of
tmtindex in relation to the norm (regression line for all
birds).
(ii) SS group. This includes species that swim slower than the FS birds.
Species diving for food have to work against buoyancy. Lovvorn and Jones
(1991) showed that buoyancy is
far more important to the locomotor costs of shallow diving than hydrodynamic
drag. Selection for increased streamlining may be the most important factor
affecting the morphology in diving birds. Furthermore, different propulsion
modes probably demand morphological differences among the different species.
No morphological adaptations for reduction of drag in the legs or feet have
been reported in these species. Because speed of movement is not predicted to
be important, force production should be favoured over speed of movement.
Therefore, large leg extensors with long muscle moment arms would be needed.
Because flexor forces may not be as important as in H and BOP birds, but more
important than for WH birds, we predict SS species to have a
dindex about average for those investigated. We further
predict that their tmtindex should be low to reduce
inertial forces.
Our predictions of the dindex and the tmtindex are summarized in Table 2.
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Results and Discussion |
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![]() | (7) |
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The PCA analysis, used to avoid problems with colinearity between
tmt and M, yielded numerically identical eigenvectors for
both of the principal components, where
![]() | (8) |
![]() | (9) |
![]() | (10) |
![]() | (11) |
The indices dindex and tmtindex for each group are presented in Fig. 3, and the mean values of the indices for each group are given in Table 3. The WH, FS and SS birds have significantly lower dindex than average for all birds investigated, whereas the BOP and the C birds have a significantly higher dindex than average. The SS group has a lower tmtindex whereas the BOP group has a higher tmtindex than average. Group H was scattered (see below).
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Agreement between our predictions and the results for the indices are shaded in Table 2. Fig. 4 shows the dindex plotted against the tmtindex for all species. A high dindex indicates a long d, and a high tmtindex indicates a long tmt. The two indices, which are completely uncorrelated, are presented together in the plot only to visualize the species separated from each other.
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The discriminant analysis shows that the probability of correctly
classifying a species using our predictions is 53.7% as compared to 17%
(100%/6 groups; Klecka, 1980)
if the species are randomly placed in a group. The accuracy of correct
classifications differed for each group according to
Table 4. The SS and the BOP
birds show the highest probability of correct classification of the groups
(82.4 and 81.8%, respectively), followed by the WH birds (61.1%).
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The first discriminant function (DF) accounts for 87.3% of the variance and
the second DF for 12.7%. Together they describe 100% of the variance. The
functions are:
![]() | (12) |
![]() | (13) |
The means of DF1 and DF2 scores for each of the groups are plotted in Fig. 5, together with the 95% confidence interval of the means. The plot (Fig. 5) shows that when using the first two discriminant functions it is possible to separate the BOP means from all other groups, except for C. The mean for C is further separated from the means of all other groups except H. Moreover, the mean for FS is separated from the SS mean, and the mean for WH is separated from the means for all groups, except for FS and H.
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Results versus predictions
Our results show several agreements with our hypotheses
(Table 2). In the WH species
the dindex is indeed low, as predicted, but the
tmtindex does not deviate from the norm represented by the
regression. Thus, it does not seem to be important to have a long
tarsometatarsus in these terrestrial species.
BOP species have a high dindex, as predicted for their ability to carry prey with flexed legs. Furthermore, they have longer tarsometatarsi relative to body size (higher tmtindex values) than average for all birds taken together, confirming prediction BOP2. Interestingly, they do not have larger tmt than WH birds (P=0.722).
The pygmy owl Glaucidium passerinum is very small (50-77 g) but
captures prey the size of small rodents and finchsized birds
(Del Hoyo et al., 1999), and a
great spotted woodpecker Dendrocopos major (90 g) has also been found
as prey in the owl's nest hole (U. M. Lindhe Norberg, personal observation).
Interestingly, the pygmy owl has a higher dindex and a
lower tmtindex than any of the other BOP species
investigated (Fig. 4). The
sparrow hawk Accipiter nisus has the opposite; this species has been
observed to move on ground and sometimes to stretch out a leg to catch a prey
in vegetation (Newton, 1979
),
which has also been observed for sparrow hawks in flight.
