Mixed gaits in small avian terrestrial locomotion

Abstract

Scientists have historically categorized gaits discretely (e.g. regular gaits such as walking, running). However, previous results suggest that animals such as birds might mix or regularly or stochastically switch between gaits while maintaining a steady locomotor speed. Here, we combined a novel and completely automated large-scale study (over one million frames) on motions of the center of mass in several bird species (quail, oystercatcher, northern lapwing, pigeon, and avocet) with numerical simulations. The birds studied do not strictly prefer walking mechanics at lower speeds or running mechanics at higher speeds. Moreover, our results clearly display that the birds in our study employ mixed gaits (such as one step walking followed by one step using running mechanics) more often than walking and, surprisingly, maybe as often as grounded running. Using a bio-inspired model based on parameters obtained from real quails, we found two types of stable mixed gaits. In the first, both legs exhibit different gait mechanics, whereas in the second, legs gradually alternate from one gait mechanics into the other. Interestingly, mixed gaits parameters mostly overlap those of grounded running. Thus, perturbations or changes in the state induce a switch from grounded running to mixed gaits or vice versa.

Full text

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SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
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Mixed gaits in small avian
terrestrial locomotion
Emanuel Andrada1,3, Daniel Haase2, Yefta Sutedja1, John A. Nyakatura3,4,
Brandon M. Kilbourne3,5, Joachim Denzler2, Martin S. Fischer3 & Reinhard Blickhan1
Scientists have historically categorized gaits discretely (e.g. regular gaits such as walking, running).
However, previous results suggest that animals such as birds might mix or regularly or stochastically
switch between gaits while maintaining a steady locomotor speed. Here, we combined a novel and
completely automated large-scale study (over one million frames) on motions of the center of mass
in several bird species (quail, oystercatcher, northern lapwing, pigeon, and avocet) with numerical
simulations. The birds studied do not strictly prefer walking mechanics at lower speeds or running
mechanics at higher speeds. Moreover, our results clearly display that the birds in our study employ
mixed gaits (such as one step walking followed by one step using running mechanics) more often
than walking and, surprisingly, maybe as often as grounded running. Using a bio-inspired model
based on parameters obtained from real quails, we found two types of stable mixed gaits. In the
rst, both legs exhibit dierent gait mechanics, whereas in the second, legs gradually alternate
from one gait mechanics into the other. Interestingly, mixed gaits parameters mostly overlap those
of grounded running. Thus, perturbations or changes in the state induce a switch from grounded
running to mixed gaits or vice versa.
When researchers analyze legged locomotion, they usually categorize discretely regular gaits (i.e. walking
or running) based on the relative contact time of limbs (limb phase and duty factor1) or uctuations
of the mechanical energy at the center of mass (CoM)2,3. e latter categorization is better suited to
discriminate between walking and running (see4 for a deeper discussion on this topic) and served as a
fruitful basis for the development of relative simple models like the inverted pendulum for walking3 or
the spring-mass model for running5. ese relatively simple models for walking and running have greatly
widened our understanding of global principles of locomotion; however, they represent only discrete ide-
alized paradigms. For human locomotion, such discrete changes may apply, but not necessarily for small
animals, as gait transitions have oen been shown to be more gradual in smaller species (e.g.4,6–8). In
particular, smooth gait changes were described for small bird terrestrial locomotion (e.g.6–11). Contrarily,
the existence of hybrid gaits (both legs exhibit a combination of two regular gaits in one stride, e.g. “pen-
dular run”12) or mixed gaits (legs display dierent gait dynamics, i.e. one step with walking mechanics is
followed by one step with running mechanics or vice versa at a relatively constant speed) during bipedal
locomotion has received little attention. Scientists usually focus on the investigation of a regular gait and
expect that deviations are due to unsteady locomotion. For example, most of the theoretical work on
bipedal locomotion is focused on one-cycle periodic gaits, and likely avoid unintentionally ‘limping’ or
‘hybrid gaits’ (e.g.5,13–15).
e discussion about hybrid gaits emerged aer numerical energetic optimizations of another simple
model (point-mass and telescopic leg) predicted such a gait during locomotion at intermediate speeds
utilizing long step-lengths, which was termed a ‘pendular run’12. More recently, Usherwood16 found hints
1Science of Motion, Friedrich-Schiller University of Jena, Germany. 2Computer Vision Group, Friedrich-Schiller
University of Jena, Germany. 3Institut für Spezielle Zoologie und Evolutionsbiologie mit Phyletischem Museum,
Friedrich-Schiller University of Jena, Germany. 4AG Morphologie und Formengeschichte, Bild Wissen Gestaltung:
ein interdisziplinäres Labor, Institut für Biologie, Humboldt University Berlin, Germany. 5College for Life Sciences,
Wissenschaftskolleg zu Berlin, Berlin, Germany. Correspondence and requests for materials should be addressed
to E.A. (email: emanuel.andrada@uni-jena.de)
Received: 03 March 2015
Accepted: 30 July 2015
Published: 03 September 2015
OPEN

