Mechanisms of homing in the fiddler crab Uca rapax 1. Spatial and temporal characteristics of a system of small-scale navigation
Division of Environmental and Evolutionary Biology, Institute of Biomedical and Life Sciences, University of Glasgow, Glasgow G12 8QQ, Scotland, UK
* Author for correspondence at present address: Department of Entomology, Cornell University, Ithaca, NY 14853, USA (e-mail: JL272{at}cornell.edu)
Accepted 11 August 2003
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Summary |
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Crabs were subjected to passive translational displacements and barrier obstructions. Responses to translational displacements were identical to those observed by previous authors, namely that crabs returned in the correct egocentric direction and distance as though no displacement had occurred. Covering the burrow entrance resulted in crabs returning to the correct position of the burrow, and then beginning to search. When a barrier was placed between foraging crabs and their burrow, crabs oriented their bodies toward the burrow as accurately as with no barrier.
Key words: fiddler crab, Uca rapax, path integration, homing, spatial orientation, central-place forager, systematic error
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Introduction |
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Many semi-terrestrial decapods, including fiddler crabs, use visual cues
such as landmarks or sky light to control their large-scale movements between
their supralittoral burrows and foraging sites near the water's edge
(Altevogt and von Hagen, 1964;
for reviews, see Herrnkind,
1968
,
1972
;
Altevogt, 1965
;
Wehner, 1992
;
Vannini and Cannicci, 1995
),
or to regain the previous foraging direction after visiting the burrow
(Luschi et al., 1997
). They
also use wave direction and beach slope
(Cameron and Forward, 1993
).
However, for their small-scale orientation to the burrow, fiddler crabs do not
utilize the same information as for the large-scale movements. All fiddler
crab species tested ignore landmarks near their burrows when displaced a short
distance (von Hagen, 1967
;
Zeil, 1998
;
Cannicci et al., 1999
), and we
have shown conclusively that Uca rapax compute a purely egocentric
home vector, indicating they use only path integration for homing
(Layne et al., 2003
). Though
we are still largely ignorant of the physiology underlying path integration in
all animals, the evidence from fiddler crabs indicates that they utilize
idiothetic information (probably proprioceptive or efferent signals;
Layne et al., 2003
; but see
Zeil, 1998
).
Path integration is a computational process that by nature is prone to the
accumulation of errors. Analysis of both experimentally manipulated and
natural outbound paths has demonstrated that the algorithm often does not
compute the correct direction and distance of home, but rather an
approximation (Bisetzky, 1957;
Görner, 1958
;
Müller and Wehner, 1988
;
Wehner and Wehner, 1990
;
Seguinot et al., 1993
). Such
coding thus contains a systematic error, which may provide hints about the
computational algorithm at work. Furthermore, due to the imprecise nature of
biology, path integration is also subject to random errors in measurement
and/or computation (Benhamou et al.,
1990
; Maurer and Seguinot,
1995
). Random errors have a greater impact on homing accuracy when
the spatial information being integrated is purely idiothetic
(Benhamou et al., 1990
).
Because the fiddler crab U. rapax homes by path integration using
only idiothetic information (the continuous calculation of a home vector using
internal measurements of their locomotion), it may be especially susceptible
to random errors.
In this paper we analyze natural foraging paths of U. rapax with the aim of understanding the relationship between the crabs' tendency to orient their bodies with respect to their burrows and the stored home vector. In particular, we look for evidence of systematic and random errors. We also discuss the unique foraging behavior of this animal in light of the way errors are accumulated by path integration algorithms.
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Materials and methods |
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To obscure the burrow visually, an L-shaped cardboard barrier was lowered slowly from above on a wire coat hanger, until it rested between a foraging crab and its burrow entrance. In the burrow-covering experiments, a sheet of mud-covered acetate attached to a length of fishing line was dragged over the burrow entrance. To translate foraging crabs, a similar sheet of mud-covered acetate (10.3 cm wide and of variable length) was attached to fishing line, which was threaded through a tent peg situated to the side of the burrow. This allowed us to move the acetate without lifting it, and thereby translate the crabs without disturbing them.
