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First published online January 8, 2007
Journal of Experimental Biology 210, 198-207 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.02657
The desert ant odometer: a stride integrator that accounts for stride length and walking speed
1 Institute of Neurobiology, University of Ulm, Albert-Einstein-Allee 11,
D-89069 Ulm, Germany
2 Institute of Zoology, University of Zürich, Winterthurerstrasse 190,
CH-8057 Zürich, Switzerland
* Author for correspondence (e-mail: matthias.wittlinger{at}gmx.de)
Accepted 8 November 2006
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By manipulating leg lengths in foraging desert ants we could also change their stride lengths. Ants with elongated legs ('stilts') or shortened legs ('stumps') take larger or shorter strides, respectively, and misgauge travel distance. Travel distance is overestimated by experimental animals walking on stilts, and underestimated by animals walking on stumps - strongly indicative of stride integrator function in distance measurement.
High-speed video analysis was used to examine the actual changes in stride length, stride frequency and walking speed caused by the manipulations of leg length. Unexpectedly, quantitative characteristics of walking behaviour remained almost unaffected by imposed changes in leg length, demonstrating remarkable robustness of leg coordination and walking performance.
These data further allowed normalisation of homing distances displayed by manipulated animals with regard to scaling and speed effects. The predicted changes in homing distance are in quantitative agreement with the experimental data, further supporting the pedometer hypothesis.
Key words: desert ant, Cataglyphis, navigation, stride integration, walking behaviour, odometer
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Introduction |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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; Wehner and
Srinivasan, 1981) (for reviews, see
Barth, 2002;
Wehner, 1992), which relies on
acquisition and summation of these two vector components. In desert ants and
honey bees, the estimation of travel direction is based on a well-studied
celestial compass, reading the polarised (and spectral) sky light pattern and
the sun's azimuth (Wehner and Lafranconi,
1981; Wehner,
1989; Wehner,
1997).
Distance measurement in insect navigation, by contrast, has long remained
controversial. Earlier experiments in flying honey bees supported the `energy
hypothesis', initially put forward by Heran and Wanke
(Heran and Wanke, 1952) (see
also Heran, 1956;
von Frisch, 1965). The energy
hypothesis states that travel distance is gauged by the energy expenditure
afforded during flight. However, in a series of elegantly designed experiments
it was demonstrated that the bees' estimation of travel distance is achieved
by the integration of self-induced optic flow experienced en route
(Esch and Burns, 1995;
Srinivasan et al., 1996;
Srinivasan et al., 1997;
Esch et al., 2001;
Tautz et al., 2004). By a
similar token, the energy hypothesis is not applicable to desert ant odometry.
For instance, desert ants assess their walking distances with amazing
accuracy, irrespective of the load they carry
(Wehner, 1992). Contrasting
with the honeybee odometer, however, the integration of visual flow-field cues
('optic-flow' hypothesis) plays a minor role in the odometer of
Cataglyphis fortis (Ronacher and
Wehner, 1995). This is true for flow-field stimuli presented in
the ventral field of vision, while lateral optic flow has no effect at all
(Ronacher et al., 2000). In
fact, without any visual experience of ongoing movement, in complete darkness
or featureless environments
(Thiélin-Bescond and Beugnon,
2005), Cataglyphis still gauge their walking distance
fairly correctly. Thus, the ants appear to rely on idiothetic cues, derived
from the movements of their legs (e.g.
Pieron, 1904). That is, they
employ a `stride integrator', as recent experiments have illustrated
(Wittlinger et al., 2006).
In this study we investigated how Cataglyphis ants measure travel distance, focussing on leg movement during walking. We manipulated leg length, and since stride length, walking speed and leg length are interdependent, we consider all three parameters in our analysis. Leg lengths were altered in ants walking back home from a feeder to their nest, by means of both, truncation and extension, reducing the animals' legs to stumps or providing them with stilts. Manipulation of leg length automatically changed stride length and walking speed, and provided critical parameters for testing the stride integrator hypothesis. We show that experimental ants striding home with manipulated leg lengths, walking on stilts or on stumps, and thus using stride lengths different from their outbound journey, misgauge homing distance in proportion to the imposed changes in (normalised) stride lengths. Nevertheless, characteristics of walking behaviour remained almost unaffected by altered leg length, demonstrating a remarkable robustness of leg coordination and walking performance.
