FRAGSTATS
Spatial Pattern Analysis Program for Categorical Maps
Historic Range of Variability Analyses
This section provides a description of the FRAGSTATS analysis done for this application, including a description of the input data generated from the RMLANDS simulation, a list of landscape pattern metrics employed and their definitions, and a description of the methods employed to summarize changes in landscape pattern metrics over time.
For purposes of this application, FRAGSTATS analysis was tightly coupled with the output of RMLANDS. The RMLANDS simulation produced a landscape snapshot for each time step and then FRAGSTATS was used to quantify the structure of each snapshot based on a variety of selected landscape metrics. We summarized the range of variation in each landscape metric to characterize the HRV in landscape structure.
Input Landscape Data
The input landscape data for FRAGSTATS was the land cover-condition grid generated by RMLANDS for each time step of the simulation. The cover-condition grid is a categorical map in which each unique combination of cover type and condition class has a unique class value. Each unique class represented a different patch type for purposes of FRAGSTATS analysis. We focused our analysis on a subset of classes that were well represented in the landscape and subject to change due to disturbance and succession (note, some cover types did not undergo any succession or disturbance-induced changes; e.g., barren, water). In addition, to facilitate computer processing we coarsened the spatial resolution of the cover-condition grids by increasing the minimum mapping unit from 0.0625-ha (25 m cell size) to 0.5-ha (i.e., 8 contiguous 25-m cells). Note, in the coarse-grained representation, the cell size was maintained at 25 m - only the minimum mapping unit was increased. We eliminated patches <0.5 ha by reclassifying cells in those patches to the class of the nearest neighboring cell in a patch >0.5 ha. Note, we expected landscape composition estimates to be insensitive to spatial resolution and indeed this was the case.
In addition to the cover-condition grid classes, we also defined several new classes based on aggregations of particular cover types and conditions. These new classes were created by reclassifying the original cover-condition grid into a smaller set of classes (Table-covcond-reclass) and similarly increasing the minimum mapping unit to 0.5 ha. These new classes represented ‘habitats of special interest’ to land managers (note, we are using the term “habitat” loosely here) and included the following:
• High elevation late-seral conifer forest - Included spruce-fir forest with and without aspen and cool moist mixed-conifer forest with and without aspen in the later stages of development (i.e., understory reinitiation and shifting mosaic conditions). This habitat consists of sparse to dense stands of a mixture of conifer tree species, including Picea engelmannii, Abies lasiocarpa, Abies lasiocarpa var arizonica, Abies concolor, Pseudotsuga menziesii, Picea pungens, Pinus flexilis, and Pinus strobiformis, although commonly only one or two of these species will be present in a stand, and is found at middle to higher elevations (>2200), although it is restricted to cooler and moister sites (e.g., north-facing slopes) at the lower elevations. This habitat is restricted to stands in the later seral stages of development; specifically, stands characterized by an abundance of canopy gaps, a multi-layered canopy consisting of multiple age cohorts or an uneven age structure, large live trees, an abundance of snags and coarse woody debris, and a patchy to well-developed understory.
• Aspen-dominated forest - Included all aspen-dominated cover-condition combinations organized into early-, mid-, and late-seral stages. For example, all mixed conifer-aspen forest types and pure aspen forest in the stand initiation and stem exclusion conditions were reclassified into early- and mid-seral aspen forest, respectively. Pure aspen forests in the understory reinitiation and shifting mosaic conditions were reclassified into late-seral aspen forest. In all cases, stands are dominated by Polulus tremuloides, although the early- and mid-seral stages may contain varying amounts of regenerating conifers in the understory. Indeed, by the end of the mid-seral stage, the mixed conifer-aspen stands may contain a well-developed mid-story of conifers. The overriding feature of all of these stands, however, is the preponderance of aspen in the overstory. This habitat is found across a wide range of elevations (2000-3200 m).
