Temporal RDF-Functions

In the previous sections the radial distance functions were always used in a static context. As stated earlier it is important to include temporal aspects in the analysis when analyzing animal observations. Now I would like to extend the RDF-plots in a way that allows for the recognition of changes in the environment of an animal's surrounding. This extension is done with techniques used in the T-plots introduced earlier.

The creation is done by calculating RDFs for each location passed by the animal (see figure 7.10). In the actual implementation the path is sampled at a very fine interval and at each sampling location a standard RDF is created.

**Figure 7.10:** The creation of a temporal RDF-plot.
$\includegraphics[scale=0.56]{images/xy.eps}$ $\framebox{ \includegraphics[scale=0.35]{images/rdf_time_creation.eps}}$

After that step all the calculations are combined into a single graph in the following way. Two axes used in the RDF plot (distance and value of parameter of interest) will be retained in the graph, although the value of the parameter will be coded in a color scheme on a z-axis instead of using the y-axis. A third axis will contain the distance values from the sampling locations. This results in a graph having the time on the x-axis, the distance from the object in the y-axis and the value of interest (e.g. amount of woodland) coded in color on the z-axis.

**Figure 7.11:** Example of a temporal RDF-plot. The amount of woodland (percent) is plotted in this example for a lynx during the observation period in 1996. Dark blue indicates high percentage of forest, green medium and yellow small percentage of forested areas around the location.
$\includegraphics[scale=0.56]{images/td.eps}$ $\includegraphics[scale=0.30]{images/rdf_t_lars.ps}$

An example is given in figure 7.11 for a lynx. Three distinct features can be easily seen in that figure. Firstly in the close vicinity of the animal there is most of the time a relatively high percentage of forest. At larger distances the amount of forests is usually medium to small. Secondly there were three periods where the animal stayed for a longer period of time in relatively open areas as indicated by the three larger yellow (vertical) bars in the second quarter of the figure (from left to right). The third feature can be seen in the two smaller and the large blue vertical bars in the second half of the figure. They indicate sojourns in large forested areas.

The main focus in this kind of analytical plot rests upon the temporal dynamics. It is important to see at what times and at which intervals or cycles the animal is using certain configurations in its surroundings.

**Figure 7.12:** Second example of a temporal RDF-plot. The amount of woodland (percent) is plotted in this example for another lynx during the observation period in 1996. Same color scheme as in figure 7.11.
$\includegraphics[scale=0.56]{images/td.eps}$ $\includegraphics[scale=0.31]{images/rdf_t_kora.ps}$

In figure 7.12 a second example is illustrated. It shows another lynx living in the same region but using it in a different way than the first one. Periods of using widely open or widely forested areas are missing. In the very close vicinity it uses areas with high amounts of forests, whereas the further vicinity consists of medium forested, relatively homogeneous areas.