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Materials and methods |
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) were
selected for experiments. The experimental season lasted from the middle of
June to the start of September in 2004 and 2005. The ants were trained to walk
a distance of 10 m in a linear alloy channel from their nest entrance to a
feeder established due south (Fig.
1). The channel was 7 cm wide and the walls 7 cm high, such that
the ants experienced a strip-like view of the sky of about 45° to almost
60°, depending on the height of the ant's eyes above ground and its actual
position on the channel floor, to read the skylight pattern and compass
information. To provide traction for walking, the channel floor was coated
with fine grey sand. This sand coating reliably prevented slipping of the
ants, as judged from high-speed video recordings (see
Fig. 3). This held in
particular after removal of the ants' tarsi, and the traction devices
associated with them, in the course of the operation procedures below. Grain
size of the sand ranged between 0.2 and 0.4 mm, to minimise visual orientation
cues such as optic flow. The channel walls were painted with matt grey varnish
to provide a featureless environment, and avoid distracting reflections.
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). Once put into the test channel, the animals immediately
took up determined homeward runs that ended when the behaviour switched to
nest searching (cf. Müller and
Wehner, 1994). This switch is marked by a conspicuous U-turn
(Sommer and Wehner, 2004),
followed by a run pacing back and forth around the assumed position of the
nest entrance. We noted the point of this switch in homing behaviour, as well
as the first six consecutive turning points
(Fig. 1, search trajectory),
for later calculation of the median and construction of search density
distributions (below, Fig. 4).
Each ant was tested twice, first straight after the manipulation of leg length
at the feeding site (Test 1, Fig.
4A); the animal was then put back into the nest and tested a
second time after having re-emerged from the nest and travelled to the feeder
again (Test 2, Fig. 4B). The
marked and manipulated ants were again caught at the feeder and immediately
transferred to the test channel. In this situation, leg length, and thus
stride length, was the same in both, outbound and homebound runs, although
different from normal due to the previous manipulations.
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Manipulation of leg length
The ants' legs were shortened either by removing the tarsal segments
(stumps I, Fig. 2) or by
severing the leg at mid-tibia level (stumps II,
Fig. 2) with a pair of small
scissors. The animals' legs were splinted and extended with adhered pig
bristles, as illustrated in Fig.
2. The pig bristles were glued to the legs with cyanacrylate glue
(Superglue) and extended for about 1 mm beyond the tarsal tips. This procedure
extended the effective leg length by about 2.0-3.0 mm since the distal tarsus
segments are normally apposed to the substrate for traction (see `normal' in
Fig. 2). Leg length in `normal'
ants was not altered and they served as controls.
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Analysis of behavioural data
The test channel was divided into 10 cm bins for distance recording, as
outlined above. First, search density distributions
(Fig. 4) were evaluated in
N=25 animals for each experimental situation. The bins of the test
channel covered by an ant during its search were noted and cumulated, that is,
the more often a channel segment (bin) was visited during the search, the
higher its value in the density distribution (see
Fig. 4, upper panels). Search
density distributions were normalised to their peak values, and their widths
at half-maximum height (half widths) were determined. Second, the median
values of the initial six turning points of the ants' nest searches were
calculated to provide an estimate of the search centre. From the median values
of N=25 ants per experimental situation, box-and-whisker plots were
constructed (see Fig. 4, lower
panels). Marked values in the box-and-whisker plots are the centre (median),
the spread (interquartile range), and the 10th and 90th percentiles (whiskers)
of search centre values.
High-speed video films
Film recordings were made with a Redlake MotionScope (Redlake MASD Inc.,
San Diego, USA) high speed camera at 250 frames s
(Fig. 3). Normal and
manipulated freely walking ants were filmed in top view whereas walking in a
pen of 10 cmx30 cm or in an alloy channel of 2 m length, both supplied
with the sandy walking substrate mentioned above (and a piece of millimetre
graph paper for calibration). Since it was not possible to film the complete
homebound travel of the above experimental ants, these high-speed video
analyses were carried out in a different set of animals. Whereas all other
experiments were performed in Maharés, some of the video recordings
were made in the laboratory at the University of Ulm to sample at slightly
lower temperatures than in the desert (
30-45°C air temperature), and
thus broaden the range of walking speeds used to calculate the regression
lines in Fig. 6. Each ant
performed at least four runs and was subsequently preserved in 70% alcohol for
later anatomical inspection and measurement of morphometric data. Stride
lengths (s2) of the left and right middle legs (l2, r2; see
Fig. 3), as well as walking
speeds were analysed from the video films. Only those runs were considered for
evaluation that showed straight walking paths without deceleration or abrupt
stops.
