CLASSES OF LANDSCAPE PATTERN

Real landscapes (at any scale) contain complex spatial patterns in the distribution of resources that vary over time; quantifying these patterns and their dynamics is the purview of landscape pattern analysis. Landscape patterns can be quantified in a variety of ways depending on the type of data collected, the manner in which it is collected, and the objectives of the investigation. Broadly considered, landscape pattern analysis involves four basic types of spatial data corresponding to different representations of landscape pattern. These look rather different numerically, but they share a concern with the relative concentration of spatial variability:

(1) Spatial point patterns represent collections of entities where the geographic locations of the entities are of primary interest, rather than any quantitative or qualitative attribute of the entity itself. A familiar example is a map of all trees in a forest stand, wherein the data consists of a list of trees referenced by their geographic locations. Typically, the points would be labeled by species, and perhaps further specified by their sizes (a marked point pattern). The goal of point pattern analysis with such data is to determine whether the points are more or less clustered than expected by chance and/or to find the spatial scale(s) at which the points tend to be more or less clustered than expected by chance (Greig-Smith 1983, Dale 1999).

(2) Linear network patterns represent collections of linear landscape elements that intersect to form a network. A familiar example is a map of streams or riparian areas in a watershed, wherein the data consists of nodes and linkages (corridors that connect nodes); the intervening area is considered the matrix and is typically ignored (i.e., treated as ecologically neutral). Often, the nodes and corridors are further characterized by composition (e.g., vegetation type) and spatial character (e.g., width). As with point patterns, it is the geographic location and arrangement of nodes and corridors that is of primary interest. The goal of linear network pattern analysis with such data is to characterize the physical structure (e.g., corridor density, mesh size, network connectivity and circuitry) of the network, and a variety of metrics have been developed for this purpose (Forman 1995).

(3) Surface patterns represent quantitative measurements that vary continuously across the landscape; there are no explicit boundaries (i.e., patches are not delineated). Here, the data can be conceptualized as representing a three-dimensional surface, where the measured value at each geographic location is represented by the height of the surface. A familiar example is a digital elevation model, but any quantitative measurement can be treated this way (e.g., plant biomass, leaf area index, soil nitrogen, density of individuals). In many cases the data is collected at discrete sample locations separated by some distance. Analysis of the spatial dependencies (or autocorrelation) in the measured characteristic is the purview of geostatistics, and a variety of techniques exist for measuring the intensity and scale of this spatial autocorrelation (Legendre and Fortin 1989, Legendre and Legendre 1999). Techniques also exist that permit the kriging or modeling of these spatial patterns; that is, to interpolate values for unsampled locations using the empirically estimated spatial autocorrelation. These surface pattern techniques were developed to quantify spatial patterns from sampled data (n). When the data is exhaustive (i.e., the whole population, N) over the study landscape, like it is with the case of remotely sensed data, other techniques (e.g., two-dimensional spectral analysis, Ford and Renshaw 1984, Renshaw and Ford 1984, Legendre and Fortin 1989; or two-dimensional wavelet analysis, Bradshaw and Spies 1992) are more appropriate. All surface pattern techniques share a goal of describing the intensity and scale of pattern in the quantitative variable of interest. In all cases, while the location of the data points (or quadrats) is known and of interest, it is the values of the measurement taken at each point that are of primary concern. Here, the basic question is, "Are samples that are close together also similar with respect to the measured variable?” Alternatively, “What is the distance(s) over which values tend to be similar?”

(4) Categorical (or thematic; choropleth) map patterns represent data in which the system property of interest is represented as a mosaic of discrete patches. From an ecological perspective, patches represent relatively discrete areas of relatively homogeneous environmental conditions at a particular scale. The patch boundaries are distinguished by abrupt discontinuities (boundaries) in environmental character states from their surroundings of magnitudes that are relevant to the ecological phenomenon under consideration (Wiens 1976, Kotliar and Wiens 1990). A familiar example is a map of land cover types, wherein the data consists of polygons (vector format) or grid cells (raster format) classified into discrete land cover classes. There are a multitude of methods for deriving a categorical map (mosaic of patches) which has important implications for the interpretation of landscape pattern metrics (see below). Patches may be classified and delineated qualitatively through visual interpretation of the data (e.g., delineating vegetation polygons through interpretation of aerial photographs), as is typically the case with vector maps constructed from digitized lines. Alternatively, with raster grids (constructed of grid cells), quantitative information at each location may be used to classify cells into discrete classes and to delineate patches by outlining them, and there are a variety of methods for doing this. The most common and straightforward method is simply to aggregate all adjacent (touching) areas that have the same (or similar) value on the variable of interest. An alternative approach is to define patches by outlining them: that is, by finding the edges around patches (Fortin 1994, Fortin and Drapeau 1995, Fortin et al. 2000). An edge in this case is an area where the measured value changes abruptly (i.e., high local variance or rate of change). An alternative is to use a divisive approach, beginning with a single patch (the entire landscape) and then successively partitioning this into regions that are statistically homogeneous patches (Pielou 1984). A final method to create patches is to cluster them hierarchically, but with a constraint of spatial adjacency (Legendre and Fortin 1989). Regardless of data format (raster or vector) and method of classifying and delineating patches, the goal of categorical map pattern analysis with such data is to characterize the composition and spatial configuration of the patch mosaic, and a plethora of metrics has been developed for this purpose (Forman and Godron 1986, O'Neill et al. 1988, Turner 1990, Musick and Grover 1991, Turner and Gardner 1991, Baker and Cai 1992, Gustafson and Parker 1992, Li and Reynolds 1993, McGarigal and Marks 1995, Jaeger 2000).

Although a large part of landscape pattern analysis deals with the identification of scale and intensity of pattern, landscape metrics focus on the characterization of the geometric and spatial properties of categorical map patterns represented at a particular scale (grain and extent). Thus, while it is important to recognize the variety of types of landscape patterns and goals of landscape pattern analysis, I will focus on landscape metrics as they are applied in landscape ecology.