Sampling and digitization
The fiddler crabs were videotaped from above at 25 frames s-1
using a CanonVision EX1 8 mm video camera on a tripod. Two lateral points on
the carapace (left and right side) were digitized 1, 5 or 25 times
s-1, depending on the speed of the crab's movement, using a frame
grabber and image analysis software (LG-3 and Scion Image, Scion Corp.,
Frederick, MD, USA). The digitized data were then analyzed using Matlab (The
Mathworks Inc., Natick, MA, USA) to determine the crab's position and
orientation. To reduce small sampling errors, the data were smoothed with a
three-point moving average having weights 1:6:1. The crab's orientation
relative to an arbitrary coordinate system (the video screen) was calculated
from the slope of the line connecting the two points on the crab. The crab's
bearing (direction from its burrow) was calculated from the slope of the line
connecting points at the crab's center and the burrow (see lower inset in
Fig. 1Ai for definitions, which
follow those of Zeil, 1998).
The crab's distance from home is defined as the distance between the center of
the carapace (the point midway between the two digitized lateral points) and
the center of the burrow; both carapace and burrow were approximately 2 cm
wide.
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Analysis
In analyzing burrow orientation with and without a barrier, we examined the
spatial and temporal characteristics of 13 foraging paths, and present six of
these graphically in order to illustrate the variability in burrow orientation
within and between foraging excursions. We excluded from the statistical
analyses of foraging behavior, though not from the figures, portions of the
digitized path that were within 5 cm of home. This is because these are so
close to home that a small change in bearing can create a disproportionately
large orientation error. Furthermore, because home is certainly within the
crabs' visual range (Zeil,
1998), this may allow the crab to tolerate very large errors in
its burrow orientation that obviously do not correspond to the home vector,
and might have affected our interpretations of orientation error in relation
to path integration. Values are reported as means ± S.D.
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Results |
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As has been pointed out by previous workers
(Land and Layne, 1995;
Zeil, 1998
), this
circumferential path is interesting because it implies that the crab must know
its distance from the burrow entrance at all times. In order to remain pointed
homeward during such loops, the crab must change its orientation as it changes
its bearing by an amount dictated by its distance from home.
In keeping with U. lactea annulipes and U. vomeris
(Zeil, 1998) and also U.
pugilator (Land and Layne,
1995
), U. rapax do not always point its long body axis
directly at home, but allows some drift and recovers the `correct' orientation
periodically. Fig. 1Aii shows
what we will call the `orientation error' bearing minus orientation
over time for the path shown in
Fig. 1Ai. For this individual,
which traveled in a counter-clockwise direction, bearing was consistently
greater than orientation; i.e. the crab did not point its transverse body axis
at home, but kept home slightly behind it. This means the error was biased
towards the positive, but was periodically reset to zero.
To examine the crab's precise strategy of burrow orientation and perhaps
gain some insight into the path integration algorithm, it is instructive to
ascertain the nature of this bias in orientation error. For instance, is the
error normally distributed around a biased mean? Or is the distribution of
orientation error skewed or, if the error were periodically reset to zero as
described above, bimodal? How do individual paths differ in this respect?
Fig. 1Aiii shows a frequency
histogram of the errors for those parts of the path >5 cm from home. The
crab had a mean of error of 7.5±6.3° and, in spite of the fact that
there are subsidiary peaks near 2° and 18°, the error distribution was
not significantly different from normal at the 95% confidence level
(D'AgostinoPearson K2 test, P=0.07;
Zar, 1996). Thus, the
orientation error tended to vary roughly equally to either side of a biased
mean. Whether or not this bias in orientation error indicates an error in the
direction of the home vector is a question we will take up below.
