Interpretation Catalogue for TT- Plots

From the observations above I shall try to provide a first interpretation catalogue for TT- $\delta$ plots. It will start with patterns that are easy to recognize. I shall then provide pattern interpretations which are intended for a more refined analysis.

In tables 5.2ff the base diagonal line from the lower left to the upper right corner is drawn in black. The objects of interest are drawn in blue. Objects mentioned in a former entry are also drawn in black.

The first catalogue entry is a square shape around the base diagonal line (table 5.2a). It indicates that the object resides at the 'same' place for a certain amount of time. In practice the square shape will not be sharply bounded at first. If needed the data can be easily filtered to display only areas that represent intra-event distances up to a defined distance. The second catalogue entry (5.2b) is a line at an angle of 90 $^\circ$ to the base diagonal to which it is connected. It shows that the object uses the same travel path in the opposite direction without leaving the original path. When the animal uses a path and after some time reuses a travel path used some time ago, the pattern in table 5.2c occurs. The disjoint lines show that the animal did not turn around and walk back, but made some kind of a loop before rejoining to the original path. In table 5.2d the line of interest is parallel to the base diagonal line. For the observation time in question it means that the animal uses the same travel path in the same direction as before. The amount of time passed between the two lines is equivalent to the horizontal distance between the two lines. Smaller distances mean a shorter interval and vice versa. The last simple catalogue entry is shown in table 5.2e. Whenever a location is visited a second time, but the animal uses a different path to and a different path from the location than the first time, a single (blue) dot occurs in the TT- $\delta$ plot. The next two catalogue entries are more complex. 5.2f is a repeated pattern of entry b. The same path is used repeatedly in both directions, describing twice a forward and backward movement. The last pattern comes from an animal running four times on a loop. It does not have to be a regular loop as a circle or a rectangle, but can be any shape which does not contain intersections.

**Table 5.2:** Basic interpretation catalogue for TT- $\delta$ plots. The shapes of interest are drawn in blue. Shapes that already occurred in previous catalogue entries are drawn in black. The black diagonal line (lower left to upper right) indicates the base diagonal line (see figure 5.10).
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat1.eps}$	a. The animal stays for a period of time at the same place. (see also table 5.3)
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat2.eps}$	b. The animal walks on the same path as it came from, but in the opposite direction. (see also table 5.4)
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat5.eps}$	c. The animal walks for some time on a path and then returns to the path used earlier, continuing its way on the same path but in the opposite direction. (see also table 5.5)
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat3.eps}$	d. The animal walks the same path some time later in the same direction as the first time.
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat4.eps}$	e. The animal passes by a location it already passed before, coming from and going in a different direction than the first time.
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat7.eps}$	f. The animal is using a path forth and back and a second time forth and back.
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat6.eps}$	g. The animal is using the same path four times in one direction (e.g. walking on a circle), then reverts its direction, walking the same path four times in the opposite direction, but still on the same path, and then again uses the path four times in the same direction as the first time.

Table 5.3 lists four extensions to the first catalogue entry (5.2a). In 5.3a1, after staying at a location for some time, the animal leaves the area using the same path as it came from. When an animal is staying for some amount of time at the same location it did some time ago, the resulting pattern (5.3a2) in a TT- $\delta$ plot is a rectangle at the same y-coordinate (t₂) but displaced to the right (t₁). How long the animal stayed in an area is proportional to the size (horizontal diameter) of the rectangle. In the special case shown in table 5.3a3 the animal stays for a longer time in an area it visited only for a short time before. This could be interpreted as some kind of searching for good places and then returning to the 'best' one. The opposite pattern is shown in table 5.3a4, where the animal passes the same location it stayed for a longer period only for a short time.

**Table 5.3:** Extended interpretation catalogue for TT- $\delta$ plots of variant a.
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat1a.eps}$	a1. The animal stays for some time at the same location and leaves it via the same path as it came from.
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat1b.eps}$	a2. The animal stays at the same place it did some time ago.
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat1c.eps}$	a3. The animal visited a place for a short time where it stayed for a longer time afterwards ('recognition tour').
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat1d.eps}$	a4. The animal visits the same place again for a short time where it stayed for a longer time before.

A finer analysis of the catalogue entries b and c (table 5.2) can reveal relative travel speed differences (tables 5.4 and 5.5). If the angle to the horizontal becomes smaller than 45 $^{\circ}$ , it reveals that the animal was walking at a slower speed than the first time (b1 and c1) and vice versa (b2 and c2). Relative speed changes are indicated by changing angles (b3, b4 and c3, c4).

**Table 5.4:** Extended interpretation catalogue for TT- $\delta$ plots of variant b.
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat2a.eps}$	b1. If the angle from the horizontal becomes smaller than 45 $^\circ$ , it means that the animal is walking slower than the first time.
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat2b.eps}$	b2. If the angle from the horizontal becomes larger than 45 $^\circ$ , it means that the animal is walking faster than the first time.
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat2c.eps}$	b3. Speed changes on the same travel path are indicated by changing angles from the horizontal. In this example the animal starts walking back on the same path very fast, then becoming slower.
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat2d.eps}$	b4. In this example the animal starts walking back on the same path very slowly, then becoming faster.

**Table 5.5:** Extended interpretation catalogue for TT- $\delta$ plots of variant c.
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat3b.eps}$	c1. The smaller the angle from the horizontal, the slower the animal is walking along the same path than it did before.
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat3a.eps}$	c2. The larger the angle from the horizontal, the faster the animal is walking along the same path than it did before.
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat3c.eps}$	c3. Speed changes on the same travel path are indicated by changing angles from the horizontal. In this example the animal starts walking on the same path very fast, then becoming slower.
$\includegraphics[scale=0.3, trim=0 0 0 -13]{images/ttd_cat3d.eps}$	c4. In this example the animal starts walking on the same path very slow, then becoming faster.