• Low elevation fire-maintained open canopy forest - Included ponderosa pine forest with and without aspen and warm dry mixed-conifer forest with and without aspen in the fire-maintained open canopy condition. This habitat develops when low-mortality fire burns a stand in the later stages of development, and it is maintained by periodic, but frequent, low-mortality fires. This habitat consists of stands characterized by moderate to dense ground cover of grasses, forbs, and sometimes patchy low shrubs (primarily Quercus gambelii), low density of large trees (primarily Pinus ponderosa) of varying size classes with a patchy distribution and open canopy, and is found principally at lower to middle elevations (1800-2800 m).
• Oak-serviceberry-dominated shrublands - Included all shrub-dominated communities containing oak and/or serviceberry (also referred to here as ‘mountain shrubland’), organized into early- and late-seral shrublands. For example, ponderosa pine-oak forest in the stand initiation condition was reclassified into early-seral mountain shrubland, as was pinyon-juniper-oak-serviceberry woodland in the herb-dominated and herb-shrub conditions. This habitat consists of moderately dense to dense stands of shrubs (up to 3 m tall), including Quercus gambelii, Amelanchier utahensis, and often Symphoricarpos spp., and is found principally at lower to middle elevations (1700-2800 m).
• Sagebrush-dominated shrublands - Included all sagebrush-dominated communities, including all mesic sagebrush as well as the early seral stages of pinyon-juniper-sagebrush woodlands. This habitat consists of sparse to dense shrublands of Artemisia tridentata and Artemisia cana, with Purshia tridentata and other shrubs present in places, plus sparse to dense grasses (e.g., Poa pratensis) and forbs (e.g., Vicia americana), and is found at a wide range of elevations, but principally at the lower to middle elevations (1400-2800 m).
Selected Landscape Metrics
Clearly, given the number and variety of components of landscape structure affected by disturbance and succession processes, it is unreasonable to expect a single metric, or even a few metrics, to be sufficient. Therefore, a truly multivariate approach is warranted in most applications. Unfortunately, the selection of a suite of fragmentation metrics is constrained by the lack of a proper theoretical understanding of metric behavior. The proper interpretation of a landscape metric is contingent upon having an adequate understanding of how it responds to variation in landscape patterns (e.g., Gustafson and Parker 1992, Hargis et al. 1998, Jaeger 2000, Neel et al. 2004). Failure to understand the theoretical behavior of the metric can lead to erroneous interpretations (e.g., Jaeger 2000). Unfortunately, it is not possible to reliably identify the “best” measures of landscape structure for this application. Rather, the measures described below provide a reasonably comprehensive, yet parsimonious, suite of metrics for quantifying landscape structure in a manner that provides for a relatively straightforward ecological interpretation.
Note, the selected metrics (below) are only briefly described here. For a detailed description, including the mathematical formula, metric units, range of values, and additional comments on each metric, see the FRAGSTATS documentation available at the FRAGSTATS website (www.umass.edu/landeco/research/fragstats/fragstats.html).
1. Percentage of landscape (PLAND)
2. Patch density (PD)
3. Edge density (ED)
4. Patch size (AREA_MN & AREA_AM)
5. Clumpiness index (CLUMPY)
6. Contagion (CONTAG)
7. Correlation length (GYRATE_AM)
8. Shape index (SHAPE_MN & SHAPE_AM)
9. Core area index (CORE_MN & CORE_AM; CAI_MN & CAI_AM)
10. Proximity index (PROXIM_MN & PROXIM_AM)
11. Edge contrast (CWED & TECI)
12. Interspersion and juxtaposition index (IJI)
13. Simpson’s diversity index (SIDI & SIEI)
1. Percentage of Landscape.–A straightforward and intuitive class metric that measures class extent in relative terms is the percentage of the landscape (PLAND) comprised of the corresponding class. PLAND approaches 0 when the corresponding patch type (class) becomes increasingly rare in the landscape. PLAND equals 100 when the entire landscape is comprised of the focal patch type; that is, when the entire image is comprised of a single patch. PLAND is a measure of landscape composition; it is not affected in any way by the spatial distribution or configuration of patches.