This is a fairly representative path. Out of 13 foraging paths overall seven without and six with barriers all were found to have a positive mean error if the crab went clockwise and a negative mean error if the crab moved counter-clockwise. This means that all crabs kept the burrow slightly behind them (in their rear hemifield). Six were found to have significantly normally distributed orientation errors at the 95% confidence level, and all of these had means that were significantly different from zero (Student's t-tests, all P values <0.05). Likewise, the grand mean (mean of the means) of the seven paths without barriers was also significantly different from zero (-6.49±5.87°, Student's t-test, P=0.026), as was the grand mean of the six paths with barriers (-8.84±2.10°, Student's t-test, P<0.001). To find this grand mean, all of the paths were normalized to the clockwise direction (the direction that results in negative orientation errors) by multiplying the counter-clockwise means (which are negative) by -1.
Fig. 1B shows the path that took the crab farthest from home, out of the 12 that we recorded. Its maximum distance (40.3 cm) was exceeded by other crabs that were not recorded, because they foraged outside the field of view of the camera. Indeed, some foraged over 1 m from home and were (subjectively) seen to remain oriented to it. Since this crab traveled clockwise around its burrow entrance, its orientation error was generally negative (Fig. 1Bii). While most of the error appears to be fairly normally distributed around a mean of -5.2±6.4°, this crab's error distribution is significantly different from normal (Fig. 1Biii; D'AgostinoPearson K2 test, P<0.001). Thus the orientation errors for different paths may or may not be normally distributed around their mean.
The example shown in Fig. 1Ci is interesting in that, during the second part of its journey, the crab walked around a mangrove sapling that blocked its view of home. Moving counter-clockwise around its burrow entrance, this crab generally maintained a positive orientation error, as expected. The interaction with the sapling introduced exceptional error values it appeared, for a short time at least, to fixate the intruding edge of the sapling, before fixating the far edge which it intended to circumvent, causing this distribution to be different from normal. Data after 100 s from this crab were therefore excluded from all statistical tests because of the influence of the sapling on its orientation, and thus on our subsequent interpretations of orientation errors in the context of path integration. The errors before t=100 s, shown in Fig. 1Ciii, were normally distributed around a mean of -13.9±7.3° (D'AgostinoPearson K2 test, P=0.32). It is notable, however, that although the interaction with an object near its burrow entrance caused the crab to assume a large orientation error, the burrow direction was recovered, abandoned, and finally recovered again when the crab returned directly home. Temporary losses of burrow orientation were also observed to occur when crabs interacted with conspecifics while foraging.
Orienting to the burrow from behind a barrier
The behavior illustrated in Fig.
1C raises the question of whether U. rapax needs to be in
visual contact with its burrow entrance to align its body with it. Other
species qualitatively appear to be able to maintain normal burrow orientation
from behind a barrier that obstructs their view of the burrow entrance
(Zeil, 1998), or at least are
able to perform successful detours around opaque barriers
(von Hagen, 1967
;
Herrnkind, 1972
;
Zeil and Layne, 2002
, but body
orientation not measured). Fig.
2Ai shows the path of a crab whose homeward line of sight was
blocked by a cardboard barrier, introduced at t=32 s, just as this
crab began its circumferential path. This experiment is similar to that
performed by Zeil (1998
) on
U. vomeris. As in Zeil's study, U. rapax appear to orient
similarly with and without such a barrier. Unlike the previous example with
the mangrove sapling, this crab did not interact with the barrier in a way
that obviously influenced its burrow alignment. Moving clockwise around its
burrow entrance, this individual showed the same error bias (bearing >
orientation) as the crabs with no barrier. While it did reduce its bias during
part of the time behind the barrier, the mean error during this time was still
positive, with a mean significantly different from zero (5.9±6.2°,
95% CI = ±1.03, Student's t-test, P<0.001). Also,
the error distribution was not significantly different from normal
(D'AgostinoPearson K2 test, P=0.21).