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Second, the video data were normalised with regard to walking speed
(v). Stride length (s) and stride frequency (f) are
the two determinants of running speed (stride length multiplied by the number
of strides per second is locomotor speed), and the relationship of these two
parameters was determined for the different experimental situations
(Fig. 6) (see also
Zollikofer, 1988;
Zollikofer, 1994b). This
relationship was then used to normalise stride lengths to a stride frequency
that occurred in all examined individuals. The relationship between stride
length (ordinate in Fig. 6) and
stride frequency (abscissa) was described by a regression line
(y=bx+a) (Fig.
5). The term of the regression line was used to normalise the
stride length data to a stride frequency of 20 Hz, that is, the data points
were shifted along the respective regression line to 20 Hz on the abscissa:
s2'20Hz=(bx20
Hz+a)+[s-(bf+a)].
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The stride length and stride frequency data were also plotted against walking speed (see Fig. 7) to provide a basis for comparison with other data in the literature (see Discussion).
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From the high-speed film analysis, linear correlations of the distributions
of walking parameters were calculated for each treatment group. Correlation
coefficients, regression coefficients and axis intercepts were tested with
student's t-test (for difference from 0, and for differences against
each other). Statistical methods are described in detail in Sokal and Rohlf
(Sokal and Rohlf, 1995).
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After testing (Test 1) the ants were put back into their nest, and they were tested again when they turned up at the feeder during one of the following days (Test 2). These animals had thus performed their outbound runs with manipulated leg and stride lengths, and they were caught at the feeder to be tested as further controls (in addition to the unmodified ants, searching around 10.20 m; as described above). We expected them to be `recalibrated' since they had the same manipulated leg length during the outbound as well as during the homebound runs. They should thus show searches centred on the correct nest-feeder distance of 10 m. And this was indeed what we observed. Each group of experimental ants, whether walking on stilts or on stumps, performed almost identical homing runs, corresponding to that of normal ants (above). Ants on stilts (stilts, N=25) searched at 10.55 m, and ants with shortened legs at 9.55 m (stumps I, N=25) or at 10.25 m(stumps II, N=25). No statistically significant difference was discernible between these groups (P=0.502).
The half widths (see Materials and methods) of the search density
distributions, as shown in Fig.
5, reflect the uncertainty of the ants' estimates of their homing
distance (Wolf and Wehner,
2005; Merkle et al.,
2006). Half width values exhibit a conspicuous relationship to the
imposed changes in leg length. In the data from Test 1 (see
Fig. 4A), half widths increase
with enlarged leg length, and they decrease with shortened legs. This effect
is still present, though much reduced, in the Test 2 data.
Striding on stilts and stumps
High-speed video analysis of running ants was initially performed to
examine the actual changes in stride lengths caused by the manipulations of
leg length (a linear relationship between leg length and stride length may not
be assumed - consider a human balancing on stilts, who takes short strides
indeed). These video analyses illustrated immediately that the overshoot in
ants with stilts, and the undershoot in ants with stumps of different lengths
(stumps I and stumps II), corresponded to the altered stride lengths in a
qualitative way. That is, ants on stilts took longer strides and ants on
stumps shorter strides than did normal animals.
Stride length in normal Cataglyphis depends on two parameters, (i)
on leg length and thus body size, as body morphology is isomorphic in C.
fortis worker ants (Wehner,
1983), and, (ii) on the velocity of locomotion. As is true for all
walking animals, the faster Cataglyphis run, the larger are the
strides they take, and the larger is their stride frequency
(Zollikofer, 1994a;
Zollikofer, 1994b). To obtain
a quantitative assessment of the altered homing distances in manipulated ants,
relative stride lengths were thus calculated to eliminate effect of scaling,
that is, of variation in body size. The effect of locomotor velocity on stride
length was eliminated by comparing the animals after normalisation to a
certain stride frequency, as described in the Materials and methods
section.