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SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
of pendular running in the terrestrial locomotion of pheasants and guineafowl by analyzing their CoM
motions derived from forceplate measurements. Given that the inverted pendulum2 is almost 40 years
old and that the spring-mass model5 is almost 30 years old, it seems fair to wonder to what degree the
walking and running paradigms inuenced and still inuence the selection and analysis of strides in
animal locomotion? is question is of importance not only in regard of avian terrestrial locomotion,
but also to terrestrial locomotion in other tetrapod groups.
It is generally accepted that birds walk at the lowest speeds, however, exceptions such as sparrows exist
(see also text below). At moderate speeds, small birds usually prefer a running gait without aerial phases,
which was termed grounded running15,17,18. eoretically during grounded running, potential (Ep) and
kinetic (Ek) energy of the CoM change nearly in phase (bouncing mechanics), and, consequently, a high
congruity occurs between both energy patterns (%congruity as a measure for CoM energy pattern see19).
In contrast, the vaulting motion of the CoM observed in walking produces EP and EK patterns that uc-
tuate out-of-phase (low congruity). However, zero congruity is not expected for compliant walking13. In
small birds, the shi between vaulting and bouncing mechanics is said to be gradual, rarely approaching
the ideal scenarios (e.g.,7,10). If this is the case, as speed increases, one can expect that %congruity values
will cross a value of 50, which is usually dened as a boundary between walking-like and running-like
gaits (e.g.7,19,20). In this ‘transition zone’, small uctuations, as birds experience on a treadmill or face in
irregular natural environments, might produce %congruity shis to either walking or running mechan-
ics. Two eects can be expected: i) in some trials running occurs at a slower speed than walking in
another trial and/or ii) mixed gaits emerge.
In the present paper, we combined a large-scale study (over one million frames) on the uctuations
of the CoM’s mechanical energy in several bird species (quail, oystercatcher, northern lapwing, pigeon,
and avocet) during treadmill locomotion, which was performed in a completely automated way, with
numerical simulations, in order to address two main points.
First, we examined whether the transition between vaulting (i.e. walking) and bouncing (i.e. running)
mechanics correlates with speed, without human inuence introduced via manual digitizing and sub-
jective choice of strides for analysis. Even though globally a trend towards increasing %congruity with
higher speeds was observed in recent investigations, at lower speeds, some birds, such as lapwings7 and
tinamous10, do not always seem to prefer walking mechanics. In contrast, quail18 and the much larger
ostrich17 seem to rely on CoM’s mechanics indicative of walking during slow locomotion.
Second, we asked whether mixed gaits exist at the boundary between walking and grounded run-
ning. Within a range of relative speeds (Froude numbers of approximately 0.5 ~ 0.6), it is frequently
observed that both walking and grounded running gaits occur in birds7,17,18. In addition, it was found
that virtual leg stiness (computed from the ground reaction forces and the length change between the
CoM and foot contact point) remain at values close to 6 during quail walking, grounded running and
running when normalized by body mass and leg-length18. By combining experimental data on quail
and simulations, Andrada and colleagues21 showed that pronograde locomotion maximizes the advan-
tages of grounded running. Moreover, they found that in order to obtain walking gaits, the eective leg,
dened as the length between the hip and foot contact point, must be less sti but more damped than a
leg tuned for running. us, they speculated that in the quail there must occur a shi to an increasing
role of elastic tissues during running as also observed in running turkeys and running humans22,23. It is
therefore conceivable that during the transition between walking and grounded running, model related
leg parameters such as leg stiness or leg damping should be suitable for both gaits, thus facilitating a
potential emergence of mixed gaits.
To address these questions, we analyzed X-ray recordings on a large quantitative scale using the
algorithms developed by Haase and colleagues24. e methodology permits an automatic tracking of
the CoM. In addition, foot contacts and aerial phases were also detected through automation. en we
determined for each step the percentage of congruity to dierentiate vaulting from bouncing mechanics.
Finally, to test whether mixed gaits are part of the repertoire of the dynamics of pronograde bipedal
locomotion, and not just a treadmill artifact, we explored numerically, based on parameters derived
from quail (cf.21), the existence of periodic mixed gaits within the overlap zone of walking, grounded
running and running by using a simple model called Pronograde Virtual Pivot Point (PVPP;21). In sim-
ulations both legs have same basic eective leg parameters such as leg length (l0), leg stiness (k), and
leg damping (c).
Results
Congruity of CoM mechanics. In general no correlation between %congruity and speed was
observed. However, some dierences among species can be established based on the scatter plots.
We recorded trials from avocets that met the criteria for analysis at speed between 0.14 ms−1 and
1.77 ms−1. Despite this speed range, avocets seem to prefer the transition zone of % congruity values
ranging between 40% and 70% (Fig. 1). No aerial phases were observed at speeds below 1.2 ms−1. At
speeds above 1.2 ms−1, only two individuals ran without aerial phases, but still exhibited in 29% of steps
%congruity values lower than 50. In this speed interval, 3 individuals ran with aerial phases in just 16%
of the steps. When generally comparing one step with the subsequent step (Table1 and Fig.2), ~52%
of these pairs of steps exhibited solely running mechanics in both steps, ~8% solely walking mechanics
walking in both steps, and ~40% mixed walking and running mechanics between steps. Most of the aerial

