1Some vertebrata with special spatial requirements still live in the north-eastern part of Germany but became extinct or has only a very small number in other areas with a similar landscape structure. Therefore, it is interesting and important to analyse its reasons. One main reason is possibly the relative low degree of fragmentation and disturbances in the living spaces of these animals.
2Only minimal disturbed, non-fragmented, non-splitted spaces stand in the centre of our interests. But at first there is a need to define the terms before it is possible to find the related spaces.
3The term "disturbance" should have the following properties :
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Disturbances should be relative discrete or chronical events which influence ecosystems, biocenoses or structures of populations and change the resources, the availability of the substrate or the physical environment.
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Anthropogenious disturbances as the results of cutting or fragmentation process, land-use and change of land-use and their consequences are considered.
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The term "fragmentation" should reflect the anthropogenious process of splitting and cutting of the landscape.
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The separation of living spaces resulting from the development of islands has to be considered.
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Border effects which can lead to new communities of animals as an extreme result have to be investigated.
4(WATERSTRAAT et al. 1996)
5The German Research Office for Natural Protection and Landscape (BFANL) examined space structures which are suitable for quiet recreation in 1977 and 1987. They defined these areas as "non-fragmented spaces with little traffic” if they are larger than 100 km² and if they are not cut by streets with a higher traffic rate than 1.000 cars per day or railway lines with more than 20 trains per day. [LASSEN, 1990]
6These result areas are at minimum 80-90 km² after subtracting the buffers around the traffic-axes from them. The buffers were created because of noise and optical effects. Then they are large enough for a day trip without necessarily crossing the axes. (see LASSEN 1990)
7In 1987 in the old federal countries of Germany there were still 296 such spaces with an area percentage of 18,5%.
8In 1991 in Mecklenburg-Vorpommern alone there were still 80 regions with an area percentage of 78,2% which can be called non-fragmented with little traffic in this sense. (Figure 1) The largest regions are the Ueckermünder Heide/Oderhaffküste (without water areas) with 733 km², the region around the lake Mueritz with 600 km², the area in the triangle Neubrandenburg-Anklam-Altentreptow with 549 km² and the region Zingst-Hiddensee-Westrügen (without water areas) with 489 km². (HERRMANN 1992)
9The determination of these spaces is too rough regarding questions of the animal ecology, because of the actual situation in Mecklenburg-Vorpommern.
10In the Previous Expert Evidential Program of Landscape of Mecklenburg-Vorpommern (German : Vorläufiges Gutachtliches Landschaftsprogramm Mecklenburg-Vorpommern 1992) the method mentioned above was combined with a rastered traffic road-index. [p.33]
11The proportional quantities of settlement and traffic areas based on topographical maps in the scale of 1.25.000 from 1985 or 1986 were measured for every quadrant (ca. 19 km²). The results were converted into an index of area consumption by using the average values for the old federal countries from 1976 which were determined by TESDORPF (1984). In 1992 LOSCH analysed the building density of the landscape for the whole Germany based on administrative areas. The lowest category was the range lower than 10%. Then the whole federal country Mecklenburg-Vorpommern only without the area of the 6 larger towns belongs to this range. Because of that fact in the investigation of this country the ranges were changed : The spaces which are larger than 80 km², which are not cut by highways and federal roads or main rail tracks and where the landscape consumption is lower than 3% or especially lower than 1,5% were determined (Figure 2).
12The area around the rivers Recknitz and Trebel (ca. 700 km²), the region around the lake Mueritz (ca. 600 km²), the swamp and sand areas of the Ueckermünder Heide and the Randowbruch (380 km²), the grassland of the Friedländer Große Wiese (ca. 400 km²) and other regions in Mecklenburg-Vorpommern fulfil this relative hard criterion. (HERRMANN 1992)
13This new method improved the concept by LASSEN, but it considered all fortified ways and streets and did not reflect their real use. All settlements were considered with their ways and streets, but a large settlement leads to a higher density of traffic in it's direct environment which increases the number of disturbances. Because of that it is still to rough for this investigation area.
14The Country Office for Environment and Nature of Mecklenburg-Vorpommern (LAUN) developed a new method especially for judging planned traffic lines like highways etc. and for reflecting the reality in a better way. The non-fragmented spaces with minimal disturbances should be the complement areas to the areas with a high intensity of disturbances.
