Burrow surveillance in fiddler crabs II. The sensory cues
Visual Sciences, Research School of Biological Sciences, Australian National University, GPO Box 475, Canberra, ACT 2600, Australia
* Author for correspondence (e-mail: jan.hemmi{at}anu.edu.au)
Accepted 30 July 2003
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Summary |
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Key words: matched visual filter, path integration system, burrow defence response, burrow surveillance, sensory cue, fiddler crab, Uca vomeris
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Introduction |
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Here, we propose that burrow surveillance in fiddler crabs is based on a
pragmatic matched filter that incorporates the invariant properties of the
topography of vision in a flat world and information from the path integration
system to provide a robust and simple solution to the crucial task of
protecting an invisible resource. We use the same data set we presented in a
preceding paper (Hemmi and Zeil,
2003a), but now ask what cues guide the crabs' response to
crab-like dummies. Part of this work has been published in abbreviated form
elsewhere (Hemmi and Zeil,
2003b
).
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Materials and methods |
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To reconstruct the visual cues involved in burrow surveillance, such as the
position and the angular size of the dummy in the visual field of the crabs,
we determined the relationship between the size of the crabs, as measured by
carapace width, and their eye height above the surface. We randomly caught 24
animals and measured their carapace width with callipers. The crabs were then
placed back onto the mudflat in front of a vertical wall opposite a horizontal
video camera, the lens of which was approximately 2 cm above ground. The crabs
were filmed while sitting at the base of or walking along the wall and were
subsequently released. From the recordings, we measured the eye height above
ground for the same crabs in both a sitting and a walking posture (see also
Zeil and Layne, 2002).
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Results |
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What cues would allow crabs to estimate the distance between a dummy and
their burrows? The determination of the distance between two objects
irrespective of viewing direction and viewing distance is a difficult
geometrical task requiring knowledge of the length of two vectors and of the
angle between them (Fig. 2). In
burrow surveillance, crabs would thus need to know their own distance from the
burrow (cb), their own distance to the dummy (cd) and the difference in
angular position of the dummy and the burrow in the visual field ().
Given that they can acquire this information, crabs could then, in principle,
exploit the relationship expressed by the equation shown in
Fig. 2 to determine the
distance (db) between the dummy and the burrow. Before we ask whether crabs
really do need to solve quadratic equations in order to protect their burrows,
we will first establish what information they have available to solve the
task.
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The sensory cues employed in burrow surveillance
We know from previous work that path integration provides fiddler crabs
with information on their own distance to the burrow and on the direction in
the visual field in which it lies (Zeil,
1998; Zeil and Layne,
2002
). While the distance to the burrow is directly available from
the path integration system, the angle between the dummy and the burrow
requires some additional visual input. Visual information on its own is, in
most cases, not sufficient to determine the location of the burrow because the
crabs cannot see the burrow entrance once they are more than 15 cm away from
it (Zeil and Layne, 2002
). The
angular separation between a dummy and the burrow can be measured directly
from their retinal position only when both are visible at the same time but
otherwise needs to be determined by combining information from the path
integration system on burrow location with the retinal position at which the
approaching dummy is seen. The computational task of implementing this sensor
fusion is actually not as complicated as it first seems because foraging crabs
also use information from their path integration system to keep their
longitudinal body axis aligned with the home vector
(Ens et al., 1993
;
Land and Layne, 1995b
;
Zeil, 1998
). The direction in
which the burrow lies is thus always viewed by the same part of the
retina.
We are left with the question of how the crabs might determine the distance
between themselves and the dummy. There are five ways in which animals with
fixed-focus compound eyes could measure the distance to an object: disparity
(stereopsis), image size, elevation, motion parallax and other image motion
information, such as the increase in apparent size of an approaching object
(looming; Collett and Harkness,
1982; Schwind,
1989
; Zeil, 2000
).