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SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
phases where observed in the area of two consecutive running steps. Individual dierences are signicant
due to one individual which used relatively more walking and less bouncing mechanics during trials
(Table1). e variation observed among the other three individuals is random.
Northern lapwings displayed a pattern similar to avocets, but with slightly enhanced dispersion of
the data. ey moved at speeds ranging from 0.06 ms−1 to 1.75 ms−1. Northern lapwings did not incor-
porate aerial phases at speeds lower than 1.0 ms−1. At speeds above 1 ms−1 they used aerial phases in
23% of the steps, but in 39% of the steps %congruity was still lower than 50 (Fig.1). When comparing
consecutive steps in general, ~40% of them exhibited running mechanics in both steps, ~44% a mixture
of walking and running, and ~16% walking in both steps (Fig.2). As observed for the avocets, individual
dierences are signicant due to one individual (B67), which used relatively more frequently walking
and less bouncing mechanics (Table1). e variation observed among the other three individuals is due
to chance.
Oystercatchers and pigeons displayed a similar pattern in their scatter plots, though in dierent
speeds ranges (oystercatchers: 0.13 ms−1 to 2.3 ms−1; pigeons: 0.07 ms−1 to .81 ms−1). Both species exhib-
ited intermediate %congruity values (between 40 and 70) at lower speeds, followed by a greater disper-
sion at intermediate and high speeds. We did not record aerial phase running in oystercatchers at speeds
below 1.4 ms−1. At speeds ranging between 1 ms−1 and 1.4 ms−1, oystercatcher exhibited in 31% of the
steps %congruity values lower than 50. At speeds higher than 1.4 ms−1, they used aerial phases in 23%
of the steps, and vaulting mechanics in 40% steps. When comparing one step with the subsequent one,
32% of them exhibited running mechanics in both steps, ~53% a mixture of walking and running, and
~15% walking in both steps. e variation observed between individuals is random (Table1).
Pigeons moving on the treadmill did not exhibit aerial phases. At speeds higher than 0.4 ms−1, pigeons
still showed in 36% of the steps %congruity values lower than 50%. %. When comparing one step with
the following step, on average ~31% of them exhibited running mechanics in both steps, ~53% a mixture
of walking and running, and ~16% walking in both steps. Individual dierences are signicant due to one
individual (200), which used relatively more walking and less grounded running during trials (Table1).
e variation observed among the other three individuals is random.
0 1 2
0
50
100
avocet
%congruity
0 1 2
0
50
100
oystercatcher
0 1 2
0
50
100
norther lapwings
%congruity
0 0.5 1
0
50
100
quail
0 0.5 1
0
50
100
pigeon
0.82 1.650.76 1.52 ~0.5 ~1
treadmill speed
[u]
[m
s]
-1
0.88 1.77 0.48 0.96
[u]
[ms]
-1
treadmill speed
Figure 1. %Congruity of CoM mechanics related to treadmill and dimensionless speed (
ˆu
). %congruity
values lower up to 50 are oen related to vaulting mechanics, while those larger than 50 are interpreted as
bouncing mechanics. Each point represent a step. Red points indicates that aerial phases occurred.

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SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
We collected data from quails locomoting at speeds ranging from 0.15 ms−1 to 0.85 ms−1. Most of the
collected data was at speeds lower than 0.6 m s−1. Similar to the pigeons, the quail did not exhibit aerial
phases within that speed range. At speeds higher than 0.4 ms−1, quail exhibited only in 14% of the steps
%congruity values lower than 50%. When comparing one step with its following one, ~29% of them
exhibited running mechanics in both steps, ~55% a mixture of walking and running, and ~16% walking
in both steps. e variation observed between individuals is only due to chance (Table1).
Simulations. We simulated quail locomotion using the minimalistic PVPP model and parameters
introduced in21. Results presented below are stable simulations. Stable walking, grounded running, and
running were already presented in21. Here, we add results for mixed gaits. In simulations, we found two
dierent types of mixed gaits, and an apparently mixed gait. In the preferred–leg mixed gait, one leg
exclusively exhibits walking mechanics and the other only running mechanics (Fig.3). In alternating
mixed gait, both legs gradually shi, out of phase, between walking and running mechanics. An appar-
ently mixed gait converges very slowly to grounded running, thus aer small perturbations, the gait
seems to be mixed (even aer 100 simulated steps, Fig.3, k = 100 Nm−1, magenta).
Mixed gaits in simulations using walking-like parameters. Using parameters obtained from walking quail
such as eective leg stiness and damping, average speed of locomotion (see methods), simulations
yielded mixed gaits at speeds ranging from 0.17 ms−1 to 0.65 ms−1.
Individual
Body
Mass (g)
Total steps i
vs i + 1v (%) b (%) m (%) p-value
Vanellus vanellus
B65+ 169.8 103 11 42 47
p = 0,003
p = 0,582+
B67 184.9 195 24 29 47
B76+ 163.2 150 13 45 42
B100+ 163.6 158 15 46 39
Haematopus ostralegus
5769 (1) 450.0 118 14 31 55
p = 0,487
5769 (4) 490.0 22 15 26 59
3970 (5) 433.3 391 17 37 46
3970 (7) 455.0 208 13 34 53
Recurvirostra avosetta
Orange+ 285.0 192 5 59 36
p = 0,034
p = 0,439+
Silber+ 348.0 193 8 53 39
Green+ 358.0 66 3 53 44
Wei ß 344.0 266 10 44 46
Coturnix coturnix
1 220 41 27 24 49
p = 0.662
2 202 67 10 33 57
5 204 63 17 26 57
8 202 29 14 31 55
9 225 49 14 30 56
Columba livia
437+ 582 108 9 35 56
p = 0,000
p = 0,32+
200 472 90 32 18 50
233+ 519 249 12 40 48
727+ 577 158 12 31 57
Table 1. Individual data. Body mass for individual study animals, total number of steps analyzed per
individual, percentage of occurrence of vaulting mechanics (v), bouncing mechanics (b), and mixed gaits
(m), and p-value chi^2 test. For pigeon, avocets, and northern lapwings is the p-value computed signicant
due to the variation of one individual (bold). e variation of the other 3 individuals (marked with+ ) among
these species is due to chance (see p+).