2. Patch Density.–A simple and direct measure of class and/or landscape subdivision is patch density (PD), defined as the number of patches per unit area. Unfortunately, at the class level this measure is difficult to interpret without also considering class area. Nevertheless, regardless of area, as the number of patches increases, technically the class or landscape becomes more fragmented (subdivided into disjunct patches). For this reason, this metric is often reported as a basic descriptor of class or landscape subdivision.
3. Edge Density.–Another simple and direct measure of class and/or landscape subdivision is edge density (ED), defined as the length of class or landscape edge per unit area. Edge density is particularly relevant for ecological processes and species affected either positively or negatively by edge effects.
4. Patch Size.–Another simple and direct measure of class and/or landscape subdivision is the distribution of patch sizes, often summarized by the mean. However, the mean patch size (AREA_MN) can be very misleading if the distribution of patch sizes is highly skewed, as is often the case, especially when there are numerous very small patches and only a few large patches. The area-weighted mean patch size (AREA_AM) is much less sensitive to small patches and provides a better overall measure of subdivision.
5. Clumpiness Index.--A useful measure of class subdivision is the clumpiness index (CLUMPY), which measures the degree to which the focal class is aggregated or clumped given its total area. CLUMPY is calculated from the adjacency matrix, which shows the frequency with which different pairs of patch types (including like adjacencies between the same patch type) appear side-by-side on the map. CLUMPY is scaled to account for the fact that the proportion of like adjacencies (Gi) will equal Pi (PLAND of the focal class) for a completely random distribution (Gardner and O’Neill 1991). Given any Pi , CLUMPY equals -1 when the focal patch type is maximally disaggregated; CLUMPY equals 0 when the focal patch type is distributed randomly, and approaches 1 when the patch type is maximally aggregated. Thus, CLUMPY has a straightforward and intuitive interpretation that indicates whether the focal class is more or less clumped than expected by chance alone.
6. Contagion Index.–A useful measure of landscape subdivision is the contagion index (CONTAG). Contagion refers to the tendency of patch types to be spatially aggregated; that is, to occur in large, aggregated or “contagious” distributions. Contagion ignores patches per se and measures the extent to which cells of similar class are aggregated and therefore conversely the degree to which cells of different classes are interspersed with each other. There are several different approaches for measuring contagion and interspersion. One popular index that subsumes both dispersion and interspersion is the contagion index based on the probability of finding a cell of type i next to a cell of type j (Li and Reynolds 1993). This index increases in value as a landscape is dominated by a few large (i.e., contiguous) patches and decreases in value with increasing subdivision and interspersion of patch types. This index summarizes the aggregation of all classes and thereby provides a measure of overall clumpiness of the landscape. The contagion index has been widely used in landscape ecology because it seems to be an effective summary of overall clumpiness on categorical maps (Turner 1989). In addition, in many landscapes, it is highly correlated with indices of patch type diversity and dominance (Ritters et al. 1995) and thus may be an effective surrogate for those important components of pattern (O’Neill et al. 1996).
7. Correlation Length.–A useful measure of the continuity or structural connectedness of a focal class or of the landscape in general is correlation length (CL)(Keitt et al. 1997), which is derived from the patch radius of gyration (GYRATE). GYRATE equals the mean distance (m) between each cell in the patch and the patch centroid and represents the average distance an organism can move and stay within the patch boundary. CL is computed as the area-weighted mean patch radius of gyration (GYRATE_AM) for the corresponding class or across all patches in the landscape. CL equals 0 when the class or landscape consists of single-cell patches and increases as the patches increase in extensiveness. CL is intuitively appealing, because as patches become smaller and more compact, they extend over less space and therefore provide for less physical continuity of homogeneous land cover across the landscape. Large and elongated patches extend over greater space and provide for greater connectedness of the same land cover. Thus, holding class or landscape area constant, as the class or landscape becomes more subdivided during fragmentation, CL decreases. CL can be interpreted as the average distance an organism might traverse the map, on average, from a random starting point and moving in a random direction, i.e., it is the expected traversibility of the map (Keitt et al. 1997).