The example shown in Fig. 2B
is somewhat unusual in that the error bias, while in the direction predicted
from its movement around the burrow entrance, clearly increases in magnitude
throughout the foraging excursion (Fig.
2Bii). Thus, more than in our other records, we had the impression
that the crab may have accumulated a substantial integration error. The
integration error does not, however, change linearly over time. The errors are
also clearly not normally distributed (-9.0±8.9°,
D'AgostinoPearson K2 test, P<0.001). Despite the impression
that this crab had progressively `lost' its correct home direction, it
proceeded immediately home after making a detour around the edge of the
barrier a detour which induced an orientation error that exceeded
80° in magnitude. This apparent loss of home direction may have been due
to an interaction with the edge of the barrier that the crab intended to
circumvent. Fiddler crabs, when confronted with obstructions to their straight
path home, make detours that seem to indicate they plan their route home
they visually assess the angle of the barrier relative to the home
vector, and go around the barrier in a way that minimizes the detour distance
(Zeil and Layne, 2002).
Our final example shows a fairly lengthy foraging path (Fig. 2C). This path has the predicted bias direction, and is normally distributed around a mean of -10.7±9.3° (D'AgostinoPearson K2 test, P=0.11).
Comparing orientation error with and without a barrier
We have seen that a barrier can influence orientation by forcing a detour,
and that this detour usually occurs without the crab making contact with the
barrier. But we may ask whether such a barrier diminishes the crabs' ability
to point towards home, or to maintain a typical orientation bias when the crab
is not attempting to circumvent the barrier. In the following statistical
comparisons between crabs with and without barriers, we used only those
portions of the paths in which the barrier lay between the crab and its
burrow; these are indicated by the double-headed arrows in
Fig. 2AiiCii. Portions
of the path where the crab had a line of sight to the burrow entrance, and
also detours around barriers, were excluded. Also, all data were normalized to
the clockwise path direction as described above, so that mean orientation
errors have a negative bias.
Two aspects of orientation error are considered the error bias, which is the mean of the measured error values (as above), and the error magnitude, which is the mean of the absolute error values. The error bias indicates in what direction crabs point their body axes relative to the burrow direction, while the error magnitude simply indicates how much error there is regardless of what direction it is in, and might be thought of as one measure of the spread of error values.
In comparing orientation errors with and without barriers, we find that the mean error bias for the seven paths without a barrier is not significantly different from the six paths with a barrier (Student's t-test, P=0.71). Likewise, their error magnitudes are also not significantly different (Student's t-test, P=0.91). This quantitative analysis has therefore failed to provide any evidence that fiddler crabs need visual contact with the burrow entrance or its immediate vicinity in order to align their bodies with it.
Temporal aspects of maintaining burrow orientation
Fiddler crabs have an error bias in the spatial sense, but does it occur
temporally as well? For instance, does the burrow-alignment mechanism require
an initial movement tangential to the burrow direction in order to calculate
an appropriate body turn? In Fig.
3 a time-lagged cross-correlation of changes in bearing and
orientation for the path in Fig.
1A (open circles) shows a fairly good correlation (coefficient =
0.59) at a 1 s lead of orientation change before bearing change. A similar
cross-correlation for the path in Fig.
1B (filled circles) shows a relatively poor correlation, but one
with a bimodal appearance orientation change both leads and lags
behind the bearing change by about 2 s. We interpret this to mean that, while
the crab did not move tangentially to the burrow and turn simultaneously, it
did one or the other first at different times.
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It is possible that the temporal correlation between changes in orientation and bearing exists on a smaller time scale than our digitization frequency of 1 frame s-1. We therefore redigitized the path in Fig. 1A at 5 frames s-1, and found that the cross-correlation coefficient was much lower (0.26), and reached a maximum at a lag of -0.6 s (i.e. a 0.6 s lead of orientation change before bearing change). The lower correlation coefficient is probably due to increased digitization noise, as subjectively there did not appear to be oscillations of body orientation or position on this fine time scale. Thus, the resolution of 1 frame s-1 time scale gives a reasonable indication of which component of the movement occurs first.