To this end, the relationships between walking speed and its two determinants, stride length and stride frequency, was analysed for the different experimental situations. Stride length is plotted versus stride frequency in Fig. 6. It is evident that manipulation of leg length changed the relationship between stride length and stride frequency, as was to be expected. Ants with elongated legs made longer strides at any given stride frequency than did normal ants, and ants with shortened legs took shorter strides. These relationships were used to normalise the stride length data of the experimental animals to a stride frequency of 20 Hz, a frequency observed in all experimental situations. This normalisation allowed direct comparison of ants walking at different speeds, be it due to different prey loads or experimental manipulation.
According to the video analysis and after the above normalisation procedures, the changes in stride length, and thus homing distances, to be expected as a result of the manipulated leg lengths were as follows. Homing distances should have been reduced by 27.7% in ants with the shortest legs, half of their tibiae being clipped (stumps II), by 15.1% in ants with severed tarsal segments (stumps I), and the homing distance would be expected to have increased by 31.5% in ants striding on stilts (Fig. 4A, hatched box-and-whisker plots). The homing distances actually reported above, when converted to percentage values, were in fairly good agreement with these expectations, amounting to 43.6%, 31.9% and 50.0%, respectively. The observed homing distances were, however, consistently farther from the real nest-feeder distance by an average 17.1% (range 15.9-18.5%) than would be expected from the altered stride lengths as recorded in the high-speed video analysis.
When the altered homing distances of the ants walking on stilts or stumps are converted into stride numbers (at a normalised 20 Hz and standard body size to make data comparable), the ants walking on stilts, normal legs and stumps I and II took an average 1066, 924, 745 and 727 strides before looking for their nest entrance. According to the altered stride lengths, as determined from the high-speed videos, all groups would have been expected to take 924 strides - the value on which the normalisation procedure was based.
Characteristics of walking behaviour in ants with manipulated leg lengths
Whereas the plot of relative stride length versus stride frequency
in Fig. 6 served primarily to
normalise the behavioural data regarding homing distance, these data may also
be used to characterise walking behaviour after the manipulation of leg
lengths. Fig. 7 presents plots
of stride frequency (Fig. 7A)
and stride length (Fig. 4B)
against walking speed. These diagrams lend themselves to direct comparison
with data from other insects, and indeed other walking animal groups (see
Discussion).
The rise in stride frequency (Fig.
7A) and the rise in stride length
(Fig. 7B) with increasing
walking speed may both be approximated with good accuracy by linear regression
lines, values for R2 ranging from 0.81 to 0.87.
Curvilinear (exponential) fits to the data points are just slightly better for
the frequency-speed relationship (R2=0.92) and indeed
worse for the stride length-speed relationship (R2=0.77).
This means that in the recorded speed range no saturation of stride frequency
was observed [compare two articles by Full and Tu
(Full and Tu, 1990;
Full and Tu, 1991)], indicative
of the absence of flight phases in the step cycle, or galloping.
Considering the different manipulations of leg length, it was to be expected that, at any given walking speed, stride frequency is higher in the animals walking on shortened legs than it was in normal ants. And animals walking on stilts exhibit even lower stride frequencies at that given stride frequency. The slopes of the regression lines show corresponding changes, the slope being highest for the animals with the shortest legs and lowest for the ants walking on stilts. The frequency range is slightly reduced at the high end in all manipulated animals (to 95% in ants with stumps), most notably in the ants walking on stilts (to 71%). The associated reduction in maximum walking speed is less pronounced (to just 82%), because of these animals' elongated legs. By contrast, maximum walking speed is clearly reduced in the ants with the shortest stumps (to 56%, and to just 80% in stumps I animals).
By the same line of argument, it was to be expected that, at any given walking speed, stride length is larger in ants walking on stilts and smaller in ants walking on stumps than it is in normal animals. The slopes of the regression lines are in the same range for all groups of animals. Maximum stride lengths are, of course, clearly reduced in ants with shortened legs (to 75% and 65%, respectively). Unexpectedly, ants walking on stilts exhibit maximum stride lengths that are just marginally larger (104%) than those of normal ants, instead of clearly exceeding the normal range. This is indicative of some impairment resulting from the operation, most probably caused by the added load of the stilts and glue on the legs. In fact, stilts and glue added about 56% to the legs mass, and in a distal position, producing disproportionately high inertial momentum. Considering this added mass it is indeed surprising that maximum stride frequency, and to a minor extent maximum stride length, are the only parameters of walking behaviour that deviated from expectations.