8. Shape Index.–Perhaps the simplest measure of patch geometry is based on the perimeter-area relationship, and is given as the perimeter-area ratio (PARA). A problem with this metric as a shape index is that it varies with the size of the patch. For example, holding shape constant, an increase in patch size will cause a decrease in the perimeter-area ratio. Patton (1975) proposed a diversity index based on shape for quantifying habitat edge for wildlife species and as a means for comparing alternative habitat improvement efforts (e.g., wildlife clearings). This shape index (SHAPE) measures the complexity of patch shape compared to a standard shape (square or almost square) of the same size, and therefore alleviates the size dependency problem of PARA. SHAPE can be averaged across all patches of the focal class or across all patches in the landscape (SHAPE_MN), and alternatively patches can be weighted by patch area (SHAPE_AM).
9. Core Area Index.–Another useful measure of patch geometry is based on the concept of “core area”, defined as the area within a patch beyond some specified depth-of-edge effect distance. Holding patch area constant, as a patch becomes more convoluted and complex in shape, core area decreases because less of the patch is greater than the specified depth-of-edge distance from the perimeter. Core area measures are particularly sensitive to class and/or landscape subdivision because, as just noted, they are sensitive to basic perimeter-area relationships. For example, holding the total class or landscape area constant, the subdivision of the class or landscape, respectively, automatically decreases core area because of the increase in the ratio of perimeter to area. Concomitant class area loss and subdivision results in an even greater decrease in class core area. Although there are many alternative ways to index core area, they all measure the same basic integrated aspect of patch geometry and are therefore largely redundant. Here, we used the core area index (CAI) which measures the percentage of a patch that is core area. CAI can be averaged across all patches of the focal class or across all patches in the landscape (CAI_MN), and alternatively patches can be weighted by patch area (CAI_AM). CAI equals 0 when there is no core area (i.e., every location within the focal class or landscape is within the specified edge influence distance from the patch edge); that is, when the class or landscape contains no core area. CAI approaches 100 when the class or landscape, because of patch size, shape, and edge width, contains mostly core area. CAI is a relative index; it does not reflect patch size, class area, or total landscape area; it merely quantifies the percentage of available area, regardless of whether it is 10 ha or 1,000 ha, comprised of core. Consequently, this index does not confound area and configuration; rather, it isolates the configuration effect. For this reason, the core area index is probably best interpreted in conjunction with total habitat area, or its relativized equivalent – PLAND.
10. Proximity Index.–A relatively simple measure of patch spatial isolation is the proximity index (PROX), which deals explicitly with the spatial context of patches, rather than the spatial character of the patches themselves. Unfortunately, isolation is a difficult thing to capture in a single measure because there are many ways to quantify context. PROX considers the size and proximity of all patches of the same class as the focal patch, whose edges are within a specified search radius of the focal patch. The index is computed as the sum, over all patches of the corresponding patch type whose edges are within the search radius of the focal patch, of each patch size divided by the square of its distance from the focal patch. PROX can be averaged across all patches of the focal class or across all patches in the landscape (PROX_MN), and alternatively patches can be weighted by patch area (PROX_AM). The proximity index quantifies the spatial context of a patch in relation to its neighbors of the same class; specifically, the index distinguishes sparse distributions of small patches from configurations where the class forms a complex cluster of larger patches. All other things being equal, a patch located in a neighborhood (defined by the search radius) containing more of the corresponding patch type than another patch will have a larger index value. Similarly, all other things being equal, a patch located in a neighborhood in which the corresponding patch type is distributed in larger, more contiguous, and/or closer patches than another patch will have a larger index value. Thus, the proximity index measures both the degree of patch isolation and the degree of fragmentation of the corresponding patch type within the specified neighborhood of the focal patch.