Similar tests for all 13 paths produced both leads and lags by orientation against bearing, and a few with zero lag. The mean of the 13 cross-correlations (using the Fisher z transform; gray triangles in Fig. 3) shows zero lag. The presence of both leads and lags of change in orientation relative to change in bearing suggests that fiddler crabs can change either one of these parameters first, then adjust the other by the appropriate amount to remain more or less aligned with an unseen home.
Homing to a covered burrow
Covered burrow experiments have demonstrated that foraging fiddler crabs do
not use the burrow itself as a landmark
(von Hagen, 1967;
Zeil, 1998
). In
Fig. 4A we show that our
results from Uca rapax conform to previous results from other
species. The figure shows three superimposed paths of frightened crabs
returning to their burrow (gray circle), which has been covered by a muddy
Perspex plate. The lines represent the paths taken by the center of each
crab's carapace. In each case they stopped on the plate within about half a
body length of home position, before searching or running again. This is in
contrast to Zeil's finding (Zeil,
1998
) that U. vomeris sometimes stopped several
centimeters short of home before commencing to search, and in fact seemed to
center their search on that point.
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Homing after passive translational displacement
Passive displacement experiments have previously been carried out by Zeil
(1998) and Cannicci et al.,
(1999
). In
Fig. 4B,C, fiddler crabs were
passively displaced on a sheet of muddy acetate, either more or less radially
(Fig. 4B) ortangentially
(Fig. 4C) away from their
burrow entrances (large gray circles). The crab's path during the displacement
of the acetate sheet is indicated by black dots, the acetate sheets before and
after movement by solid and broken rectangles, respectively, and the motion
vectors of the acetate sheets by arrows. The positions of fictive burrow
entrances (large open circles) were calculated by adding the motion vector of
the acetate sheet to the position of the burrow entrance. As in the previous
studies cited above, U. rapax invariably returned to the fictive
burrow when homing, and then commenced to search. As noted by Zeil
(1998
), this persistent homing
to the fictive burrow, despite walking during and after the passive
displacement (Fig. 4B),
indicates a well-defined home vector derived from active, but not passive,
movements, even when these occur simultaneously. Some of these experiments
were done in the presence of clear local landmarks (as were some by
Zeil, 1998
), and all were on a
sunny day. Thus, crabs must have used route-based information only, not in
combination with local visual landmark cues as in, for example, the spider
Agelena labyrinthica (Moller,
1970
; Moller and Görner,
1994
).
Path integration errors
Here we ask whether the path integration system of fiddler crabs
accumulates errors over the course of a foraging trip. Two types of errors are
possible in a path integration system, systematic errors and random errors.
Systematic errors should be small, having been minimized by natural selection
(Benhamou and Poucet, 1996),
and they are usually only discovered by experimentally restricting the outward
path. However, on rare occasion, naturally foraging desert ants reveal a
systematic error when the path is heavily biased in its turning directions
(Wehner and Wehner, 1990
).
Indeed, a systematic error in fiddler crabs should by definition create a
change in the orientation error that is consistently related to some temporal
or geometric aspect of the foraging path. If, for instance, many crabs
performed clockwise circumferential foraging paths, and their orientation
error became progressively more negative as their path lengthened, this might
be analogous to the desert ants' homing error, or the well-documented tendency
for vertebrates and invertebrates alike to bias their returns after following
an L-shaped path (e.g. Etienne et al.,
1998
). To test whether a systematic change in orientation error
exists, we again normalized the 13 foraging paths to the clockwise direction.
By so doing, we compared errors that had putatively been induced by similar
biases in locomotion. After combining the data, we calculated regression lines
relating orientation error to each of three path parameters that might be
associated with a source of systematic error, namely time, cumulative path
length and cumulative turns (i.e. the cumulative sum of all changes in body
orientation). The relationships determined in this way should indicate whether
orientation error changed with an increase in any of these three independent
variables.