In the following, we will analyse the behavioural evidence we have on burrow
surveillance in fiddler crabs with the aim of identifying the mechanism of
distance judgement involved.
Disparity
It is very unlikely that the crabs can rely on disparity cues to determine
a dummy's distance for the following reasons. Like most fiddler crabs, Uca
vomeris carry their eyes close together on long, vertical stalks. With an
eye separation of approximately 5 mm and a horizontal inter-ommatidial angle
of 2° (Land and Layne,
1995a; Zeil and Al-Mutairi,
1996
; Zeil et al.,
1986
), binocular disparity cues do not allow the crabs to
distinguish distances between 14 cm and infinity
(Burkhardt et al., 1973
). In
addition, the accuracy and range of distance judgements based on binocular
disparity decrease sharply in the lateral field of view, where the effective
eye separation approaches zero. As foraging crabs are always oriented sideways
towards their burrows (Ens et al.,
1993
; Land and Layne,
1995b
; Zeil,
1998
), disparity cues provide no useful distance information where
it is needed most for burrow surveillance. Finally, the median distance
between crab and dummy at the time of response in our experiments was 30 cm
(Hemmi and Zeil, 2003a
), which
is well outside even the crabs' maximal range of stereopsis in the frontal
visual field. We can therefore rule out disparity as a cue to distance in the
context of burrow surveillance.
Image motion
Our behavioural evidence also speaks against image motion as providing
possible cues to the distance of a dummy. The crabs generally do not move
before they respond to an approaching dummy
(Hemmi and Zeil, 2003a) and
therefore do not generate motion parallax signals that would indicate its
distance. We can also rule out other image motion cues to distance, such as
the expansion rate of the dummy's apparent size, the rate at which the dummy's
elevation changes, and time to contact. For these to be reliable indicators of
distance, the dummy would have had to approach the crab more or less directly,
which was rarely the case in our experiments. In fact, the movement direction
of the dummies relative to the crabs differed greatly for the different
approach directions. In addition, time to contact and other measurements that
rely on the speed of retinal change should be proportional to the dummy's
speed of motion. We found, however, no effect of the dummy's speed on the
crab's probability of response or on the timing of the response
(Hemmi and Zeil, 2003a
).
Image size and elevation
We are thus left with image size and elevation as possible cues for the
crabs to measure the dummy's distance. The apparent size of an object is one
of the simplest distance measures available to animals, and crabs are known to
use this cue in a variety of behavioural situations
(Land and Layne, 1995a;
Nalbach, 1990
). The
distance-size ambiguity that affects apparent size measurements may not matter
in the context of burrow surveillance since, for a given burrow owner, only
crabs from a narrow size class of conspecifics pose a threat to the burrow:
much larger crabs would not be able to enter the burrow and much smaller
animals are easily evicted.
Assuming that the crabs used the apparent size of the approaching dummy to determine when to respond, we would expect the distance between the crab and the dummy at the time of response to increase with increasing dummy size. However, as documented in Fig. 3A, the crab-dummy distance at this moment is independent of both the dummy's vertical (filled dots) and horizontal (open dots) size. On the other hand, assuming that the size of the dummy (real or apparent) does not affect the crab's decision of when to respond, we would expect the mean angular size at the moment the response is triggered to increase with the absolute size of the dummy. This is true whatever the response criterion may be and regardless of whether the crabs assess the dummy relative to themselves or relative to the burrow. The dummy's mean apparent size at the time of the response is indeed strictly correlated with its real size (Fig. 3B; vertical size, filled dots; horizontal size, open dots). For small angles, the different angular sizes should all fall on a straight line through the origin, the slope of which is determined by the mean response distance between the crab and the dummy. The line in Fig. 3B connects the origin and the horizontal angular size value for the 2.25 cm-wide dummy, for which we have the largest number of measurements. The fact that all other angular size measurements are accurately predicted by this theoretical line demonstrates clearly that the apparent size of the dummy did not influence the crabs' decision when to respond. Note that the absence of a size-distance ambiguity (Fig. 3A) is strong evidence that the crabs know the distance to the dummy at the moment they respond.
