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First published online November 10, 2003

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Mechanisms of homing in the fiddler crab Uca rapax 1. Spatial and temporal characteristics of a system of small-scale navigation

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 (38K): [in a new window]   Fig. 1. (A–C) Three examples of natural foraging paths, digitized at 1 frame s-1. (Ai–Ci) Positions of transverse body axis of fiddler crab, with the arrow pointing toward the `homeward' side, as seen in the boxed inset in Ai, for each digitized frame. The boxed inset also shows the convention for egocentric directions used throughout this paper. Numbers correspond to elapsed time (s). The center of the carapace is connected between frames. The burrow is the large open circle. Scale bars in Bi apply to Ai–Ci. The small gray circles in Ai adjacent to the burrow represent calculated burrow positions for each digitized step, assuming the burrow entrance were to lie directly in line with the crab's transverse axis on its the homeward side (see Results for details). Open inset in Ai is a diagrammatic representation of the orientation error (see below). The hatched solid area in Ci is the base of a mangrove sapling. (Aii–Cii) Orientation error (degrees), defined as bearing minus orientation (inset in Ai), over time (s). The double-headed arrow in Cii indicates the time when the burrow was blocked from view by a mangrove sapling. (Aiii–Ciii) Frequency histogram showing the distribution of orientation errors in 1° bins, with an ideal normal probability density function overlaid (solid line).

View larger version (36K): [in a new window]   Fig. 2. (A–C) Three examples of foraging paths performed with a barrier (solid lines in Ai–Ci) between crab and burrow, digitized at 1 frame s-1. Horizontal arrows (Aii–Cii) indicate when the barrier was between the crab and burrow. Conventions as in Fig. 1.

View larger version (23K): [in a new window]   Fig. 3. Time-lagged cross correlation between change in orientation and change in bearing. Data shown are from paths in Fig. 2A (open circles), Fig. 2B (filled circles), the Fisher z-transformed mean of seven paths (filled triangles) and the 95% confidence interval (broken lines). Correlation coefficient is plotted on the y-axis, lag on the x-axis; a negative lag means change in bearing preceded a change in orientation.

View larger version (16K): [in a new window]   Fig. 4. Results from experiments involving (A) covering the burrow, (B) radial translational displacement and (C) tangential translational displacement. (A) Data from three different crabs were overlaid and aligned with one burrow entrance (filled gray circle); lines represent the center of each crab's carapace. (B,C) Position of muddy, mobile acetate sheet before (solid rectangles) and after (broken rectangles) displacement, with the sheets' motion vectors indicated by gray arrows. Fictive burrow entrances (large open circles) are found by adding this motion vector to the true burrow entrance (gray filled circles). Lines represent the center of each crab's carapace, the period during which the crabs were on a moving substrate being indicated by connected black dots. In these figures, `start' indicates the beginning of the digitized track; in A, only the homeward part of the crabs' tracks were digitized, while in B and C both outward and homeward journeys were digitized. Scale bar in C also applies to B.

View larger version (16K): [in a new window]   Fig. 5. (A) Escape directions of foraging crabs in relation to the true home direction and (B) the difference between escape and home direction in relation to the crabs' orientation error at the start of the escape run. All directions are in egocentric terms, and follow the convention in Fig. 1A inset. The line of best fit, calculated by the method of least squares, is shown in A.

View larger version (26K): [in a new window]   Fig. 6. Escape path of a crab having a large orientation error when it was frightened. (A) crab's transverse body axis during foraging (black arrows) and escape (gray arrows); it was frightened at t=65. Foraging behavior was digitized at 1 frame s-1, while escape was digitized at 25 frames s-1. (B) Plot of egocentric running direction (dotted line) and egocentric home direction (solid line) plotted against time during escape (i.e. from 65 to 65.4 s); (C) Changes in orientation (body turns; solid line) and changes in egocentric running direction (dotted line) during fast escape. (D) Time course of running velocity of escaping crab (open circles) compared to the similar time course for eight other escaping crabs (gray circle, broken gray line shows ± S.D.). For correlating two behaviors in time, it must be remembered that turns and running direction are first derivatives of orientation (a position measurement), and change in running direction is a second derivative of orientation. It then follows that, if orientation has n observations, then turns and running direction have n-1 observations, and change in running direction has n-2 observations. We therefore associate the `nth' turn or running direction with the nth orientation (see running direction vs. home direction in B), and the nth change in running direction with the nth+1 turn (see running direction change vs. orientation change in C).