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SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
e mixed gait domain is a long, inclined volume that comprises almost the whole range of VPP
heights (Fig.3 le, cyan volume with black mesh). For lower VPP height, damping values are the highest
and decrease with increasing VPP height. e domain also stretched from mean trunk angles between
120° and 135°. Interestingly, the mixed gaits domain is located far from parameters that induce the model
to exhibit walking. e latter were observed at a more prone trunk position. Mixed gaits made up 5%
of the total solutions.
Mixed gaits in simulations using bouncing-like parameters. Using parameters obtained from bouncing-like
quail gaits (see methods and table1), mixed gaits existed in ve small separated volumes (Fig.3 right,
cyan volumes with black mesh). e largest one is located at damping values exceeding 6.5 Nsm−1 with
relatively shallow trunk angles between 112° and 120° and VPP heights up to 0.03 m. Again, mixed gait
domains are located far from parameters which induce the model to exhibit walking. Using bouncing-like
parameters, mixed gaits made up only 2% of the total solutions.
Independent of parameters being walking- or bouncing-like, the mixed gait produces an imbalance in
the GRFs. In Fig.4A we present a comparison between the GRF obtained for grounded running and for
preferred-leg mixed gait with identical model parameters though diering leg compression. During this
mixed gait, the peak of the GRF measured in the grounded running leg increased by 54% while maxi-
mal value of the vertical GRF in the vaulting leg decreased by the same value. Both gaits oscillate about
similar system energy (SEgr ~ 0.246 J; SEm ~ 0.248 J); however the dimensionless specic cost of transport
is about 20% higher for mixed gait (CoTgr = 0.211, CoTm = 0.254).
Discussion
We asked whether small birds predominantly use vaulting mechanics at lower speeds, and bouncing
mechanics at the higher speeds. Alternatively, small avian locomotion is less discrete and permit the
0 50 100
0
20
40
60
80
100
avocet
%congruity step i+1
%congruity step i
0 50 100
0
20
40
60
80
100
oystercatcher
%congruity step i
0 50 10
0
0
20
40
60
80
100
quail
%congruity step i
0 50 100
0
20
40
60
80
100
northern lapwings
%congruity step i+1
%congruity step i
0 50 100
0
20
40
60
80
100
pigeon
%congruity step i
0 50 10
0
%congruity step i
0
20
40
60
80
100
III
III IV
III
III IV
II
I
III IV
III
III IV
III
III IV
II
I
III IV
1
2
3
4
58
710
11
12
6
9
13
14
15
16
17
18
19
20
21
22
Figure 2. Values of %Congruity in step i vs. step i + 1. Quadrant I and IV depict mixed gaits. In I
%congruity shis from walking values in step i to values representing running mechanics in step i + 1. e
inverse occurs in IV. II and III portray regular gaits of running and walking mechanics, respectively. Red
points indicates that aerial phases occurred. For individual/marker type correspondence see Table1. Bottom
right shows a single trial from individual “3970(7)” comprised of 23 steps at 2.1 m s−1. Note that it combines
mixed gaits, grounded running, running (red), and walking. Arabic numbers indicate step sequence.

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SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
existence of mixed gaits such as those in which one step with walking mechanics is followed by one step
running mechanics or vice versa at relative constant speed. To test this with reasonable degree of gen-
erality, we conducted an automated large-scale study on CoM movements in a limited number of rela-
tively small, phylogenetically and morphologically diverse species of neognath birds (quail, oystercatcher,
northern lapwing, pigeon, and avocet), using a recently published methodology24.To complement the
experimental data, we also modelled gaits at the transitions between walking, grounded running, and
running based on parameters derived from live quail (cf.21). Still, further studies including data from
paleognath birds, i.e., tinamous and ratitites, will be necessary to test the broader generality of the results
presented here.
Our experimental results show no clear correlation between %congruity and speed. is suggests that
at least the birds studied do not strictly prefer walking mechanics at lower speeds or running mechanics
at higher speeds. Moreover, our results clearly display that the birds in our study engage mixed gaits more
oen than walking and, surprisingly, maybe more/as oen than/as grounded running (Table1, Fig.2). In
general, our statistics show that a bird displaying a walking step on the treadmill only had a chance of ca.
15% to repeat walking in the subsequent step. In contrast, if it exhibits a bouncing step, the probability
to exhibit again a bouncing step rises to ca. 40%. us, for large sequences, as shown in Fig.2, there is a
high chance to see combinations of dierent gaits. Accordingly, we found only in shorter video sequences
(5 to 10 steps) singular gaits such as walking, grounded running or mixed gaits (see Fig. S2).
Recent studies have already shown that some small to medium sized avian species such as lapwings or
tinamous do not always exhibit walking mechanics at lower speeds7,10,11. Other studies have shown that
grounded running may be the most frequently used gait in avian locomotion11,15,18. ese experimental
observations might not be entirely explained by a more compliant leg in small birds. It has been shown
that in mammals, leg stiness scales as the two-third power of body mass25,26, regardless of whether this
is quantied using a virtual leg dened as the length between the CoM and foot contact point or using
the eective leg. In other words, leg stiness is independent of body mass when normalized by body
mass and leg-length27. us, more probably, birds engage running-like or mixed gait mechanics oen
because of their pronograde trunk orientation. Andrada and colleagues recently showed through numer-
ical simulations with the PVPP model that most of the stable solutions obtained using quail parameters
are indeed grounded running21. ese results and those presented here add a functional criterion, namely
the need for stability, to the frequently observed occurrence of grounded running and, as demonstrated
in the current study, mixed gaits.
020406080100
0
20
40
60
80
100
%congruity step i
%congruity step i+1
020406080100
%congruity step i
0
20
40
60
80
100
%congruity step i+1
I I
II II
IIIIIIIV IV
b
a
a
Figure 3. Fields of stable locomotion for walking-like (le) and bouncing-like (right) parameters
(see methods). Grounded running (gr), running (r), walking (w), mixed (m), and apparently mixed
(a-m). Mixed gaits are: (a) preferred-leg mixed gait, a combination of one step walking and one step
grounded running, or (b) alternating mixed gait, the legs alternate gradually between walking and running
mechanics(i.e. while one leg changes from walking to grounded running, the contralateral leg changes in the
opposite way). Apparently mixed gaits converge to grounded running aer ca. 1000 steps. Subplots display
congruity changes between one step and the next for two examples of alternating mixed gaits. For every
simulation, both legs have same leg parameters, such as length at touch-down l0, stiness k, and damping c.