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) is in fact neither applicable to bees
(Esch and Burns, 1995), nor to
desert ants (Wehner, 1992;
Schäfer and Wehner,
1993). And the `optic flow hypothesis', although elegantly proven
for flying bees (Esch and Burns,
1995; Srinivasan et al.,
2000), plays only a minor role, if any, in desert ant navigation
[a minor role was implicated for optic flow in the ventral visual field
(Ronacher and Wehner, 1995)
(below); no contribution at all for the lateral visual field
(Ronacher et al., 2000)]. The
remaining, and actually most straightforward, idea is the `step counter
hypothesis' proposed by Pieron (Pieron,
1904). More correctly, this hypothesis should be termed `stride
integrator hypothesis' since insects most probably do not literally count but
rather integrate some parameter associated with rhythmic leg movement in
walking (below) (Franks et al.,
2006). We thus use that latter term in the present study. The
`stride integrator hypothesis' has been confirmed in principle recently by
studying the homing behaviour of desert ants with imposed changes in leg
length (Wittlinger et al.,
2006). However, detailed analysis of walking behaviour in ants
with manipulated leg lengths was not performed in that study. Such analysis is
indispensable for a quantitative assessment of the pedometer hypothesis,
though, due to possible changes in walking behaviour brought about by the
manipulations. This has been pointed out in a recent review on distance
estimation in flying and walking insects
(Collett et al., 2006). In a
tentative calculation, because of the lack of appropriate data such as those
presented here, the authors conclude that desert ants might indeed
systematically change their walking behaviour in response to the stilts and
stumps manipulations, for example, regarding the swing phase of leg movement
and thus stride length. This possibility is clearly ruled out by the present
data set (see below: possible physiological bases of the stride integrator).
In fact, our present results are in unequivocal agreement with the above
hypothesis - that desert ants employ a stride integrator, or pedometer, for
distance measurement in navigation. And our data demonstrate a remarkable
robustness of walking behaviour, since all major characteristics remained
within expectations, despite the often severe manipulation of leg length. According to the pedometer hypothesis, ants that have travelled to the feeder on normal legs, and had their leg length modified at the feeder, should cover a different distance on their homebound journey. This is because the same number of strides made during the outbound travel, and registered by the stride integrator, will presumably carry them over a different homebound distance after modification of leg length at the feeder. Animals walking on stilts would be expected to cover longer distances with the same number of strides, and animals walking on stumps, shorter distances. And later, upon re-emerging from the nest with their legs still modified, the number of strides will be the same again for outbound and inbound travel (even though different from the situation with normal legs). No such straightforward interpretation is possible for the energy hypothesis or the optic flow hypothesis.
For a quantitative assessment of the pedometer hypothesis it was necessary to determine the actual changes in stride lengths brought about by the manipulations of leg length. This was achieved by the evaluation of high-speed video recordings of ants walking on modified legs (Fig. 6). For a useful comparison, the resulting data of stride lengths had to be normalised with regard to both body size and walking speed, since these two parameters influence stride length independently of the experimental manipulations (Fig. 6;details see Materials and methods). The predictions derived from the observed changes in stride length are in good agreement with the experimental data of the homing experiments (Fig. 4A, lower panel), providing further quantitative support for the stride integrator hypothesis.
There are, however, small but consistent differences between the observed and the predicted homebound travel distances (compare filled and hatched box plots in Fig. 4A, lower panel). These differences are in the range of 17% (or roughly 1.75 m) of the total homing distance, and intriguingly they always point away from the correct nest-feeder distance. That is, the animals do not just run too short, for instance, because of possible impairment by the manipulation procedures. Rather, ants on stilts run too far and ants on stumps, too short, all groups searching a bit farther from the true nest-feeder distance than would have been expected from the imposed change in stride length. This consistent observation rules out a number of immediate explanations, since these should always have the same effect, that is, bias the data either towards too short or too far distance estimates. For example, any serious impairment, such as slipping as a result of removal of the tarsal segments, would tend to shorten the ants' homebound runs, independent of the preparation procedure. The animals walking on stilts clearly travelled for much longer distances than the normal controls, however, and they did so with apparently normal vigour and motivation. Indeed, experimentally modified ants were observed to stilt or stump through their habitat on successful foraging trips several times a day, and for many days.
