QUICK SEARCH:   [advanced] Author: Keyword(s):
Home     Help     Feedback     Subscriptions     Archive     Search     Table of Contents

First published online November 10, 2003

This Article Summary Full Text Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Layne, J. E. Articles by Duncan, L. M. J. Search for Related Content PubMed PubMed Citation Articles by Layne, J. E. Articles by Duncan, L. M. J.

Mechanisms of homing in the fiddler crab Uca rapax 2. Information sources and frame of reference for a path integration system

John E. Layne^*, W. Jon P. Barnes and Lindsey M. J. Duncan

Division of Environmental and Evolutionary Biology, Institute of Biomedical and Life Sciences, University of Glasgow, Glasgow G12 8QQ, Scotland, UK

View larger version (20K): [in a new window]   Fig. 1. Illustration of the method used for deriving imposed- and self-translation. (A) Hypothetical experiment in which a crab is rotated on a disk (see text). The crab's transverse axis is denoted by an arrow on its body pointing to the homeward side. Numbered green open circles indicate the crab's position at each time point. The red circle indicates the final position of the crab if it had not moved (see text for details). (B) The experiment between times t0 and t1. The absolute translation vector (violet arrow) is digitized from video. The imposed translation vector (red arrow) is normal to the radius (red broken line) bisecting the crab's position at t1 and t2 (green open circles), and thus estimates the mean of all (unmeasured) imposed directions between the two discrete sampling times. It is the same length as the arc passing under the spot bisecting the crab's position at t1 and t2 (gray arc). The self-translation vector (blue arrow) is the vector subtraction of the imposed from the absolute translation vector; i.e. violet – red = blue. (C) Illustration of the imposed- and self-translation vectors (red and blue, respectively) for each step in the path shown in A. Green circles correspond to those in A.

View larger version (11K): [in a new window]   Fig. 2. Possible paths recorded by the model path integrator. (A) Different versions of the hypothetical path shown in Fig. 1. Three of these paths (black, blue and violet) rely on an external compass for direction information (allothetic), while four of them (red, orange, green and gray) rely on an internal source of direction information (idiothetic). The latter include an arrow for the transverse body axis, signifying that all directions are measured against this. (B) Summary of possible paths from A. All integration mechanisms record the outward path (large black arrows); thereafter they diverge. Idiothetic paths show the final recorded orientation of the body axis (small black arrows) and the angle of the home vector measured against this (colored arcs). Home vectors are all in broken arrows. (C) Hypothetical home vectors for all seven model paths. See text and Table 1 for a description of the path-integration mechanism used to obtain each path.

View larger version (33K): [in a new window]   Fig. 3. Example of a trial in which a crab fully compensated for disk rotation. (A) Transverse axis of the crab's body (inset), digitized at 200 ms intervals, shown from the start of disk rotation until the crab reached home. Numbers are in seconds after rotation began. Large tinted circle, rotating disk; white circle, position of crab when disk rotation started; blue circle, position of crab when rotation disk ceased. (B) Orientation and bearing of crab and disk over time. Compensatory body rotation by the crab was assumed to have ceased at the time indicated by the black arrow. Note the similarity of this body orientation with that at the beginning of the experiment. (C) Crab and disk angular velocity, and crab angular velocity relative to the disk over time. (D) Reconstruction of seven possible home vectors computed by the path integrator, superimposed on the crab's actual path as in A. See text for details.

View larger version (24K): [in a new window]   Fig. 5. Example of a trial in which a crab under-compensated for disk rotation, and had significant self-translation during disk rotation. (A) Crab's transverse body axis digitized at 200 ms intervals; conventions as in Fig. 3. (B) Orientation and bearing of crab and disk over time. Black arrows, two abrupt compensatory turns occurring after disk rotation ceased, the second of which is in mid-return; note the coincident large change in bearing, caused by the run home. (C) Crab and disk angular velocity, and crab angular velocity relative to the disk over time. (D) Reconstruction of seven possible home vectors computed by the path integrator, superimposed on the crab's actual path as in A. See text for details.