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SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
A clear separation between vaulting and bouncing mechanics can be useful to describe human loco-
motion. However, birds show a greater dispersion in the %congruity values. One explanation for these
ndings may lie in the pronograde trunk position in birds. Together, trunk, neck, and head make more
than 80% of the total mass of an individual, and have a relative motion with respect to the leg (the trunk
oscillates about the hip) so that leg compression and releases do not necessary oscillate in phase with
trunk rotation10,20,28,29. Such a phase shi may vary based on the relation between the inertia of the trunk,
the torque in the hip joint, and viscoelastic properties in the leg. It follows, that dierent anatomies may
favor diverse relationships between potential and kinetic energy. Taking a closer look at the scatter plots,
hints of species-related dierences become evident. Northern lapwings and especially avocets, move
mostly at %congruity values between 40 and 70 independently of speed, and choose bouncing gaits as
oen as mixed gaits if not more frequently. Such a locomotion may be distinctive for birds with relatively
long legs and svelte bodies. e rather bulky pigeon and oystercatcher displayed a dierent pattern.
%congruity values mostly indicate bouncing mechanics at lower speeds. Interestingly, as speed increased,
the dispersion of the %congruity values increased, and even at higher speeds (see Fig.1), they exhibited
vaulting mechanics in ca. 40% of the steps. Quail are predominantly terrestrial birds; however, they did
not show a clear trend towards vaulting or bouncing during locomotion on the treadmill. Quail, pigeon
and oystercatcher seem to employ mixed gaits more frequently than bouncing gaits.
e scarcity of the red points in Fig.1 indicate that running with aerial phases represent a rare event
in our experiments. In our dataset, quail and pigeon did not use aerial phases. Here, the fact that they
0.03
0.04
0.05
0.06
0.07
0.08
mixed
gr
0
0.
5BW
BW
1.
5BW
2BW
AB
0.06
0.07
0.08
0.09
0.1
0.06
0.07
0.08
0.09
0.1
mixed
gr
mixed
gr
CD
CoM's vertical position [m]
CoM's vertical position [m]
CoM's vertical position [m]
Figure 4. Switching between preferred-leg mixed gait and grounded running. In the overlapping
zones of Fig.3, two limit cycles exist for the same model parameters. (A) Model ground reaction forces
(grounded running dashed lines, mixed gait solid line). (B) Step down simulation, grounded running
(black) and preferred-leg mixed gait (cyan). In the simulations presented here model parameters are equal.
During unperturbed locomotion (B, before vertical grey line), just the leg compression decides whether
the gait converges to grounded running (y0 = 0.088) or to a mixed one (y0 = 0.074). e %congruity
values aer 50 steps are: grounded running (leg 1 = leg2 = 89); mixed (leg1 (A, red solid line) = 31.6, leg2
(A, black solid line) = 84.2). Aer step up (D) or step down (B) perturbation, both gaits converge to the
same preferred-leg mixed gait; however, if the gait is mixed before the step-down perturbation, aer the
perturbation it converges much faster to the xed point. Aer step-up-step-down perturbation (C, 20% leg
length), grounded running converges to preferred-leg mixed and preferred-leg mixed to grounded running.
Parameters: Ψ0 = 140°, rVPP = 0.07 m, k = 100 Nm−1, and c = 2.9 Nsm−1, φ
0 = 50.