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Retinal elevation
We have thus ruled out all the possible cues to distance the crabs could
exploit, with the exception of retinal elevation. In a flat environment, the
retinal elevation of an object's point of contact with the ground is uniquely
determined by the distance of the object from the observer
(Schwind, 1989;
Sedgwick, 1983
;
Zeil et al., 1986
). To
determine the elevation at which the crabs saw our dummies, we needed to
estimate the height of their eyes above ground. In order to do this, we
established the relationship between the height of the eyes and the carapace
width of 24 U. vomeris, both when they were sitting and when they
were standing or running (Fig.
4). There is a clear linear relationship between eye height and
carapace width. To avoid having to capture the animals involved in the
behavioural experiments, we determined their carapace width from 5-10 video
frames per crab. The standard error within crab measurements was less than 15%
in all cases. Assuming that the crabs were standing when making their decision
to respond, we used the following equation to determine their eye height in
our experiments (Fig. 4): eye
height = -0.11 + (1.2 x carapace width).
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The median elevation of the dummy at the time of response is -4.4°, and
75% of the responses occur when the dummy is at an angular distance from the
burrow of between -2.3° and -11° (upper and lower 12.5th percentile;
Fig. 5). Less than 2% of the
responses happen when the dummy has an elevation of less than -1.5°. An
elevation of -1.5° translates into a distance of 76 cm for a crab with a 2
cm eye height. Note that for the same crab, the limit for depth perception
based on elevation lies beyond 2 m, assuming a 2 cm eye height and a vertical
inter-ommatidial angle of 0.5° close to the horizon
(Land and Layne, 1995a;
Zeil and Al-Mutairi, 1996
).
The elevation of the dummies at the time of response is thus clearly within
the range of angles that can, in principle, be resolved by the crabs. A large
part of the variation in the histogram of dummy elevations is due to the fact
that a dummy's elevation at response time depends strongly on its approach
direction (Fig. 1B).
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It therefore appears that the crabs have all the information they need to determine a dummy's distance from their burrows. They know their own distance from the burrow, they can measure the angle between the dummy and the burrow and they can determine how far the dummy is away. To work out the dummy's distance from the burrow, however, the crabs would need to combine these measurements along the lines suggested by the equation in Fig. 2. How could this be achieved?
How crabs determine a dummy's distance from their burrows
The relevant visual parameters that allow a crab to determine a dummy's
position relative to the burrow are the dummy's azimuth and its elevation in
the visual field. Fig. 6 shows
the paths of the dummies, as seen by a crab, in retinal coordinates. To
generate these retinal paths, we assume that the crab's longitudinal body axis
was always aligned with the home vector such that one side always pointed
directly at the burrow (azimuth=0°; Ens
et al., 1993; Land and Layne,
1995b
; Zeil,
1998
). Because the eyes of the crabs are roughly cylindrical in
shape, such a Cartesian representation appears justified. The dummies
approached from a distance and are therefore initially always seen at high
elevations, moving down in the visual field as they come closer. As we already
know from the previous analysis, the retinal positions of the dummies at the
time a crab responds are widely scattered throughout the visual field
(Fig. 6A-C, large black dots).
However, the elevation of the dummy at the time of response tends to decrease
with increasing azimuth distance between the dummy and the burrow. This is a
direct consequence of the fact that the crabs respond at a roughly equal
dummy-burrow distance irrespective of the direction from which the dummy
approaches. For each azimuth, there is a critical elevation where the dummy is
a given distance away from the burrow, and these combinations of elevation and
azimuth angles define on the substrate a circle of a given radius around a
crab's burrow.