The small but consistent shift of the search centres away from the correct
nest-feeder distance might most easily be explained by the contribution of
another odometer mechanisms. A candidate mechanism is optic flow in the
ventral visual field, which has been demonstrated to make a small contribution
to the Cataglyphis odometer
(Ronacher and Wehner, 1995).
Indeed, ants walking on stumps will experience a higher optic flow than normal
ants since their eyes are closer to the ground (and the reverse is true for
animals walking on stilts). And that increased optic flow might prompt the
ants to search for the nest earlier than expected from the manipulations in
leg length alone. However, a significant contribution of optic flow would
appear unlikely since this has already been ruled out
(Ronacher and Wehner, 1995). A
contribution of not quite 8% may be calculated from their data. Further, we
strove to minimise visual cues in our experiments, mainly through reducing any
visual contrast in the animals' field of view, through grey paint on the
channel walls and even coating of the channel floor with fine-grained sand.
The grain size was selected to be well below the visual resolution of the
Cataglyphis eye at the given eye-substrate distances
(Zollikofer et al., 1995) (see
also Materials and methods). Nevertheless, it remains to be determined whether
or not the relatively small differences between predicted and observed homing
distance may indeed be due to another odometer mechanism, notably optic flow
perceived in the ventral visual field.
The time-lapse integrator hypothesis may be regarded as a variant of the
step counter hypothesis. Considering the rather constant walking speed of
Cataglyphis ants under normal conditions
(Zollikofer, 1988),
integration of travel time might function as the odometer in vector
navigation. However, the time-lapse integrator hypothesis is readily refuted
by the observation that homing performance remains unaffected by changes in
walking speed, for instance, due to heavy (prey) loads
(Zollikofer, 1994c). In the
present experiments homing performance did not conform to this hypothesis
either, in particular, since the ants on stilts often walked more slowly than
normal ants, their maximum speed being reduced to about 82% of expectations.
Nevertheless, these animals overestimated homing distance by about 50%.
Possible physiological bases of the stride integrator
Only speculations are possible with regard to the possible physiological
bases of the desert ant stride integrator. The fact that the animals account
for changes in stride length associated with changes in stride frequency and
walking speed in their estimation of travel distance would appear to imply the
contribution of sensory feedback from leg receptors. Candidate receptors are
campaniform sensillae that monitor cuticular stress and deformation, and coxal
and trochanteral hair fields that signal joint angles and movements (see
Markl, 1962). Internal muscle receptors and chordotonal organs are also
candidates (for a review, see Bässler,
1983), but these possibilities can only be addressed by future
experiments. Considering the relatively close coupling of the major parameters
of leg movement in walking, namely, stride length and stride frequency, a
central nervous integrator of walking pattern generation is a distinct
alternative, however.
There exists a wealth of literature on kinaesthetic orientation in other
animals, and in arthropods (for a review, see
Wehner, 1992), and spiders in
particular (e.g. Görner and Claas,
1985; Seyfarth and Barth,
1972; Seyfarth et al.,
1982) (for a review, see Barth,
2002). Many spider species are able to navigate in complete
darkness, employing leg mechanoreceptors as an important means of path
integration (e.g. Seyfarth et al.,
1982). Slit sense organs and lyriform organs are used to determine
both, direction and distance of travel
(Seyfarth and Barth, 1972).
This makes a comparison with desert ants difficult since those animals rely on
different sensory modalities for determining these two parameters.
Nonetheless, it is evident that leg mechanoreceptors, and perhaps indeed
campaniform sensillae, may suffice in principle to provide input to a
pedometer and determine walking distance.