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moved at dimensionless speeds (
ˆ
u
) lower than 1 may explain the absence of aerial phases. Our quail
subjects were mostly not cooperative to locomote at speeds higher than 0.7 m s−1. Aerial phases were
nonexistent or rare in former quail treadmill and trackway studies11,18.
Our results suggest that mixed gaits are a ubiquitous feature in neognath avian locomotion. erefore,
it is reasonable to analyze numerically the existence of mixed gaits with input data of one species. e
PVPP model incorporates three key features of bird locomotion: (i) the pronograde trunk, (ii) asymmet-
ric compliant leg behavior along the leg axis, modelled as a parallel spring-damper system, and (iii) a
xed aperture angle as a leg alignment strategy. All three features were inferred from in vivo experiments
involving quail (for more details see21). By simulating quail gaits using the minimalistic PVPP model in
conjunction with parameters obtained through experiments with live quail, we were able to nd dier-
ent stable mixed-gaits: i) “preferred-leg mixed gait”, in which one step walking is followed by one step
grounded running or vice versa, or ii) “alternating mixed gait”, in which a gradual shi from one gait
mechanics into the other, occurring out of phase for each leg. ese two types of mixed gaits emerged
with both legs having same leg length (l0), stiness (k), and damping (c) parameters. Interestingly, no
matter whether leg parameters are vaulting or bouncing like, the parameter spaces belonging to mixed
gaits are not located close to the boundaries between walking and grounded running, but rather at the
boundaries between grounded running and running (Fig. 3). is should not be understood only in
terms of speed, which is a state of the model. In fact, in contrast to12,16, our model found mixed gaits in a
wide range of middle to higher speeds. In agreement with the model predictions, both mixed gaits can be
observed in the experimental data. An example of preferred-leg mixed gait is shown in the ESM Fig. S2,
while the example presented in Fig.2 can be understood as an alternating mixed gait (cp. Fig.3).
Our simulation ndings may explain the remarkable dispersion in the %congruity values observed
in our experimental data. Recall that mixed gaits parameters mostly overlap those of grounded running
(Fig. 3). is means that in the overlapping zones, for the same combination of parameters, two limit
cycles may exist (two stable periodic solutions). In those cases, simply changes in a state variable such as
leg compression or perturbations in CoM height may induce grounded running to change to mixed gaits
or vice versa. One example is presented in Fig.4. ere, both solutions exhibit similar system energy, but
the management of the energy-ow among legs and trunk vary. In addition, the subplots in Fig.3 reveal
that if birds engage alternating mixed gaits, the same gait will be categorized either as mixed, grounded
running, or even walking, depending only on the moment of the observation.
To what degree locomotion on normal ground vs. treadmills diers among avian species is a question
that remains unresolved. Our results discussed here are not free from the issue of potential treadmill
artifacts in the data (i.e. birds not moving normally due to the substrate moving beneath them). On the
other hand, locomotion across tracks is frequently unsteady and limited to freely selected speed ranges
and a few number of observed steps. Nevertheless, simulations support to a certain degree that mixed
gaits are part of the dynamics of pronograde bipedal locomotion and not just a treadmill artifact.
However, our model predicts mixed gaits for only 5% of the solutions when using walking-like param-
eters and only 2% when using bouncing-like parameters, while the measured birds employ it in a large
percentage of their strides. We think there are some possibilities to explain this paradox: a) birds might
use very frequently a combination of leg parameters that are close to the attraction zone of mixed gaits,
b) locomoting without visual ow might represent a disturbance to the animal enforcing such mixed gait
patterns due to the relation between trunk motions and head bobbing20,29, or c) our simple 2D model,
which has identical leg parameters and lacks of medio-lateral motions, fails in showing the complete
solution space for mixed gaits. To investigate possibility ‘b,’ experiments with projected environments
moving matched to the treadmill’s speed would be helpful.
Finally, the data presented here raises the question of the importance or advantages, for example in
terms of energy or stability, that mixed gaits might oer robotics in transitioning between grounded
running and running or in improving eciency. At rst view, mixed gaits seem to confer disadvantages
in terms of visual cue (cf. discussion in10,20) and leg load, because of the larger CoM vertical ampli-
tudes and GRF imbalance. In addition, our simulations indicate that mixed gaits are less ecient than
grounded running at same system energies. e 20% higher requirement of energy obtained from our
simulations poses new questions about trade-os between metabolic optimality and stability that cannot
be completely resolved in this study. However, if metabolic optimality was the only determining factor,
one might expect that small birds would avoid mixed gaits completely. is expectation was clearly not
supported in our experimental results. One way to mitigate the negative metabolic eects of mixed gaits
might be to limit/reduce the %congruity imbalance between legs (see Supplementary Information Fig. S2).
For small animals the terrain is almost always uneven30, and thus, for some leg settings, mixed gaits
might emerge as the only self-stable way of movement.
Methods
e main goals of the study were to determine how the congruity of CoM mechanics correlate with
speed and if small birds really use mixed gaits. In light of this, we used available X-ray videos from the
server of the Institut für Spezielle Zoologie und Evolutionsbiologie in Jena from a range of species across
the avian phylogeny. By sampling a limited number of phylogenetically diverse (we sampled species
from three clades: galliformes, columbiformes, and charadriiformes) and morphologically diverse (we