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For a given dummy-burrow distance, this set of critical elevations is only
affected by the distance of the crab to its own burrow. The dotted lines in
Fig. 7 show the fitted retinal
projection of a circle with a 25 cm radius around the crab's burrow. The five
lines show the projections of the same 25 cm circle for five different
crab-burrow distances between 10 cm and 30 cm. When the crab is close to its
burrow, say 10 cm away, the projection of the 25 cm circle around the burrow
appears rather flat across the visual field
(Fig. 7, solid black line). As
the crab moves further away from the burrow, the projection becomes steeper
until the whole 25 cm circle is seen in the frontal visual field, once the
crab itself has moved further than 25 cm away from the burrow. The grey dots
on each of these projections correspond to the position where dummies,
approaching from different directions, would reach a dummy-burrow distance of
25 cm (see inset for the grey-level code of approach directions). To
demonstrate that the resolution with which the crab can measure an object's
elevation is adequate for the task at hand, we have schematically added the
vertical component of the crab's sampling array as a vertical row of black
dots along the y-axis (see Land
and Layne, 1995a).
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Fig. 8 shows the fitted
values of the statistical model (see Hemmi
and Zeil, 2003a) predicting the dummy's position (dots) for
different approach directions (grey-level coded line segments) at the time of
the response for a crab-burrow distance of 15 cm
(Fig. 8A) or 25 cm
(Fig. 8B). The same data are
shown in retinal coordinates for a collapsed visual field (0°
azimuth
180°) in the bottom panels (Fig.
8C,D). The solid and dotted curves in
Fig. 8C,D show the projection
of the mean response distance ± 2 S.E.M.. (solid and dotted
circles in Fig. 8A,B). For a
given response distance, the relationship between the azimuth and the
elevation at the time of response becomes steeper as the crabs move away from
the burrow, as predicted by Fig.
7. However, the effect is not as strong as expected, because the
crabs at the same time increase the mean response distance, which counteracts
the effect that the increased crab-burrow distance has on the projection
(compare Fig. 8A with
Fig. 8B; see also fig. 11A in
Hemmi and Zeil, 2003a
).
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We have marked the position of the burrow in the crabs' visual field
(Fig. 8C,D), although in most
situations the crabs cannot actually see their burrow
(Zeil, 1998;
Zeil and Layne, 2002
). To
appropriately adjust the elevation of the dummy at which they initiate their
response the crabs thus have to rely on path integration to inform the visual
system about the distance to the burrow.
Our statistical model predicts that for crab-burrow distances of more than 25 cm, the mean response distance would be less than the crab-burrow distance. In this situation, however, the crabs appear to treat dummies passing very close to them differently, in that they respond by retreating towards their burrows whenever the dummy threatens to pass them. Fig. 8C,D also shows that the direction in which the dummy moves across the retina prior to the response (straight line segments leading up to the response position marked by the dot) hardly influences the response timing, despite the fact that the directions of motion of the dummy's image are quite different depending on whether the dummy's path crossed the crabs home vector on the crab's side of the burrow or not.
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Discussion |
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A matched filter for burrow surveillance
The most interesting aspect of the results shown in
Fig. 8 is that they suggest a
structure for a matched filter (sensu
Wehner, 1987), which the crabs
could use to relate a dummy's azimuth and elevation to its distance from the
invisible burrow. Rather than solving difficult geometrical equations, they
may be able to use the predictable geometry of their environment to employ a
comparatively simple retinal filter to detect dummies or other crabs that have
approached to within a certain distance of the burrow. Prerequisites for such
a `built-in' surveillance system are (1) that the crabs keep their body
aligned with the home vector, which they do
(Ens et al., 1993
;
Land and Layne, 1995b
;
Zeil, 1998
;
Zeil and Layne, 2002
), and (2)
that they are able to account for their own distance away from the burrow
(von Hagen, 1962
;
Zeil, 1998
;
Zeil and Layne, 2002
). What
would such a neural filter look like?