15These areas are settlements, streets and railway lines together with their "zones of disturbances” which directly bordering them.
16These zones around settlements are determined by size classes of the settlements.
17(Table 1). The extension of the corridors of disturbances around traffic roads were determined administratively. The population of settlements is commonly unknown, only for communities it was possible to get this data, but it would be to rough. In the villages and small towns the area of the settlements indicates it's population relatively well. Therefore the area of the settlement has been taken as a parameter for it's population. The real traffic densities are only known for federal roads and highways. Because of that the traffic lines must be classified by using the administrative order.
|
Landscape element
|
corridor of disturbances
on both sides
|
|
Traffic roads
|
|
|
Highway
|
500 m
|
|
Federal Road
|
300 m
|
|
Country Road
|
150 m
|
|
District Road,
Village Road
|
50 m
|
|
Way, possible use for cars
|
50 m
|
|
Main railway line
|
100 m
|
|
other railway lines
|
50 m
|
|
Settlements
|
|
|
1
|
-
|
<
|
10 ha
|
100 m
|
|
10
|
-
|
<
|
100 ha
|
200 m
|
|
100
|
-
|
<
|
1000 ha
|
500 m
|
|
|
>
|
1000 ha
|
1000 m
|
Table 1 - corridors of disturbances
18The whole federal country in the scale of 1 :50.000 and some reference areas (around 1.000 km²) in the scale of 1 :10.000 were determined by using this method. The results for the area of Mecklenburg-Strelitz is shown in the figure 3.
19Later if we would have data of traffic densities for all traffic lines a new classification would be more useful.
20But in a first step, this practicable method leads to results which reflect the spatial effects of disturbances and cuttings. This method should and will be used (incl. further refinings) examining spaces for the next time.
21A necessary addition to all these methods consists in the description of the wanted complement spaces by using measures of size and shape to evaluate these areas for the investigated animals. Neglecting the inhomogenity of food in an area and only considering the cutting and disturbance effects the shape of the non-fragmented area is critically for the choice of location for the animals (e.g. for kennels or eyries). But these shapes differ very widely. (Compare fig. 3)
22It is easy to characterise the non-fragmented spaces by using the area and/or the perimeter of the space or combining these parameters. Each of these parameters alone is not sufficient to characterise the spaces, because e.g. a very long and only 1 m width rectangle would get the same value as a circle with the same area. But such a rectangle would be very unsuitable for the animals.
23KOSTRUBIEC (1972) and GARTEN (1976) found shape measures by using these parameters which solve these problems. GARTEN (1976) used a form factor FT to characterise physiotops in the classification of natural spaces :
24This form factor of the space T is computed as the quotient of the square of the perimeter of T and it's area.
25This parameter and the shape index by KOSTRUBIEC (1972) which is calculated as the quotient of the perimeter and the perimeter of a circle with the same area :
26and which can be derived from the form factor are useful for a first step evaluation of the spaces.
27Figure 4 shows some constructed geometrical objects with special properties to visualise the evaluation methods :
28All these objects have the same maximum incircle. The objects 7 and 8 have the same perimeter and the same area and the objects 9 and 10 have the same area.
29If a tested evaluation method seems to be good it must at minimum evaluate this special example shapes in the sense of these investigations here.
30In this case because of their construction the objects 7 and 8 get the same form factor and shape index and the same value for every other measure which only combines the area and the perimeter.
31But the position of the slot in these objects (7 and 8) could be very important for the suitability of this area for the investigated animals. The resulting useful area on one side could become to small to be suitable for the animals. In practice such slots are often seen (See fig. 3), e.g. if a fortified way leads to a little settlement.
32Therefore these evaluation methods are not suitable for the questions in this research project in must be looked for other methods..
33In 1964 BOYCE and CLARK tried to characterise the individual peculiarities of the shape of a given area. They defined a centre point for this area and measured the distance to the points on it's periphery . (example figure)
Method of shape measure by BOYCE and CLARK 1964
34(SCHMIDT ET AL. 1986, p.164)
35(compare SCHMIDT ET AL. 1986)
36But the angle between the n distance straightlines with the length ri must be constant. Then they computed the shape measure SBC with the following formula :
37BOYCE and CLARK chose 16 straightlines. With an increasing similarity to a circle this measure converges to 0. This parameter depends strongly on the position of the centre and on the number of distance straightlines.