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9
SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
included three species of shorebirds with highly diering limb segment proportions), we could reason-
ably discern with a limited sample of just a few species whether shi of %congruity and mixed gaits are
a more ubiquitous feature of small avian terrestrial locomotion and not a peculiarity of isolated species.
Note that our study included only neognath birds, therefore, similar studies on tinamous and ratities
will be necessary for a higher level of generality. e methods reported below describe in general the
experimental setup. For the purposes of this study, we reanalyzed previously recorded data.
Our large scale analysis covers 757 treadmill trials of ve species (common quail: Coturnix coturnix,
Eurasian oystercatcher: Haematopus ostralegus, northern lapwing: Vanellus vanellus, domestic pigeon:
Columba livia, and pied avocet: Recurvirostra avosetta), totalizing 7749 steps and 1,267,320 image frames.
Animals were obtained from local breeders and housed in spacious cages with access to food and water
ad libitum at the Institut für Spezielle Zoologie und Evolutionsbiologie in Jena, Germany. e Committee
for Animal Welfare of the State of uringia, Germany, approved the animal keeping and all experimen-
tal procedures (registry number 02-47/10). Animals were kept and all experiments were carried out in
strict accordance with the approved guidelines.
e treadmill was covered with a tunnel made of Plexiglas so that the animals were not able to
y away from the treadmill. When the treadmill was started the animals usually started to walk on
their own. While walking and running on the treadmill at dierent speeds, high-speed X-ray videos
were recorded from the lateral and ventral projection (fully digital X-ray device Neurostar, Siemens
AG, Erlangen, Germany). Additionally, two standard light cameras were synchronized with the X-ray
camera and lmed from a fronto-lateral and a frontal perspective. All recordings were obtained at a rate
of either 0.5 kHz or 1 kHz. Each frame was taken as a digital image with a resolution of 1,536 × 1,024
pixels (X-ray camera) and 512 × 512 pixels (standard light cameras), respectively. e X-ray source oper-
ated at 40 kV and 95 mA. Prior to analysis all X-ray recordings were undistorted using a freely availa-
ble MATLAB (e MathWorks Inc., Natick, MA, USA) routine (www.xromm.org) provided by Brown
University (Providence, USA).
We are aware that locomotion is a 3D phenomenon and that birds do not operate limbs only parasag-
ittally29,31,32. However, for the determination of a gait, it is sucient to use CoM oscillations in the sagittal
plane (e.g.2,3,16,18,33,34). us, for the automatic estimation of CoM position and %congruity we only used
the lateral projection of the available X-ray videos.
Removing background and automated CoM estimation. e method published by Haase and
colleagues24 is able to approximate the position of the CoM without any kind of user interaction, solely
based on the automatic analysis of the images of a given X-ray sequence. e main idea of this approach
is to relate each pixel of an image to the mass of matter it represents. e theoretical basis for this process
is the Beer–Lambert law35,36, which describes the absorption of electromagnetic waves traversing an arbi-
trary material. To resolve ambiguities arising from the fact that only one X-ray view is available (cf.36,37),
this method assumes volumic mass and X-ray absorption coecients to be identical for all materials, but
relative errors caused by this approximation are small for materials encountered in X-ray animal anal-
ysis (namely water, fat, tissue, and bone). As the CoM calculation is solely based on image gray values,
it is crucial to remove all background information from the images. Based on the Beer–Lambert law, a
known background component (e.g. obtained by recording an empty sequence) can be removed from an
image via a pixel-wise division by the background image. However, in many cases such as for previously
recorded datasets, the background is not known and thus has to be estimated from the image sequence
itself. Because this is an ill-posed problem (i.e. an innite set of solutions exists), we regularize the esti-
mation to maximize the information explained by the background. e regularized problem has a unique
solution which can eciently be computed as the pixel-wise maximum overall images of a sequence.
Artifacts in the background estimation may appear when the animal remains relatively static over the
course of an entire sequence, but can easily be corrected using inpainting techniques (e.g.38). For more
detailed derivation and discussion of the algorithm please refer to24. An implementation of the algorithm
can be found for Matlab and C + + free for use under http://www.inf-cv.uni-jena.de/locomotion.
Automated detection of foot contacts, aerial phases, and visibility of bird. Touch-down
detection: we found that when the pixel values of the leg of every frame are projected onto the x-axis,
the obtained 1D-curve display at TD a maximal bimodality. We measured the bimodality value of the
1D-curve by comparing it to a normal distribution of same mean and variance using histogram inter-
section distance. Frames in which a TD event occurs are then found by identifying all local maxima of
the bimodality score over all frames (Fig.5).
Aerial phase: for each frame of a trial, we computed the minimum distance between the lowest point
of the legs and the bottom of the image. Aerwards, a threshold was used to classify each frame as
“aerial phase” or “stance phase” based on its leg height. For each sequence, the threshold was estimated
automatically in such a way that only frames in which the legs are substantially higher than the median
leg height are classied as “aerial phase” (see Supplementary Information, Fig. S1).
Visibility: to account for cases in which the birds le the eld of view, for every frame of each trial we
computed the number of pixels in which the bird is visible (‘bird-pixels’). % of congruity was computed,
only when the measured number of bird-pixel during all frames of a stance phase was higher than 80%
of the maximal computed number of bird-pixels of the complete trial.

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e algorithms described in this section were implemented in the programming language R and are
freely available to download and use from http://dx.doi.org/10.6084/m9.gshare.1471629.
Percentage of congruity. To dierentiate vaulting from bouncing gaits, we used %congruity19.
%congruity is the percentage of overall frames making up a step which feature frame-to-frame changes
in Ep and Ek of equal sign. Note that %congruity does not consider the magnitudes of mechanical ener-
gies, and therefore cannot account for the amount of energy conversion or recovery. On the other hand,
this method permits the analysis of CoM dynamics without the need of calibration of the X-ray videos.
Ideally, %congruity would be 100% in a perfect bouncing (running) trial and 0% in an ideal vaulting
(walking) trial. Ep was calculated as
=()
Emgy 1
p
Figure 5. Touch-down detection for an exemplary quail sequence. e plot in the upper part of the gure
shows the computed bimodality scores for each frame of the sequence. Touch-down is detected at local
maxima of the score (marked by vertical dotted lines). For each frame, the bimodality score is assessed by
(1) projecting the pixel values of the legs onto the x-axis, and (2) using the histogram intersection distance
to compare the resulting distribution to a Gaussian distribution of same mean and variance (red curves).
Examples of this process are shown in the lower part of the gure for ve frames between two touch-down
events. e leg-only images are computed automatically based on a projection of the pixel values onto the
y-axis.