For a given crab-burrow distance, a single neuron with a large receptive field could provide an accurate intruder-burrow-distance-related signal. Such a cell needs to be sensitive to small objects and it needs to respond more strongly the closer an object is seen near the burrow. Since the longitudinal body axis of crabs is aligned with the home vector, such a burrow-distance-dependent output could be achieved by appropriately weighting the contributions of local input elements across the retina according to the map of distances to burrow, shown as a `view from the cockpit' of a fiddler crab in Fig. 9A. The input elements are likely to be local motion or flicker detectors. A distance cell of this kind would provide no information on where an intruder actually is but would accurately monitor its distance from the burrow. The output of such a neuron would, however, only be correct for a small range of crab-burrow distances: 10 cm in the case of Fig. 9A. This limitation could be overcome by having a small number of such cells each tuned to a range of crab-burrow distances (Fig. 9B,C). A signal from the crab's path integration system, which monitors the crab's own distance from the burrow, could then select the cell or the combination of cells with the appropriate distance mapping for the crab's current position. A very small number of large field cells would be sufficient to accurately measure an object's distance from the burrow, irrespective of the object's approach direction and the crab's own position relative to the burrow. Burrow surveillance thus requires an integration of information from the path integration system with visual information about the retinal position of other crabs.
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However, we have also shown that the crabs respond only to dummies that
actually approach the burrow and ignore dummies that move away from it, even
if those dummies are close to the burrow
(fig. 9B in
Hemmi and Zeil, 2003a). The
probability that the crabs respond to a dummy approaching the burrow is more
than three times higher compared with when the dummy moves away. This
observation suggests that the crabs are not only sensitive to the distance of
an intruder from the burrow but also to its direction of movement relative to
the burrow. There are two basic ways in which this sensitivity could be
implemented at the neural level. The first possibility is to monitor the
output of distance neurones exhibiting properties as we proposed above. An
increase of these cells' output would indicate that an object is approaching
the burrow; a decrease would signal that the object is moving away. If the
underlying distance weighting is strong, this simple and robust method would
make the crabs sensitive to changes in object position in the order of one
inter-ommatidial angle. The second possibility is that the distance neurones
are also sensitive to the direction of the local retinal image motion by
integrating over a regularly spaced array of appropriately aligned motion
detectors with the appropriate input weights. An object approaching the burrow
must have a motion component pointing along the gradient of a burrow-distance
map (arrows, Fig. 9C) but it
does not matter whether the object moves directly towards the burrow or not.
All that is needed in order to measure this motion component is an alignment
of the directional selectivity of local motion detectors with this
burrow-centred distance gradient (the local direction on the eye in which the
distance to the burrow changes fastest). Such directionally sensitive distance
neurones would then only respond when there is a motion component towards the
burrow.
It is interesting to note that, as a direct consequence of the perspective
distortion, the retinal image of an object that moves over flat ground
directly towards the burrow (solid line through the burrow in
Fig. 9A-C) does not always move
directly towards the retinal position of the burrow nor does it move along the
distance gradient towards the burrow (arrows,
Fig. 9C). The neurones we
proposed above could therefore monitor whether an object approaches the burrow
or not, but their activity would not allow the crab to decide how directly the
object was aiming at the burrow. This can be verified by comparing the solid
line passing though the burrow in Fig.
9C, which indicates the retinal path of an object that approaches
the burrow directly, with the local distance gradient (arrows). This
performance of the cells is in accordance with the behavioural results showing
that crabs are able to distinguish between dummies that move towards and those
that move away from the burrow but cannot distinguish between trajectories
that pointed more or less directly at the burrow (figs
8,
9 in
Hemmi and Zeil, 2003a).
However, as long as there is a motion component in the direction of the
burrow, these neurones will signal it.
