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1. Capturing landscape structures: Tools

Gerd Eiden*, Maxime Kayadjanian*, Claude Vidal**
(*CESD Communautaire, Land Use Program, **Eurostat Directorate F)

In general the spatial structures of  landscapes are associated with the composition and configuration of landscape elements. Composition refers to the number and occurrence of different types of landscape elements, while configuration encompasses the physical distribution or spatial character within a landscape (McGarigal et al. 1994). The quantification refers to the measurements of diversity, homogeneity or heterogeneity.

Landscape elements can be described and categorised under different aspects: as biotopes, as habitats or, in a more "simplified" and aggregated way, as land cover categories. Such land cover categories represent the interface between natural conditions and human influence both over time and in different historic periods. 

The spatial mosaic of landscape elements determines to a great extent the physiognomy, the visual appearance and the human perception of a landscape. On the other hand the spatial configuration and composition of landscape elements (habitats and biotopes) play an important role in the ecological functionality and biological diversity. Particular landscape ecology is dealing with the relationship of spatial patterns and ecological processes (e.g. biodiverstiy, succession) at different spatial and temporal scales (Neill et al., 1988; Turner, 1989; Turner et al., 1991). 

In this context numerous mathematical indices have been developed that allow the objective description of different aspects of landscapes structures and patterns (McGarigal et al. 1994). The following chapter will give a brief explanation of the meaning of landscape metrics used in the studies. Due to the important role the input data additional details on the CORINE Land Cover data set are also presented. 

1.1     Landscape Metrics: significance

1.1.1. Patch Density (PD):
A patch represents an area, which is covered by one single land cover class (figure 1.1). In the example below the entire area under investigation is composed of a mosaic of patches of different land cover classes (or patch types).
Figure 1.1: Example of a land cover map composed of numerous patches
of different land cover classes (patch types)
The patch density (PD) expresses the number of patches within the entire reference unit on a per area basis (100 ha). It is calculated as:
PD = Patch Density (per 100 ha)
n = Number of Patches
a = Area 
Patch density increases with a greater number of patches within a reference area. In figure 1.2 two different "landscapes" are presented, both composed of 3 different land cover classes (or patch types), covering the same area. The difference between the two areas concerns their homogeneity or conversely their heterogeneity, which can be expressed by the number of patches of each class. In general Patch Density depends on the "grain size" of the input data, i.e. the size of the smallest spatial unit mapped and the number of different categories distinguished in the nomenclature. 

The index is a good reflection of the extent to which the landscape is fragmented and therefore fundamental for the assessment of landscape structures, enabling comparisons of units with different sizes. 

Figure 1.2: Patch density
    1.1.2. Edge Density (ED) or Perimeter/Area Ratio (PAR):

    An edge refers to the border between two different classes. Edge density (in m/ha) or alternatively Perimeter/Area Ratio as used in the context of Chapter 2, equals the length (in m) of all borders between different patch types (classes) in a reference area divided by the total area of the reference unit. The index is calculated as:

      E = total edge (m)
      A = total area (ha)
    In contrast to patch density, edge density takes the shape and the complexity of the patches into account. Edge density is a measurement of the complexity of the shapes of patches and, similar to patch density an expression of the spatial heterogeneity of a landscape mosaic. Like patch density, edge density is a function of the size of the smallest mapping unit defined (grain size): the smaller the mapping unit the better the spatial delineation is measured, resulting in an increase of the edge length (figure 1.3).

    Figure 1.3: Edge density
    1.1.3. Number of classes (NC):

    The simplest way of capturing the diversity of the earth's surface is to count the number of different categories, in our case land cover classes in a unit area.

    The more classes there are the more diverse or rich the area is. The advantage of this index is that it can be calculated and interpreted easily. But, as in all richness measures, the result might be misleading, because the area covered by each class and thus its importance is not considered. Even if a certain class covers only the smallest possible area, it is counted (figure 1.4).

      Figure 1.4: Number of Classes (NC) Index

    1.1.4. Shannon's Diversity Index (SHDI):

    The Shannon Diversity Index quantifies the diversity of the countryside based on two components: the number of different patch types and the proportional area distribution among patch types. Commonly the two components are named richness and evenness. Richness refers to the number of patch types (compositional component) and evenness to the area distribution of classes (structural component). 

    The Shannon Index is calculated by adding for each patch type present the proportion of area covered, multiplied by that proportion expressed in natural logarithm, according to the formula:

          m = number of patch types 
          Pi = proportion of area covered by patch type (land cover class) i
    Shannon Diversity Index increases as the number of different patch types (=classes) increases and/or the proportional distribution of the area among patch types becomes more equitable. For a given number of classes, the maximum value of the Shannon Index is reached when all classes have the same area. The following examples try to illustrate the influence of richness and evenness on the index.

    In figure 1.5 the effect of evenness is shown: two different reference units, both composed of four classes, i.e. with an equal richness, are presented. The share of the surfaces occupied by the four classes varies. The effect of this variation of evenness is reflected by the SHDI: the more equal the share of the classes, the higher the Shannon Index.

      Figure 1.5: Influence of area proportion (evenness) of different classes
      on the Shannon Index

    In the following example the evenness is constant i.e. the proportional percentage of the area covered by each class is constant, but the number of classes is rising (increasing richness). 

    As a result of the increasing number of classes the Shannon Index is increasing (figure 1.6). The Shannon Index can be used as a relative index enabling the comparison of different "landscape" units or enables their comparison at different times. However, due to the fact that the index is a combination of richness and evenness, the interpretation is somewhat difficult.

      Figure 1.6: Influence of number of classes (richness) on the Shannon Index

    1.1.5.  Interspersion and Juxtaposition Index (IJI):

    The Interspersion and Juxtaposition Index is the only measurement, which explicitly takes the spatial configuration of patch types into account. This index considers the neighbourhood relations between patches. Each patch is analysed for adjacency with all other patch types and measures the extent to which patch types are interspersed i.e. equally bordering other patch types. The index is calculated with as similar strategy to the Shannon Index but the formula includes a denominator, which standardises for the number of classes.

          m = number of classes,
          Eik = length of edge between class i and class k.

    Low values characterise landscapes in which patch types are distributed disproportionally or clumped, e.g. classes are bordering only a few other classes.

    Figure 1.7: Interspersion and Juxtaposition Index

    High values result from landscapes in which the patch types are equally adjacent to each other, e.g. each class has a common border with all others.

    The example above illustrates the basic concept of the Interspersion and Juxtaposition index. Each of the three areas is composed of five classes, which are all covering the same area (i.e. Shannon's diversity index remains the same). The difference lies in the way the classes are adjacent to each other. In the first case (left) the yellow class for example has a common edge only with blue and grey classes. In the middle diagram this class is adjacent to 3 and in the right hand to 4 classes. In addition the length of edge between the different classes increases from left to right. The greater complexity is reflected in an increase in the Interspersion and Juxtaposition Index. IJI reaches its maximum when all classes are equally adjacent to each other and when the length of edges between classes becomes equal. The index is independent of the number, size or dispersion of patches. 

    The Interspersion and Juxtaposition Index is a relative index that represents the observed level of interspersion as a percentage of the maximum possible given the total number of patch types (McGarigal et al. 1994).

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