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Radial Distance Functions (RDF)

In the previous chapter the main focus was set on the analysis of the pure locational component ignoring any environmental attributes. In this chapter I will work on methods on how to link observations of an animal to its environment using the spatial domain.

Professor Hans Kummer at the University of Zurich once tried to explain the concept of motivation in ethology to a group of students. A plant as an immobile organism needs all resources at the same location. If one resource is missing, the plant cannot exist at that spot. Animals overcame this restriction by 'inventing' locomotion. This enabled the organisms to use resources dispersed over space and made areas accessible to them which do not contain everything at the same spot. But locomotion required another system which urges the animal to move to another location: this is called motivation. An inner mechanism to provoke the animal to do something.

By putting animal observations into one of today's GIS, the ability of locomotion is removed from the animal in most cases. In a subsequent habitat analysis this fact often vanishes in the minds of the researchers and gets replaced by an acribic application of sophisticated statistical tools. Traditionally three methods for describing the environment at an animal's location have been used. These are:

Today these are still the standard methods. GIS technology made them very efficient, but up to now it did not generate new or enhanced methods of how to measure the environment around an animal.

Figure 7.1: A cow in the middle of a road in Zurich (Switzerland). This picture illustrates three widespread problems in performing calculations with animal locations in GIS. 1. The accuracy of the determined location is often less precise than the GIS data. 2. The resources an animal needs are distributed throughout space and can hardly be determined by point in polygon tests. 3. One of the most important abilities of animals is mostly ignored in GIS: locomotion (note the concrete underneath the cow).
\includegraphics[scale=0.6]{images/kuh2.ps}

There are several unsolved problems when using these description methods. In the case of measured distances often only the closest object is considered and further ones are ignored in today's habitat analysis methods. In the traditional point pattern analysis such approaches exist for describing the clustering of a point pattern (e.g., MacLennan, 1991), but they have not been adopted for habitat analysis in animals. When describing parameters such as the amount of one vegetation type, a reasonable or 'correct' areal extent (e.g. a hectare) has to be chosen. It is widely accepted that animals interact with the environment at different scales. This makes guessing of a 'correct' diameter for such measurements hard for any researcher7.1.

It is important to point out the difference between the European and American definition of the term habitat. In the American literature the term habitat is used as a type of surface cover class (e.g. woodland, pasture etc.). In Europe most of the time habitat refers to the sum of factors influencing a location (e.g. shrub density, altitude, soil humidity etc.). This makes a habitat analysis conducted in Europe a very tricky task involving a lot of decisions on how to measure the habitat parameters. On the American continent a habitat analysis can be performed very easily by using a point in polygon test to see in which habitat class the animal was located7.2.

Nevertheless measurement of habitat parameters within a defined area around an observation remains the standard technique, sometimes enhanced by picking two different diameters. Moving to a more general level, the configuration of the habitat is mostly ignored, even papers calling their models 'spatially explicit' use only a fraction of the information on the spatial configuration. 'Spatially explicit' if often reduced to an inclusion of the nearest neighbor fields in calculations of gridded data (e.g., Augustin et al., 1996). Another problem that often arises in studies of wild animals but is almost never considered in their analysis is the problem of spatial autocorrelation in the environmental data. Sampling data at distances where spatial autocorrelation in the environmental parameters is still present reduces the validity of the analysis. Nevertheless this is almost never considered (e.g., Warrik and Cypher, 1998). This may also be a reason for the findings by McClean et al. (1998) that different habitat analysis methods produce contradictory results.

The human (and most probably animal) perception is absolutely brilliant in recognizing a habitat configuration by looking at it in the field. But for a scientific analysis we need to break that information apart into different pieces. This process is very hard for complex environments and cannot be done by simply looking in the field because of visibility limitations and large perspective distortions.

It is often desirable to integrate the environment around an observation for further analysis of the requirements of an animal. Minimum (spatial) resource requirements are very difficult to determine. It requires that the spatial configuration of such resources are included in such an analysis, but how?

There are different scientific fields that work on spatial structures. In landscape ecology the concepts of interdispersion, juxtaposition and fractal dimensions (Olsen et al., 1994) are used among others to describe landscape structures. They are methods to reduce the spatial information to single values which are often scale dependent (see chapter 1). Using these values in habitat analysis of animal requirements again raises the problem of point measurements at the location of the observation.

The aim of this chapter is to enhance the description of environmental factors. We should overcome the restriction of point measurements and start including the spatial arrangement of habitat features in the analysis. This may lead to a different way of analyzing the requirements of animals of their environment. It will be a lengthy and difficult process to develop scale independent, spatially explicit analysis methods. The aim of this work here is to provide a first step and a conceptual framework for further research in this direction.

In this chapter I will provide a new method for approaching these problems. As in the previous chapter the method and its extensions is explained first. In the second part two sets of biological data will illustrate their use.



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next up previous contents
Next: Creation of RDF-Functions Up: Development of Methods Previous: Myotis myotis from Portugal   Contents