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11
SCIENTIFIC RepoRts | 5:13636 | DOI: 10.1038/srep13636
where m is mass, g is gravitational acceleration, and y is the vertical oscillation of the CoM. Ek was
calculated as
=. (+
)()

Emxy05 2
k
22
where

x
and

y
are the horizontal and vertical velocities, respectively. Note that mechanical energies are
not in SI units.
For the sake of simplicity, we dened a step, as the period between the touch-down of a leg and the
touch-down of the contralateral leg. For computing %congruity we did not include the rst and last steps
of each trial, because they are usually incomplete. en, to avoid erroneous %congruity calculation due
to stumbles or speed changes, we used only steps of a trial which exhibited similar contact times. To
accomplish that, we computed the median of the contact periods of the steps of a trial (in frames). Only
contact periods within ±10% of the median were used for further calculations. Further, we discarded
steps if the step-to-step horizontal variation of the CoM was larger than 20 pixels (approx. 5 mm). en,
we used an elliptic high-pass lter to reduce negative eect of dri (2 Hz cut-o frequency) in the com-
putation of congruity. Finally, we low pass ltered at 100 Hz both coordinates of the CoM.
For selected trials (one walking and one bouncing for each individual), we computed the relative
position of the CoM related to the pelvis and the eective leg length. Eective leg length was com-
puted in SI units. For that purpose, we digitized landmarks corresponding to the hip, distal part of the
tarsometatarsus and tip of the middle toe from both lateral and ventral X-ray views using Winanalyse
(Mikromac, Germany). A calibration object into which metal beads were inserted at known distances
was also recorded in both projections at the end of each recording day. Direct linear transformation
(DLT) was performed in Winanalyse to 3D calibrate the recorded space. Eective leg length was then
computed in Matlab from the sagittal projection of the 3D-coordinates.
For appropriate comparisons of bipedal locomotion among the ve species, we calculated the dimen-
sionless speed (
ˆ
u
), dened as
=/
()
ˆ
uvgL
3
where v is the treadmill speed, g is the gravitational acceleration, and L is the eective leg length dened
as the mean distance between the hip and the tarsometatarso-phalangeal joints during the stance phase.
Statistics. To analyze whether the variation of the individual gait-preference observed among every
species is due to chance we used the Chi-square test (PASW Statistics for Windows, Version 18.0. Chicago:
SPSS Inc.; asymptotic method for expected frequencies above 5, exact method for frequencies below 5).
Numerical model. e sagittal plane PVPP model21 consists of a rigid body of mass m with a moment
of inertia J connected at the hip to two massless legs modeled as parallel spring-damper elements
(Fig.6B). e trunk can pivot freely about the hip axis. e CoM of the model is located at a distance
rh from the hip at an inclination θ from the vertical (Fig.6B). e location of the VPP is given by the
distance rVPP from the CoM and the inclination
ψ0
from the body axis (Fig.6B). e equations of motion
are:
=()
̈
mFx4
x
=− +()
̈
mmgFy5
y
θθψθψ=( (− )− (− )) ()
̈
JrFFcossin
6
VPPx y00
where Fx and Fy are respectively the sum of the horizontal and vertical components of the GRF of the
legs, g is gravitational acceleration,
̈
x
,
̈
y
, and
θ
̈
are the horizontal, vertical, and rotational CoM accelera-
tions, respectively. e GRF is calculated to point towards the given VPP.
We use the same two gait categories of initial parameters used by Andrada and colleagues (2014),
which is based on the parameters obtained from vaulting and bouncing gaits of live quail: (i) walking-like,
with k = 75 Nm−1, φ
0 = 45°, and horizontal initial velocity vx0 = 0.4 ms−1, and (ii) bouncing-like with
k = 100 Nm−1, φ
0 = 50°, and vx0 = 0.6 ms−1. Just as in the experiments with living animals, we relied on
%congruity to discriminate vaulting from bouncing, and then distinguished running from grounded
running by checking for aerial phases (i.e., when no leg has contact to the ground). A rigorous analysis
of stability was not the aim of this paper. Also following our previous work21, we dened stability as the
ability to cope with undetected perturbations of the ground level. Finally to compare eciency between
gaits, we used the dimensionless specic cost of transport, CoT = energy used/(weight x distance trave-
led) (7) (see ESM for more explanations on stability and CoT).

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Acknowledgements
Rommy Petersohn, Ingrid Weiß, Henriette Weise, Nadine Grimm, Irina Mischewski and Itziar Candeal
helped with X-ray data acquisition. Silvia V. Lehmann generated the data basis and computed relative
position of CoMs. is research was supported by DFG (German Research Council) grants Bl 236/22-
1/3, Fi 410/15-1/3, De 735/8-1/3.
Author Contributions
E.A., B.M.K., D.H., J.A.N, J.D., M.S.F. and R.B. conceived the study; B.M.K. and J.A.N. conducted the
experiments; D.H. developed the tracking algorithms, E.A. analysed the experimental data; E.A. and Y.S.
conducted simulations, and E.A. draed the manuscript. All authors contributed to the interpretation of
the results and revised the manuscript.
Additional Information
Supplementary information accompanies this paper at http://www.nature.com/srep
Competing nancial interests: e authors declare no competing nancial interests.
How to cite this article: Andrada, E. et al. Mixed gaits in small avian terrestrial locomotion. Sci. Rep.
5, 13636; doi: 10.1038/srep13636 (2015).
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