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Figures
- Fig. 1.
The retinal size and position of the dummy on the crab's retina at the time of response. Each measure is plotted as a histogram against the dummy's approach direction (track angle; see inset at the top). Vertical lines mark 1 s.e.m.. above and below the mean. (A) Vertical retinal size increases with track angle (REML; N=419, Wald/d.f.=31.86, d.f.=8, P<0.001). The results for the horizontal angular size of the dummy are equivalent. (B) Dummy elevation in the crabs' visual field at the time of response increases with track angle (black bars). The elevation of the burrow (grey bars), by contrast, varies little, indicating that the crab-burrow distance was relatively constant across different track angles. (C) The azimuth directions relative to the burrow at which the dummy is seen become larger with track angle. Due to the strong asymmetry of these distributions, means for A and B were determined on a logarithmic scale.
- Fig. 2.
The geometry of the burrow surveillance task. A crab needs to measure the dummy-burrow distance (db) independent of its own crab-burrow distance (cb) and the angle (α) between the direction in which it sees the dummy and the direction in which the burrow lies.
- Fig. 3.
The effect of dummy size on response distance. Due to the strong asymmetry of the apparent size distribution, means were taken on a logarithmic scale. The vertical lines represent the 95% confidence interval. (A) The crab-dummy distance at the moment of response is independent of the dummy's vertical (black dots; REML; N=419, Wald/d.f.=2.01, d.f.=1, P=0.156) and horizontal (open dots; REML; N=419, Wald/d.f.=1.03, d.f.=1, P=0.309) size. (B) The apparent size of the dummy at the moment of response is accurately predicted by both its vertical (black dots; REML; N=419, Wald/d.f.=13.75, d.f.=1, P<0.001) and its horizontal (open dots; REML; N=419, Wald/d.f.=7.18, d.f.=1, P=0.007) size. The line connects the right-most point with the origin.
- Fig. 4.
The relationship between eye height and carapace width for sitting (grey dots) and standing (black dots) crabs. The straight lines are least squares fits to the two distributions (Zeil and Layne, 2002).
- Fig. 5.
The elevation at which the dummy appears in the crab's visual field at the moment of response. Elevation is measured relative to the horizon at the point of contact between the dummy and the ground.
- Fig. 6.
Dummy paths in retinal coordinates as they would have been seen by the crabs. The paths (grey dots) are shown from the moment the dummies became visible in the recording area until the crabs reacted (black dots). Paths are selected in A-C according to the retinal elevation of the burrow entrance (large grey circles) at the start of each experiment, which is a function of crab-burrow distance and eye height above ground: (A) -20° to -7°, (B) -7° to -5° and (C) -5° to 0°. The lower the burrow is seen in the visual field, the closer a crab was to its burrow.
- Fig. 7.
Retinal position of all points in the visual field of a crab that are 25 cm away from the crab's burrow. The positions are shown for different crab-burrow distances (solid and dotted lines), as labelled. On these lines of equal dummy-burrow distances we marked the positions of dummies approaching from different directions with grey dots. The approach directions are grey-level coded, with smaller track angles being represented by progressively lighter greys (see inset). Note how the position of the burrow moves upwards in the visual field of a crab as it moves further away from its burrow (grey circles at 0° azimuth). The vertical line of small black dots along the y-axis indicates the elevation in which consecutive neighbouring vertical rows of ommatidia are facing, to show the pronounced increase in vertical resolution towards the horizon and the approximate level of resolution with which the dummies are seen by the fiddler crab eye (after Land and Layne, 1995a; Zeil and Al-Mutairi, 1996).
- Fig. 8.
Model fits for the position of the dummy relative to the burrow and the crab at the time of response for a crab-burrow distance of (A) 15 cm and (B) 25 cm. The fits are made for all dummy approach directions (track angles) and crab side values (see Fig. 1C) used in the model (Hemmi and Zeil, 2003a). For each track angle/crab side combination, we plotted the dummy's trajectory as a solid line from a distance of 50 cm to the burrow until the crab reacted (dot). For example, the black line at the top of A, just above and slightly to the left of the crab symbol, shows the approach path of a dummy for a track angle of 10° (0-20° track-angle bin) at the median track distance of 10 cm and a crab-side value of one. The crab initiates the reaction when the dummy reaches the black dot at the end of the line. The radius of the solid circle equals the fitted mean of all response distances ±2 s.e.m. (dotted circles). (C) and (D) show the same data in retinal coordinates as seen by the crab. The continuous and dotted lines in C and D are the projection of the mean response distances± 2 s.e.m. (circles in A and B).
- Fig. 9.
The mapping of burrow distance onto the ommatidial array. Shown is the visual field of a crab that is (A) 10 cm, (B) 20 cm or (C) 30 cm away from its burrow. The burrow location is marked by a grey circle. The labelled contour lines within each plot correspond to positions in space that have a fixed distance from the crab's burrow. Contours have been drawn for 5, 10, 15, 20, 25, 30, 40 and 50 cm. The solid black lines show the retinal path of a set of two fictitious dummies that approach the burrow from a distance of 50 cm and move either directly over the crab's burrow or move 10 cm past the burrow. In contrast to the previous figures, elevation has been transformed into facet rows. The x-axis (azimuth) scale has been adjusted such that individual ommatidia would take up equal space along the x- and the y-axes. These transformations reduce but do not eliminate the effect of perspective foreshortening. The white arrows in C show the local directions of the distance to burrow gradient on the eye.
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