The width of search density distribution reflects navigation uncertainty
One may interpret the widths of the search density distributions
(Fig. 4) as signs of the
animals' navigation uncertainty (Wolf and
Wehner, 2005; Merkle et al.,
2006), an uncertainty that increases with increasing nest-feeder
distance in a more or less linear fashion. With regard to the distance
component of this uncertainty, one would expect that it is related to the
mechanisms of distance measurement, that is, to the stride integrator. The
widths of search density distributions should accordingly reflect the
(relative) error per stride and thus depend on both, the number of strides, or
nest-feeder distance, and stride length, that is kept more or less constant by
the ants under normal circumstances
(Zollikofer, 1988). However,
in the present experiments stride length was manipulated, affording a unique
opportunity to examine not only the stride integrator hypothesis but also
uncertainty of distance measurement. And indeed the half widths of the search
density distributions were clearly related to stride length
(Fig. 5, Test 1). In fact, an
average 24.8% change in stride length produced an average 27.8% change in
distribution width, in the same direction (the differences between
experimental groups decreased in Test 2 since the numbers of strides were
again the same for out- and inbound travel, and thus also relative and
absolute errors of distance estimation). This result is in clear agreement
with the above interpretation regarding navigation uncertainty. The data
further suggest that the half width of the uncertainty distribution per step
cycle is in the range of 25%, at least under the present experimental
conditions.
Walking behaviour is robust with regard to imposed changes in leg length
The plots of stride frequency and stride length vs walking speed
(in normal ants) follow the general observations made in other animals, and in
insects in particular (e.g. Full and Tu,
1990). As noted above, there were no indications of galloping in
the present experimental conditions, although in principle,
Cataglyphis may gallop
(Zollikofer, 1988;
Zollikofer, 1994b). The
agreement of our data with previous results
(Zollikofer, 1988;
Zollikofer, 1994a;
Zollikofer, 1994b)
corroborates and extends the rules governing walking behaviour
(Full and Tu, 1990;
Full and Tu, 1991) to a very
small insect, the desert ant of about 10 mg body mass.
All else being equal, a linear relationship between stride frequency and
walking speed (Fig. 7A) would
be expected. Any increase in the number of strides per second yields a
corresponding increase in speed, as long as stride length stays constant. The
fact that stride length increases in conjunction with stride frequency, though
usually less pronounced (in normal ants, a doubling in stride frequency is
associated with an increase in stride length of just about 130%), will just
increase the slope of the graph as long as the latter relationship is linear.
And the intercept of this curve should be zero. Non-linearity is introduced
into the frequency-speed relationship by the fact that there is a maximum
sustainable stride frequency (Full and Tu,
1990). Beyond that, frequency stride length is further increased
by adding flight phases into the step cycle, yielding a horizontal graph
beyond maximum sustainable stride frequency
(Full and Tu, 1990). As noted
above, though, maximum sustainable stride frequency was apparently not reached
by our experimental animals and thus a linear fit to the data points is almost
as good as an exponential fit. Finally, the `stilts' and `stumps' operations
should yield curves with different slopes, if indeed the manipulations in leg
lengths resulted in consistent increases in stride length. The differences in
slopes represent the relative increases or decreases in stride length brought
about by the respective manipulations.
It is evident from the graphs in Fig.
7A that they conform to the above expectation almost perfectly.
The only notable feature is the reduced maximum stride frequency in ants with
stilts, as noted in the Results section. This conformity indicates that
walking behaviour remains largely unaffected by careful manipulation of leg
length. This is remarkable considering the actual impediments brought about by
the operations. The stumps II animals carry their body close to substrate, and
among other things, increasing the risk of stumbling and getting caught on
uneven structures. The ants on stilts carry 56% excess mass on their
legs. Both groups have poorer ground contact because of the missing tarsal
pads.
By a similar line of argument, a linear relationship would be expected between stride length and walking speed (Fig. 7B). At any given stride frequency, an increase in stride length yields a corresponding increase in speed. And as noted above, stride frequency increases in conjunction with stride length, producing a steeper slope of the relationship. A curvilinear relationship should occur beyond stride length at maximum sustainable stride frequency - a situation not relevant here. The stilts and stumps operations should yield curves with similar slopes, because of basically unchanged stride width-walking speed relationships. The intercepts should differ, though, and reflect the changes in stride length imposed by the altered leg lengths: at any given speed, the stride lengths would be expected to differ by the same amount (and vice versa, at any given stride length, stride frequency will differ depending on the manipulations, resulting in different speeds).
Again, the graphs in Fig. 7B conform to expectation almost perfectly. And as noted above, this observation indicates that walking behaviour remains remarkably unchanged by the manipulations.
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References |
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TOPSummaryIntroductionMaterials and methodsResultsDiscussionReferences |
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