Real landscapes 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 spatial heterogeneity, although in practice these fundamental conceptual models of landscape structure are sometimes combined in various ways. These basic classes of landscape pattern look rather different numerically, but they share a concern with the characterization of spatial heterogeneity:

**Spatial point patterns**-- 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, and a variety of methods have been developed for this purpose (Greig-Smith 1983, Dale 1999).**Linear network patterns**-- Linear network patterns represent collections of linear landscape elements that intersect to form a network. A familiar example is a map of shelterbelts in an agricultural landscape, wherein the data consists of nodes (intersections of the linear features) and segments (linear features that connect nodes); the intervening area is considered the matrix and is typically ignored (i.e., treated as ecologically neutral). Often, the nodes and segments 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 segments that is of primary interest. The goal of linear network pattern analysis with such data is to characterize the physical structure (e.g., network density, mesh size, network connectivity and circuitry) of the network, and a variety of metrics have been developed for this purpose (Forman 1995).**Surface patterns**-- Surface patterns represent quantitative measurements that vary continuously across the landscape (i.e., there are no explicit boundaries between patches). Hence, this type of spatial pattern is also referred to as a "landscape gradient". 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). 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 (Bailey and Gatrell 1995). These geostatistical 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., quadrat variance analysis, Dale 1999; spectral analysis, Ford and Renshaw 1984, Renshaw and Ford 1984, Legendre and Fortin 1989; wavelet analysis, Bradshaw and Spies 1992, Dale and Mah 1998; or lacunarity analysis, Plotnick et al. 1993 and 1996, Dale 2000) are more appropriate. All of these geostatistical 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?", and "What is the dominant scale(s) of variability in the measured variable?"While the geostatistical properties of surface patterns has been the focus of nearly all surface pattern analysis in landscape ecology, recently it was revealed that surface metrology (derived from the field of structural and molecular physics) offers a variety of surface metrics for quantifying landscape gradients akin to the more familiar patch metrics described below for categorical maps (McGarigal and Cushman 2005). Like their analogous patch metrics, surface metrics describe both the nonspatial and spatial character of the surface as a whole, including the variability in the overall height distribution of the surface (nonspatial) and the arrangement, location or distribution of surface peaks and valleys (spatial). Here, the goal of the analysis is to describe the spatial structure of the entire surface in a single metric, and a variety of surface metrics have been developed for this purpose (McGarigal et al. 2009).

**Categorical (or thematic; choropleth) map patterns**- Categorical map patterns represent data in which the system property of interest is represented as a mosaic of discrete patches. Hence, this type of spatial pattern is also referred to as a "patch mosaic". 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 (patch mosaic) 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, McGarigal et al. 2002). While these patch metrics are quite familiar to landscape ecologists, scaling techniques for categorical map data are less commonly employed in landscape ecology. This is because in applications involving categorical map patterns, the relevant scale of the mosaic is often defined a priori based on the phenomenon under consideration. In such cases, it is usually assumed that it would be meaningless to determine the so-called characteristic scale of the mosaic after its construction. However, there are many situations when the categorical map is created through a purely objective classification procedure and the scaling properties of the patch mosaic is of great interest. Lacunarity analysis is one technique borrowed from fractal geometry by which class-specific aggregation can be characterized across a range of scales to examine the scale(s) of clumpiness (Plotnick et al. 1993 and 1996, Dale 2000).