Our data do not allow us to decide at this stage whether or not burrow
surveillance in fiddler crabs involves directionally sensitive neurones. The
two alternatives, distance monitoring and directionally sensitive distance
cells, would both allow the crabs to measure whether the object approaches the
burrow or not (fig. 9 in
Hemmi and Zeil, 2003a) but
would not provide clear information on whether it does so on a direct path
(fig. 8 in
Hemmi and Zeil, 2003a
). The
only available information addressing this issue is the observation that the
dummy's speed has no effect on the response probability or on the response
distance. This result would favour the notion that the crabs monitor the
direction of motion through the distance-monitoring cells rather than relying
on direction-sensitive distance neurones. Further experiments should allow us
to distinguish between the two alternative models. If the crabs relied on
directionally selective motion sensitivity, the response probability for a
given dummy-burrow distance should vary with a dummy's direction of motion,
while there should be no such variability if the crabs only monitored
dummy-burrow distance.
Neurones like the ones we suggest to be involved in burrow surveillance are
not unknown in invertebrates. The large tangential neurones in the lobula
plate of the fly, for instance, act as neural filters tuned to rotatory optic
flow fields (e.g. Krapp et al.,
1998). Barnes et al.
(2002
) have recently recorded
from large-field interneurons in the crab lobula, the local directional motion
sensitivities of which are arranged across the receptive field in such a way
that they are likely to respond to translatory optic flow fields. However, in
contrast to these examples, the neurones that we suggest to be involved in
burrow surveillance in the fiddler crab should only respond to small objects
and not to global image motion. The lobula giant motion detector (LGMD) of the
locust does seem to have the appropriate blend of properties. It is a large
neuron with a wide receptive field, it is sensitive to small objects, and the
direction tuning of its local motion sensitivity varies systematically across
the receptive field (e.g. Gabbiani et al.,
2001
; Rind and Simmons,
1999
). However, the local directional sensitivities of the LGMD
are arranged such that the neuron also responds to looming stimuli that are on
a direct collision course with the locust, a property which we would not
expect to see in burrow surveillance neurones.
Conclusion
What on first sight appeared to be a complex geometrical problem, namely to
determine the distance between two objects independent of viewing direction
and distance, can thus be reduced to a relatively simple task, the information
for which is available directly from the retina. The decision rules exploit
the predictability of the crab's visual world and rely on the crab's path
integration system for the information about the burrow position. The
underlying neural machinery is thus yet another candidate for a matched neural
filter, not only matched to the physical environment but also to the social
environment in which the crabs live. It allows crabs to be very selective and
respond to other crabs only when they are actually threatening burrow
ownership. It allows them to ignore more distant crabs and neighbours that are
close to the burrow but do not actually approach it. And it allows them to
optimise the time they spend in burrow defence by recruiting information from
the path integration system to adjust the distance at which they respond to an
intruder depending on how far away from the resource they are themselves. We
would finally like to point out that the structure of the matched filter we
suggest is eminently testable in both behavioural and neurophysiological
experiments.
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Acknowledgments |
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References |
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![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Barnes, W. J. P., Johnson, A. P., Horseman, G. B. and Macauley, M. W. S. (2002). Computer-aided studies of vision in crabs. Mar. Freshwater Behav. Physiol. 35, 37-56.
Burkhardt, D., Darnhofer-Demar, B. and Fischer, K. (1973). Zum binokularen Entfernungssehen der Insekten. I. Die Struktur des Sehraums von Synsekten. J. Comp. Physiol. 87,165 -188.
Cannicci, S., Fratini, S. and Vannini, M. (1999). Short-range homing in fiddler crabs (Ocypodidae, genus Uca): a homing mechanism not based on local visual landmarks. Ethology 105,867 -880.[CrossRef]
Collett, T. S. and Harkness, L. I. K. (1982). Depth vision in animals. In Analysis of Visual Behaviour (ed. D. J. Ingle, M. A. Goodale and R. J. W. Mansfield), pp. 111-176. Cambridge, London: MIT Press.
