Measuring structural features

The next level of complexity in methods for analysing movement involves measuring the spatial position of relevant body parts during a display. These can be plotted to provide an indication of the trajectory of various body parts. For example, von Hagen (1983) traced the position of the claw-tip and elbow during fiddler crab claw-waving displays by projecting video sequences filmed at crab- eye level onto a sheet of paper, and plotting body positions frame-by-frame. This method allowed for the quantification of structural differences in the claw-waving displays of two sympatric species, U. mordax and U. burgersi. Similar methods using custom-made video analysis software are used in chapters 3 and 5 of this thesis to analyse variations in the signals of Australian fiddler crab species.

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Using shape analysis techniques (MacLeod, 1999) it is possible to calculate mean claw-tip trajectories from multiple wave traces (Fig. 2.4A). Briefly, this method requires each claw-tip trace (Fig. 2.4A, middle) to be reassigned with a fixed number (in this case 300) of evenly spaced x-y coordinates. The mean claw-trace can then be calculated by simply averaging each of these newly assigned coordinates over the full number of traces (Fig. 2.4A, right). This technique provides an estimate of the average shape of the trajectory, but the process of reassigning evenly-spaced coordinates loses temporal information needed to calculate parameters such as claw-tip speed. Also, small-scale structural features can be lost, such as the small pauses in the upstroke of some fiddler crab displays (see chapter 3, Fig. 3.8). The loss of temporal and structural features can be minimised by breaking the display up into sequential components. For example, in the analysis of the display of U. perplexa in figure 2.4, the structure of the movement was divided into three main parts, the lateral unflexing of the claw (stage 1), the claw uplift (stage 2) and the claw down-swing (stage 3). The mean shape of each of these three stages was calculated separately using the methods above and then combined.

Another example of the use of such trajectory analysis techniques is the comparative analysis of lizard head and body movements performed by Purdue and Carpenter (1972). These researchers plotted seven key body parts from video sequences of displays viewed from the side of four different closely- related lizard species (Fig. 2.4B). By analysing angular changes during the different displays they were able to compare statistically the divergence in signal design across the study species.

Figure 2.4. Trajectory analysis. A) Illustration of claw-tip trajectory for a single lateral wave (left), 37 long-range lateral waves (middle) and mean lateral wave (right) for the fiddler crab Uca perplexa. The mean shape was calculated for each of the three stages independently. B) Stick diagrams of the ascending portion of push-up displays for four lizards of the genus Sceloporus

(redrawn from Purdue & Carpenter, 1972).

Measurements of movement trajectories during displays can also be analysed over time. Hyatt (1977) compared the waving displays of juvenile and adult fiddler crabs using a similar method to that used by von Hagen (1983). By plotting the change in claw-tip to body angle over time he was able to show that juveniles have a temporally and spatially different movement signal to conspecific adults (Fig. 2.5A). Salmon et al. (1978), used the same method to study the effect of sympatry on claw-waving display structure in fiddler crabs. Such display action pattern techniques (DAP; Carpenter & Grubitz, 1961) have been used extensively to define lizard displays (e.g. Carpenter et al., 1970; Jenssen, 1977; Martins & Lamont, 1998; Ord & Martins, 2006). One such study, on the head-bobbing and dewlap extension displays of the colourful Caribbean anole lizard (Anolis auratus), was performed by Fleishman (1988). By plotting head elevation and dewlap extension over time during different display contexts,

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Fleishman showed that ‘assertion’ and ‘challenge’ movement displays differ in pattern and intensity (Fig. 2.5B).

Figure 2.5. Time series of movements during visual displays in three different species. A) Claw- tip to body angle during the claw-waving display of the male fiddler crab Uca pugilator. Red band represents results for small crabs (8-12mm) and yellow band represents large crabs (17-18mm) (redrawn from Salmon & Hyatt, 1983). B) The visual display of the lizard Anolis auratus. Both head-bobbing (grey) and dewlap extension (orange) differ between assertion and challenge displays (redrawn from Fleishman, 1988). C) The claw-waving display of U. seismella

represented by changes in pixel intensity for an image slice over time. Red line in the original image (left) indicates the position from which the vertical slice was taken. Pixels from this image slice are plotted frame-by-frame (right). Red arrows indicate the five points of maximum claw elevation during the display.

Another method for displaying movement is to plot the one-dimensional brightness distribution of a pixel-wide slice through a video sequence over time. This technique is commonly used to illustrate movement in test patterns for studying motion vision (e.g. Borst & Egelhaaf, 1993) and has also been used previously to illustrate background movement in natural scenes (Zeil & Hemmi, 2006). In the example in figure 2.5C, a slice is taken through a video sequence of a waving fiddler crab (Uca seismella; vertical red line in Fig. 2.5C, left) and the pixels from this slice are plotted over time. This results in a graphical representation of movement within the display, in which the claw is raised and lowered in a repeated series of 5 waves (red arrows in Fig. 2.5C, right). Essentially, this represents the temporal sequence of changes in light intensity that a strip of photo-receptors might experience in the visual field of the observer. However, this method fails to resolve movement in directions other than vertical and is vulnerable to the aperture effect (diagonally moving objects appear to move vertically).