View larger version (23K): [in a new window]   Fig. 4. Example of a trial in which a crab under-compensated for disk rotation, and had little self-translation during disk rotation. (A) Crab's transverse body axis digitized at 200 ms intervals; conventions as in Fig. 3. (B) Orientation and bearing of crab and disk over time. Compensatory body rotation ceased when disk stopped, and the crab homed immediately thereafter. (C) Crab and disk angular velocity, and crab angular velocity relative to the disk over time. (D) Reconstruction of seven possible home vectors computed by the path integrator, superimposed on the crab's actual path as in A. See text for details.

View larger version (32K): [in a new window]   Fig. 6. Comparison of the homing accuracy of the seven path-integration models, i.e. the error angle between the model vector and the observed homing direction, as illustrated in (A). Polar plots are for counter-clockwise disk rotation and show the mean error angle () plotted with respect to the observed homing direction (set to 0°). Values are ±95% confidence intervals; r is the mean vector length. (B–D) exocentric paths, (E–H) egocentric paths, (I,J) the smaller of the absolute error values between (I) black and blue and (J) red and gray paths. See text for details.

View larger version (26K): [in a new window]   Fig. 7. Examination of the input–output relationships of the crab's compensatory rotation on the disk. Means (solid lines) and S.D. (broken lines) of time-lagged cross-correlations for all 15 trials, between: crab egocentric and disk angular velocities (sign reversed, blue line with circles); crab egocentric angular velocity and crab orientation (sign reversed, red line with triangles); crab egocentric angular velocity and orientation error (this is affected by both rotation and translation; black line with squares). Positive lags indicate disk angular velocity, crab orientation or orientation error leading in time, negative lags indicate crab egocentric angular velocity leading.

View larger version (21K): [in a new window]   Fig. 8. Example of a slippery patch experiment. (A) The crab was frightened when situated at `start', ran over the slippery patch (gray rectangle), and stopped at the filled arrow, before finding its way home. (B) Plot of crab running velocity against distance run. The shaded area indicates when the crab was on the slippery patch.

View larger version (38K): [in a new window]   Fig. 9. Running velocity of escaping crabs. (A) Running velocity plotted against relative distance home (d/D). Red lines, crabs that ran over the patch and stopped before reaching home; blue lines, crabs that ran over the patch but did not stop before reaching home; black lines, control crabs that did not run over a patch. Red and blue lines are solid where the crabs were on the patch. (B) Mean of running velocity profiles plotted against relative distance home (d/D). Controls (including both no-patch and non-slippers), black line; slippers, red line; lines are mean running velocity ± S.D. (dotted lines). (C) Mean of running velocity profiles of controls (no patch, black line) and non-slippers (blue line) plotted against relative time until first stop (t/T); lines are mean running velocity ± S.D. (dotted lines). (D) Same data as in B but plotted against relative time until first stop (t/T).

View larger version (11K): [in a new window]   Fig. 10. Estimation of length of home vector from time spent running by slipping crabs. (A) Observed running distance Dobs (open circles) and estimate of home vector length Dest (filled circles) plotted against starting distance D, which is assumed to be equal to true home vector length. (B) Relative error in estimate of home vector length (Dest/D) plotted against observed running time. Lines of best fit, calculated by the method of least squares. See text for details.

View larger version (14K): [in a new window]   Fig. 11. Relationship of frequency of stepping to overall running velocity in fiddler crabs. Data for Uca pugnax reanalyzed from Barnes (1975). Because of the limitations imposed by the 64 frames s-1 filming rate, sequences of running with velocities above 35 cm s-1 were not analyzed in the original report. The continuous line is the line of best fit for the data calculated by the method of least squares, while the broken line is a theoretical line which assumes that increases in velocity are produced entirely by increases in stepping frequency. The fact that the actual line is steeper than this indicates a small additional role for increases in step length (ca. 12% of total). Values (N=27) are means for sequences of locomotion varying in duration from 0.4 to 14 s.

View larger version (9K): [in a new window]   Fig. 12. Proposed system for selective integration of voluntary locomotion (in the form of commands from the CNS), and for avoiding integration of involuntary locomotion (originating from the optomotor response). This is a simplified version of this system. In reality, the efference copy would require a gain that matched that of the optomotor portion of the circuit.