Ens, B. J., Klaassen, M. and Zwarts, L. (1993). Flocking and feeding in the fiddler crab (Uca tangeri): Prey availability as risk-taking behaviour. Neth. J. Sea Res. 31,477 -494.[CrossRef]
Gabbiani, F., Mo, C. and Laurent, G. (2001).
Invariance of angular threshold computation in a wide-field looming-sensitive
neuron. J. Neurosci. 21,314
-329.
Hemmi, J. M. and Zeil, J. (2003a). Burrow
surveillance in fiddler crabs. 1. Description of behaviour. J. Exp.
Biol. 206,3935
-3950.
Hemmi, J. M. and Zeil, J. (2003b). Robust judgement of inter-object distance by an arthropod. Nature 421,160 -163.[CrossRef][Medline]
Krapp, H. G., Hengstenberg, B. and Hengstenberg, R.
(1998). Dendritic structure and receptive-field organization of
optic flow processing interneurons in the fly. J.
Neurophysiol. 79,1902
-1917.
Land, M. F. and Layne, J. (1995a). The visual control of behaviour in fiddler crabs I. Resolution, thresholds and the role of the horizon. J. Comp. Physiol. A 177, 81-90.
Land, M. F. and Layne, J. (1995b). The visual control of behaviour in fiddler crabs II. Tracking control systems in courtship and defence. J. Comp. Physiol. A 177,91 -103.
Nalbach, H.-O. (1990). Visually elicited escape in crabs. In Frontiers in Crustacean Neurobiology (ed. K. Wiese, W.-D. Krent, J. Tautz, H. Reichert and B. Mulloney), pp.165 -172. Basel: Birkhäuser Verlag.
Rind, R. C. and Simmons, P. J. (1999). Seeing what is coming: building collision-sensitive neurons. Trends Neurosci. 22,215 -220.[CrossRef][Medline]
Schwind, R. (1989). Size and distance perception in compound eyes. In Facets of Vision (ed. D. G. Stavenga and R. C. Hardie), pp. 425-444. Berlin: Springer Verlag.
Sedgwick, H. A. (1983). Environment-centered representation of spatial layout: Available visual information from texture and perspective. In Human and Machine Vision (ed. J. Beck, B. Hope and A. Rosenfeld), pp. 425-458. New York, London: Academic Press.
von Hagen, H.-O. (1962). Freilandstudien zur Sexual- und Fortpflanzungsbiologie von Uca tangeri in Andalusien. Z. Morphol. Ökol. Tiere 51,611 -725.
von Hagen, H.-O. (1967). Nachweis einer kinästhetischen Orientierung bei Uca rapax. Z. Morphol. Ökol. Tiere 58,301 -320.
Wehner, R. (1987). `Matched filters' - neural models of the external world. J. Comp. Physiol. A 161,511 -531.[Medline]
Zeil, J. (1998). Homing in fiddler crabs (Uca lactea annulipes and Uca vomeris, Ocypodidae). J. Comp. Physiol. A 183,367 -377.
Zeil, J. (2000). Depth cues, behavioural context, and natural illumination: some potential limitations of video playback techniques. Acta Ethologica 3, 39-48.[CrossRef]
Zeil, J. and Al-Mutairi, M. M. (1996). The
variation of resolution and of ommatidial dimensions in the eyes of the
fiddler crab Uca lactea annulipes (Ocypodidae, Brachyura, Decapoda).
J. Exp. Biol. 199,1569
-1577.
Zeil, J. and Layne, J. (2002). Path integration in fiddler crabs and its relation to habitat and social life. In Crustacean Experimental Systems in Neurobiology (ed. K. Wiese), pp. 227-246. Heidelberg: Springer Verlag.
Zeil, J., Nalbach, G. and Nalbach, H.-O. (1986). Eyes, eye stalks, and the visual world of semi-terrestrial crabs. J. Comp. Physiol. A 159,801 -811.
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