38But for the problem of the non-fragmented areas it is difficult to define the centre point, because sometimes the centre of the incircle can not obviously be determined, but from the animal point of view it's position would better describe the main point than the centre of gravity. Therefore this measure can not be used in this project.
39BUNGE developed another method (BUNGE 1962, pp. 72-88), which not can be easily translated into a computer algorithm. Therefore it is not practicably for large data sets, but it should be mentioned here.
40The searched area will be matched by a 8-sided polygon with sides of equal length. All the vertices of the polygon are made to fall on the boundary of the shape. BUNGE used a mathematical theorem which considers that for every polygon such an octagon exists. But of course sometimes it is very difficult to be find.
41Then the distances between all vertices of this octagon lag-one are summed, lag-two are summed, lag-three are summed. (illustrative aid) The distances lag-one are squared and then summed, lag-two are squared and then summed, lag-three are squared and then summed. Then each shape will enjoy a one-to-one correspondence with one of these 6 sums. (BUNGE 1962, PP. 76, 77)
llustrative aid of the BUNGE - method (BUNGE 1962 p. 77)
a - the octagon
b - lag-one are summed, i.e. the distance between vertices 1 and 3, 2 and 4, 3 and 5, etc.
(skip one vertex) are measured and then summed
c - lag-two are summed, that means 2 vertices are skipped
d - lag-three are summed - 3 vertices are skipped
The operations in b,c and d lead to 3 parameters.
The other 3 parameters are get in an analogous way by summing of the squared distances.
42In practice he found this octagon as a result of heuristic experiments by using an overhead projector. Then he determined the set of 6 parameters to describe the shape. But he could not point out an algorithm to find such an octagon for arbitrary polygons. Therefore his method of shape measure is also not very practicable for our investigated spaces.
43Another method for evaluating such non-fragmented spaces, in the sense of the investigated animals, seems to be better than the methods we introduced before. It is based on the maximal incircle for every area. The advantage seems to be that "fine circular" spaces have a greater incircle than other irregular shapes with the same area. This method can be easily determined by using a computer and it is implemented in some GIS - we used e.g. InfoGIS.
44But the example shapes which are already known from figure 4 show the problem in figure 5 : The maximal incircle of all given shapes have the same radius.
45Of course the radius of the maximal incircle of an object corresponds to it's area. Because of that fact it seems to be sufficient if the radius (or the area, perimeter ...) of it's incircle will be combined with the area of the object. But the parameter "incircle - radius" depends on the area of the object and figure 5 shows that objects with the same area and the same incircle - radius get the same value after combining of these parameters (object 7 and 8, object 9 and 10). But the position of the slot in these objects (7 and 8) could be very important for the suitability of this area for the investigated animals. The resulting useful area on one side could become to small to be suitable for the animals. In practice such slots are often seen (See fig. 3), e.g. if a fortified way leads to a little settlement.
46Therefore another shape measure must be used in evaluating such spaces for animals.
47One solution for all these problem was found by O. KAPPLER and T. STEINFELD in 1997.
48The circle shape index was calculated for every well-known and shown object in figure 6. This parameter does not depend on the area of an object and characterise the difference of a shape from the circle shape. In comparison to the other introduced methods (See figure 4 and figure 5) only this evaluation method describes all the example shapes in the wished sense.
49The circle shape index CSI can be computed by using the formula :
A is the area which has to be evaluated, r is the radius of a circle with the same area to A and 
is the minimal distance between the point (x,y) of A to it's periphery.
50The index has it's maximum at 1 for a circle.
The index for a square can be analytically calculated as 
(ca. 0,886).
51The circle shape index is independent from the area. Therefore this index can be multiplied with the area. In practice this multiplication must be done because a very large area with a bad shape ( = a low CSI) could be also very suitable for such an animal if it is large enough and a very small area with a high CSI could be not large enough for such an animals. Because of that relations a combination of both parameters is necessarily.
52Figure 7 shows the calculated values for the reference area Mecklenburg-Strelitz. For example it can be seen that the space with the highest value got it because of it's extension and the low number of slots. Spaces with lower extensions get only high values if their CSI is high, i.e. their shape is suitable and their extension is still large enough.
53The circle shape index represents the evaluation of the non-fragmented areas from the point of the investigated animals relatively well. Of course this measure also can be useful for other kinds of space evaluations.
54How is it possible to consider special kinds of animals in the evaluation process of these determined non-fragmented areas in a better way ?