The C species were predicted to have short tarsometatarsi, but the tmtindex does not deviate from the norm. The dindex is higher than average for all birds, which indicates that force production at ankle flexion during climbing is more important than speed of flexion to these species.
The H birds form two subgroups (Figs
3B,
4), where birds of one subgroup
(including the Parus and Regulus species) have larger
tmtindex than expected by the norm. The high
tmtindex in the small Parus species, and
particularly in the very small Regulus (M=6 g), may be an
adaptation to foraging among conifer needles
(Norberg, 1979). The
dindex does not differ between the two subgroups and their
indices do not deviate from the mean for all birds. Parrots have considerably
smaller values of the tmtindex, in accordance with our
prediction. Furthermore, there is a great variation in
dindex among the parrots
(Fig. 4). The yellow-crowned
parrot Amazona ochrocephala (Ao) and the grey parrot Psittacus
erithacus (Pe) forage while perching, often holding the food item with
one foot (Forshaw, 1977
). This
behavior requires stability, which it is suggested is attained with short
tarsometatarsi (Schulenberg,
1983
; Grant,
1966
). These species spend almost no time at all on the ground,
whereas the budgerigar Melopsittacus undulatus (Mu) and the cockatiel
Nymphicus hollandicus (Nh) both prefer to feed on grass seeds on the
ground. Walking on the ground may require some speed of movement, which may
help explain why the relative moment arm is comparatively short in these
species.
Among the swimmers, the FS species have a low dindex,
as predicted, which makes a high stroke frequency and hence a high swimming
speed possible. The results correspond with the findings of Johansson and
Lindhe Norberg (2001) that the
great crested grebe Podiceps cristatus increases speed by
predominantly increasing the swim stroke frequency. The mean for the
tmtindex does not deviate from the average value for all
birds, but it is significantly higher in the FS than in the SS birds
(P=0.049; see also Fig.
3B).
The FS species form two subgroups (Fig.
4). One, including the mergansers Mergus sp. (M) and the
cormorant Phalacrocorax carbo (P), shows a lower
tmtindex and somewhat higher dindex
than the other (including the loons Gavia sp. and grebes
Podiceps sp.). The FS species may have different diving techniques
(L. Christoffer Johansson, personal communication), which probably affect the
morphology of their legs. Furthermore, a preliminary investigation indicates
that the cormorant and mergansers do not show the same streamlining of the
tarsometatarsus as the loons and grebes. Lovvorn
(1991) suggested that the
flattening of the tarsometatarsus is an adaptation to reduce drag during fast
underwater swimming. This is supported by our results, showing that species
with a more streamlined tarsometatarsus also have a higher
tmtindex. The drag-reducing flattening of the
tarsometatarsi may compensate for increases in inertial forces due to long
legs.
In the SS species the tmtindex was significantly lower than average for all species, as predicted. The dindex, too, was significantly lower than average, indicating that speed of flexion may after all be of some importance to these species.
We predicted that the dindex should be larger in swimming birds than in the WH birds because of the increased density of water compared to air, but the results do not show such a difference (P=1.00 for both the WHFS and WHSS comparisons). Thus, increased drag due to differences in density between two media does not seem to have any significant effect on the length of the in-force moment arm.
It is obvious that the forces affecting the tarsometatarsus during flexion differ between the groups, and it is quite clear from the results that most of these differences are correlated with the length of the in-force lever arm, but some results, such as the average H values, are difficult to interpret. However, the species can be reorganized so that those that have to withstand their own body mass or the mass of a prey during leg flexion (BOP, C and H birds) form group 1, while those that are affected by smaller forces (such as drag from air or water; WH, FS and SS birds) form group 2. dindex for group 1 is 0.93±0.23 (mean ± S.E.M., N=43) and for group 2 is -0.50±0.072 (N=24) (see also Table 2). These two groups differ significantly from each other (P<0.001, ANOVA) and from the norm (P<0.001 for both groups), which means that species flexing the tarsometatarsi against a considerable force have long moment arms (as compared with the norm), whereas those affected by smaller forces have shorter moment arms. A similar effect was not obtained for the tarsometatarsus length (indicated by the tmtindex) when comparing group 1 with group 2. Here, only two groups deviate significantly from the norm (BOP and SS, Fig. 3B), indicating that counteracting selection forces may have created trade-offs, which are difficult to interpret. Furthermore, this result also indicates that the length of the tarsometatarsus is a less suitable measurement to represent the out-force lever arm.