We found that ten out of thirteen paths showed a significant correlation between orientation error bias and time (Table 1, row `bias'). Of these ten, six showed a decrease in error bias, the other four showing an increase. Similarly, while eight of the thirteen paths showed a significant correlation with increasing path length, four of these eight showed a decrease in error bias while four showed an increase. A similar pattern was seen in the relationship with cumulative turns. Thus crabs may show an increase, decrease or no change in orientation error, and which of these they show does not relate to any parameter we have found. For instance, we found no significant correlation between the slopes of these regressions and total foraging time, total path length, total turns or total arc sector (which is derived largely from turns and increasing path length; least mean squared regressions, all P>0.229). We see no compelling evidence of a systematic error in these results.
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The path integration system might, nevertheless, commit random errors. If error magnitude (the absolute value of orientation error) tended to grow as the path lengthened, then this might indicate growing inaccuracy in the home vector that does not favor a particular direction. Using the same regression technique as described above for systematic errors, we found that the results again show a balanced outcome for each comparison (error vs. time, path length and turns). In all three comparisons, just under half of the paths showed a significant correlation, and half (or just over half) of the significant ones showed a decreased error with the remainder showing an increased error (Table 1, row `magnitude'). Given this balance, it is not surprising that, once again, there was no correlation between the slopes of these regressions and total foraging time, total path length, total cumulative turns and total arc sector (least mean-squared regressions, all P>0.349). We therefore see no compelling evidence for substantial random errors. This is also not surprising, in light of the fact that, at the end of each foraging excursion, each crab successfully returned home without searching.
However, if fiddler crabs do use path integration, it is not reasonable to assert that there are no errors at all. We therefore prefer to conclude that any random errors accrued were not large enough to preclude homing, and that accumulated random error in the home vector was not responsible for a significant proportion of the observed orientation error. The same argument may be applied to the question of systematic error, and will be taken up again in the Discussion. For the moment, the invocation of a systematic error is not necessary. Instead, we assume the pattern of orientation error arises from the fact that there is significant alignment flexibility afforded by the path integration system, but that deviations from perfect alignment are fully integrated.
The home vector and fast escape
The possible relationship between the orientation error and home vector
warrants further scrutiny. Since fiddler crabs only point roughly towards
home, the question arises as to whether they have access to the correct home
vector even while they are not aligned with home, or whether the observed
variation in orientation is a reflection of variation in the home vector
itself. If orientation errors were kept very small, the easiest mechanism for
returning home would be to walk laterally to the side opposite the one used
during the outward journey. This would be a version of the simple
`route-reversal' mechanism (Lorenz,
1943), made even simpler by the fact that crabs need not turn
180° to make the return trip. The small gray circles in
Fig. 1Ai are `false burrows',
calculated by assuming the memory-stored burrow entrance position had the
correct, integrated distance, but that its direction is determined by the
crab's orientation (the arrow direction). The spread of these false burrows is
considerably greater than the spread of home vectors we infer from observing
homing crabs and, given that this crab homed perfectly, we doubt that its home
vector ever pointed at these false burrows.
Any time a crab is frightened by an experimenter, it is likely to be
misaligned to some degree (e.g. Fig.
1). The fact that it invariably returns directly home appears to
support the idea that the crab has a continual memory of its own misalignment;
i.e. that it has constant access to the correct home vector. However, since it
is likely that fiddler crabs use visual contact with their burrow to help
guide the final stage of the return home
(Zeil, 1998), a slightly
inaccurate home vector (possibly indicated by an orientation error) may not
result in missing home. It would thus not be visible to the experimenter as a
homing error. Comparing the direction of fast escape to home direction in
foraging crabs with different initial orientation errors reveals that escape
direction matches home direction very closely
(Fig. 5A; l ms regression,
y=0.9989x-1.1734, r2=0.9006,
F=81.53, P<0.001), and that the difference between escape
direction and home direction is not related to the crabs' initial orientation
error (Fig. 5B; F=9.6x10-5, P=0.9924).