55If the question for the quality of a space will be asked in another way - not : how similar to a circle, how compact is the space - if it will be asked : how many habitats of a determined minimal dimension can exist in this space - then an answer can be given.
56If the animal food has an uniform distribution the animal would not expand his habitat arbitrarily. That means, if the space is sufficient big the animal would only use a part of it. Therefore, beyond the limit of the habitat area the area of the space does not play any role for the animal. Then a non-fragmented space can be evaluated for a group of animals with the quantity of possible disjoint habitat areas. Then such a habitat can be considered as a circle. The question would be : how many disjoint circles with a given radius can be inscribed at maximum into the space ?
57Of course, the radius must be determined by the zoological investigations. Later it is also possible to consider intersections between the habitats of the animals.
58If the shape of the habitat can be modelled by a circle the spaces can be evaluated by using a modified Kappler-Steinfeld-algorithm.
59As an example the reference area Mecklenburg-Strelitz was evaluated with a radius of 1 km (= CSI1000) because it is a "normal" habitat-radius for the Lesser Spotted Eagle (lat. : Aquila pomarina, germ. : Schreiadler) in the first breeding phase in this region (Figure 8). Of course the largest areas get also high values in this case. But other areas with a relative low CSI get higher values than in the "normal" CSI-Evaluation (Compare fig. 7) because of this modified question here. The shape of such a space was evaluated low (See fig. 7) but a relative high number of these habitat circles can be incribed in this space. Therefore these spaces get a relative high modified so-called CSI1000-value.
60The value of the radius differs from animal to animal and region to region. It's necessary to discuss which cutting elements have to be considered and for which kind of animals the spaces can be characterised.
61But it also can be used to determine these values for another kind of spaces which are not results of a cutting process, e.g. spaces of constant food potential.
62The complex of all these methods still contains a series of problems :
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The very different behaviour of different animal groups in relation to the "elements of cutting or fragmentation” and the spatial "radiation effects” of these objects (for example pollution, loudness ...) and the specifics of the objects (e.g. the "range” of the sources of disturbances differ for every different object) can not be represented very well by using these methods.
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The pragmatic determination of "zones of disturbances” does not include the forms of landscape in the right way (e.g. the orographic properties) or the real densities of traffic (because of the administrative classification of traffic ways). This method can not be transferred without problems to other landscapes and traffic densities.
63These are only some of the possible problems in the search for terms and methods for the determination of "fragmentations” and "disturbances” which can be used in the practice of natural protection. Therefore it must be looked for new methods, to reflect the reality in a better way, to integrate the actual methods and results, to solve the problems and to apply the methods in practical natural protection.
64Such methods have to be combined with biological information to consider the requirements to space, the needs and the behaviour of the animals. Biological models of the structure of the ideal living spaces for the investigated animals have to be compared with the real landscape structure. The habitat circle method is a first step in this direction.
65Other methods reach this goal by using satellite data. The recognition of land use information which is important to decide the existence of biological conditions in the investigated area could be realised by the use of special developed filters. These data could be improved by the use of geographical information in a GIS. It is possible that potential living spaces for the investigated animals can be determined using this way. Such methods were developed and applied by D. LAFFLY for the capercaillie (lat. :Tetrao urogallus, germ. : Auerhuhn, fr. :Grand Tétra) in a mountain area. [BROSSARD et.al., 1993 ; LAFFLY, 1995].
66But for large scales (more than 1 :10.000) it is necessary to use terrestrial investigations and to find models which combine the biological behaviour data with the real landscape structure in the living space. The space resistance method which was developed by KAPPLER in 1995 seems to be one possible solution for these problems for large scales (KAPPLER 1995, 1996, 1997). This method consists of the definition of a general space property, the space resistance, which can theoretically be determined for all geographical objects and which contains all known "cutting and disturbance objects”. Then it will be possible to define all searched terms exactly by using these base term and to compute them with well-known mathematical methods. The quantitative determination can specifically be done for all groups of animals, of course in practice only for large scales. The main difficulties in using this method consists in getting the data of animal behaviour. Therefore it is still in a test phase.
67But in the near future the disturbance corridor method in combination with the circle shape index or the habitat circle method will be stay the most practicable method for the determination of non-fragmented spaces with minimal disturbances.
68In the future it could be interesting to apply these methods of shape measurement to other fields of space evaluations.