Discrimination of the groups
The discriminant analysis shows that 53.7% of the species were placed in
the correct group. This may not seem high, but if each species were randomly
placed in a group the chance of a correct classification is only 17% (100/6%;
Klecka, 1980).
Table 4 shows to what extent
the species were assigned to the correct group. The SS species were classified
into the correct group in 82.4% of cases, followed by BOP (81.8%) and WH
(61.1%). The analysis placed 75% of the FS species in the WH group and 25% of
them in the SS group. This indicates that the FS birds are not recognizable as
a group using the Mahalanobi's distances and the variables presented in this
investigation. All (100%) of the C species were classified as BOP birds,
leading to similar conclusions as for the FS group. However, the C group
contains only four species, which may be too small a sample size for the group
as a whole. But when the means of the discriminating functions (1 and 2) are
combined, including the 95% confidence interval, it is evident which of the
group means are separated from each other
(Fig. 5). The H and the BOP
groups show a large variation in the mean values, whereas birds of the WH, FS
and SS groups show a smaller variation. The mean values of DF1 and
DF2 for FS seem to coincide with those for WH. Furthermore, the
mean values for the SS and the FS groups are completely separated from each
other, which may indicate that the species of these two groups face different
selective pressures regarding the lengths of the moment arms. The means for C
and H are almost completely separated, although the m. tibialis cranialis has
to work against the gravity of the body mass in both groups. This indicates
that the speed of movement required to hop up tree trunks also is
important.
Fossil birds
Proportions of the hind limb bones have been used to interpret the
locomotor habits of Archaeopteryx and other Mesozoic birds
(Hopson, 2001), and body
masses of fossil animals have been estimated from regressions on allometric
relationships between skeletal measurements and body masses of extant birds
(e.g. Alexander, 1989
).
Assuming geometric similarity and using a known length, body mass can be
obtained from the regression equation. It is possible to estimate the distance
d of the insertion of the ankle flexor from the proximal end of the
tarsometatarsus in fossil birds (see, for example,
Brett-Surman and Paul, 1985
),
and if mass is estimated (from a skeletal part other than the tarsometatarsus)
it is then possible to calculate dindex, which may add to
our information about extinct species.
Conclusions
This is a comparative analysis based on skeleton measurements, observed or
expected behaviours of ankle flexion, and simple mechanics; it is not a
detailed biomechanical analysis. Our results may function as a basis for a
more detailed mechanical analysis, which may confirm our results and visible
trends.
The method used in the present study allows us to consider the length of the tarsometatarsus (tmtindex) as independent of body mass, and the length of the moment arm of m. tibialis cranialis (dindex) as independent of both body mass and tmt. That is, the birds should all be viewed as being of equal size with equally long tarsometatarsi (the latter regarding the dindex). The aim was to use these indices to separate birds into groups that were exposed to different magnitudes of force during ankle flexion. Most of the mean values of the groups are separate from each other (Fig. 5). The mean value for the discriminant functions for the group containing hanging birds (H) was the most difficult group to separate from the others (it could be separated completely only from the BOP group), while the mean values for the BOP and the SS groups could be separated from all but one group. The discrepancies may be related to counteracting selection forces, differences in muscle physiology and morphology or specific adaptations in some species, which may alter the conditions for force development and speed determination. In the species where the muscle must counteract a large force, such as the body mass of the bird or the mass of the prey, the moment arm is long (Fig. 4). Furthermore, species exposed to smaller forces during flexion, such as the drag from air or water, have a short moment arm compared to the average for all the birds investigated.
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