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We also try to address the issue of a crab's access to an up-to-date home vector by analyzing the temporal characteristics of the return path of a crab that had a large orientation error at the time it was frightened.
Fig. 6 shows a male fiddler crab `out of alignment' by 29.3° at the time it was frightened (Fig. 6A, second 65). The foraging path (065 s) was digitized once per second, and the escape path (65 to 65.4 s) was digitized 25 times per second. The crab responded to the threat by engaging three components of its escape behavior simultaneously:
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These are the closed-loop versions of the behaviors recorded open-loop by
Land and Layne (1995).
Combined with the change in bearing, these activities caused the crab to
reduce its orientation error by 62% while reducing its distance to home by 26%
within 120 ms of beginning its escape. This fast correction of body alignment,
especially when compared to running distance, indicates that the crab had
instant access to the correct homing vector, which was different from its
initial orientation error. It also appears that this access is continuous.
In order to continue running towards home, it is not enough to execute the
direction and distance components of the home vector in an arbitrary manner.
It would be correct, for instance, to execute the direction component by
turning, then the distance component by running, but it would not be correct
to do these in reverse order. The fastest way to return home may be to begin
running immediately, and to run in a straight line. However, unless the crab
is perfectly aligned with home, this requires something considerably more
complex than the method just described: any change in orientation (i.e. body
turn) must be equal but opposite to a change in egocentric running direction
for each step of the way. If the crab's motor system is capable of producing
such an agreement between these two components of escape, then in theory fast
escape would not require the continued involvement of the path integration
system. It would only need the initial direction and distance, and escape
could proceed in a ballistic manner; i.e. without feedback. In the case shown
here, changes in orientation occurred with a slight lead compared to changes
in running direction (Fig. 6C),
leading to an error of about 7° in egocentric running direction during
midescape (Fig. 6B). A
cross-correlation analysis of changes in orientation and egocentric running
direction showed that changes in running direction lag behind changes in
orientation by 0.04 s (max. correlation coefficient = -0.7166). This
discrepancy was corrected at the end of the run, but made for a very slightly
curved path. More analyses of fast escape are needed, but it seems likely that
the motor system does not produce turns identical to its changes in running
direction, and so even crabs in fast escape must continue to update the home
vector as they run, and adjust their locomotion to correspond to it. This
behavior is a good example of separate control systems (for turning and
egocentric running direction) that must operate in a highly cooperative manner
to produce an adaptive behavior (escaping predators as quickly as possible).
They apparently operate without information about the absolute position or
direction of their burrow entrance that would provide feedback about their
errors (Layne et al., 2003),
but they may be able to make a continuous comparison with the stored memory of
the home vector. The home vector, as an integrator of the crab's motor output
(whether this is measured as efference copy or proprioceptive input), may
provide error signals which mediate the relative outputs of the turning and
direction systems during escape. Land and Layne
(1995
) showed that the turning
and direction systems can, in fact, be dissociated, and it is an interesting
question how the timing and magnitude of each are tuned to make the running
crab hit its mark, and avoid being eaten.
It has been suggested that the reason fiddler crabs align themselves side-on to their burrow entrances is to facilitate escape. Since they run fastest sideways, maintaining this orientation may reduce the time needed to reorient their bodies before or during escape. This leads to the hypothesis that speed of escape may be inversely related to initial orientation error. However, the crab in Fig. 6 had one of the fastest escapes, despite starting with one of the largest orientation errors of any we observed. Fig. 6D (open circles) shows the escape velocity of the crab shown in Fig. 6A plotted along with the mean escape velocities of ten other crabs similarly frightened (solid gray line) and their 95% confidence intervals (dotted gray circles). The path is relatively short compared with the other eight, but the shape of the velocity profile for the escape is very similar. Linear regression analysis of eleven escape trajectories shows that both the mean and maximum escape velocity are not related to initial orientation error (mean initial orientation error = 13.9±9.8°; vs. mean velocity: F=2.35, P=0.164; vs. maximum velocity: F=1.034, P=0.339). This suggests that, within the limits of the orientation error normally seen in fiddler crabs (maximum around ±30° for U. rapax, unless faced with an obstacle), the velocity of their home runs is not impeded by misalignment. Nevertheless, the speed-of-escape hypothesis may still explain why orientation error is usually kept within ±30°.
A large initial orientation error would seem to necessitate greater coordination between changes in orientation and running direction. This coordination may be imprecise, which leads to the hypothesis that the curvature of the escape path will be inversely related to the strength of correlation between changes in orientation and running direction. Linear regression reveals that this relationship between path curvature, defined as straight-line distance divided by the distance traveled by the crab, and the maximum (z-transformed) correlation coefficient is significant (F=5.65, P=0.0490). This means that the coordination of turning and changing running direction does affect how straight the crab runs, but it does not affect how quickly the crab escapes. Escape velocity does not depend on path curvature (F=1.02, P=0.341), probably because crabs simply do not escape along very curved paths (maximum recorded escape path curvature was 0.9720), regardless of their orientation error or level of coordination.
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Discussion |
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Effect of locomotory style and foraging path shape
The first conclusion above raises questions about the sensory modes that
might be used, and the neural mechanisms that might underlie the measurement
and integration of locomotory information; these are addressed in the
accompanying paper (Layne et al.,
2003). The second general observation, that fiddler crab foraging
paths are characterized by extremely restricted locomotory patterns, raises
questions about the computation of the home vector, and the effect of this
type of locomotion on the computational accuracy. Analysis of natural foraging
paths indicates that the integration algorithm does not contain a systematic
error, but it also fails to detect any substantial random measurement errors.
Thus, we must also question the potential for fiddler crab foraging paths to
reveal the nature of the computational algorithm. Two hypotheses must be
considered: (1) that the unique foraging behavior minimizes the types of
movements that are sensitive to random measurement errors, or (2) that it
minimizes the types of movements that exacerbate a systematic error. Either
way, the behavior may obscure the truth about whether fiddler crabs employ a
geometrically correct or incorrect solution. Since we have not observed
fiddler crabs to make homing errors (but see below), we cannot use observed
errors to formulate a candidate algorithm containing the putative systematic
error, as Müller and Wehner
(1988
) did for desert
ants.
Burrow orientation may exist to ensure that the crab can race back towards
home in the event of a threat to its burrow or itself. However, we have shown
above that the homing speed is not diminished when the orientation error is
near its natural maximum. Thus, alternatively, we can speculate that burrow
orientation might arise from a physiological problem in the integration
process, such as progressive failure with time of the memory-stored
orientation error. Such a problem might be somewhat alleviated if the
orientation error were frequently `zeroed', as we have observed in fiddler
crabs, if memory failure increased nonlinearly with time. However, we have
observed one foraging crab to seemingly switch its orientation to a
neighboring burrow for nearly 2 min (requiring a mean orientation error
relative to the original burrow of about 30°), and then return home to the
original burrow. The memory of navigational vectors is an interesting issue in
fiddler crabs, since there are observations that some species may retain the
relative positions of several burrows for long periods of time
(Zeil and Layne, 2002).
Returning to these burrows does not necessitate landmark memory or an external
compass (Benhamou et al., 1990
;
Maurer and Seguinot, 1995
),
but if not it would indicate a fairly elaborate system of vector memories. The
only crab we have seen to miss home without experimental manipulation was one
that, while investigating a neighboring burrow, made a voluntary turn of about
170°. This crab seemingly overestimated its turn by about 10°, and
performed a short search before finding home again. More observations of these
infrequent naturally occurring errors are clearly required, since they might
indicate whether errors are random or systematic. Our current data do not
provide any compelling evidence for a systematic error.
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Acknowledgments |
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References |
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