11. Edge Contrast.–Another aspect of spatial isolation emphases the role of edges or patch boundaries, where these linear features may either facilitate or impede ecological flows and thereby either decrease or increase, respectively, patch isolation. Contrast specifically refers to the relative difference among patch types. For example, mature forest next to younger forest might have a lower-contrast edge than mature forest adjacent to open field, depending on how the notion of contrast is defined. Relative to the focal patch, if patch types with high contrast lead to greater isolation of the focal patch, as is often the case, then contrast will be inversely related to isolation (at least for those isolation measures that consider all patch types). At the patch level, the edge contrast index (ECON) measures the degree of contrast between a patch and its immediate neighborhood. Each segment of the patch perimeter is weighted by the degree of contrast with the adjacent patch. Total patch perimeter is reduced proportionate to the degree of contrast in the perimeter and reported as a percentage of the total perimeter. Thus, a patch with a 10% edge contrast index has very little contrast with its neighborhood; it has the equivalent of 10% of its perimeter in maximum-contrast edge. Conversely, a patch with a 90% edge contrast index has high contrast with its neighborhood. Note that this index is a relative measure. Given any amount of edge, it measures the degree of contrast in that edge. In other words, high values of ECON mean that the edge present, regardless of whether it is 10 m or 1,000 m, is of high contrast, and vice versa. For this reason, this index is probably best interpreted in conjunction with total edge or edge density. At the class and landscape levels, FRAGSTATS computes a total edge contrast index (TECI). Like its patch-level counterpart, this index quantifies edge contrast as a percentage of maximum possible. However, this index ignores patch distinctions; it quantifies edge contrast for the landscape as a whole. FRAGSTATS also computes an index that incorporates both edge density and edge contrast in a single index. Contrast-weighted edge density (CWED) standardizes edge to a per unit area basis that facilitates comparison among landscapes of varying size. Unlike edge density, however, this index reduces the length of each edge segment proportionate to the degree of contrast. Thus, 100 m/ha of maximum-contrast edge (i.e., weight = 1) is unaffected; but 100 m/ha of edge with a contrast weight of 0.2 is reduced by 80% to 20 m/ha of contrast-weighted edge. This index measures the equivalent maximum-contrast edge density. For example, an edge density of 100 means that there are 100 meters of edge per hectare in the landscape. A contrast-weighted edge density of 80 for the same landscape means that there are an equivalent of 80 meters of maximum-contrast edge per hectare in the landscape. A landscape with 100 m/ha of edge and an average contrast weight of 0.8 would have twice the contrast-weighted edge density (80 m/ha) as a landscape with only 50 m/ha of edge but with the same average contrast weight (40 m/ha). Thus, both edge density and edge contrast are reflected in this index. For many ecological phenomena, edge types function differently. Consequently, comparing total edge density among landscapes may be misleading because of differences in edge types. This contrast-weighted edge density index attempts to quantify edge from the perspective of its functional significance. Thus, landscapes with the same contrast-weighted edge density are presumed to have the same total magnitude of edge effects from a functional perspective.
12. Interspersion and Juxtaposition Index.--McGarigal and Marks (1995) introduced the interspersion and juxtaposition index (IJI) that increases in value as patches tend to be more evenly interspersed in a "salt and pepper" mixture. In contrast to the contagion index, which is based on cell adjacencies, IJI is based on patch adjacencies; only the patch perimeters are considered in determining the total length of each unique edge type. Each patch is evaluated for adjacency with all other patch types; like adjacencies are not possible because a patch can never be adjacent to a patch of the same type. IJI measures the extent to which patch types are interspersed (not necessarily dispersed); higher values result from landscapes in which the patch types are well interspersed (i.e., equally adjacent to each other), whereas lower values characterize landscapes in which the patch types are poorly interspersed (i.e., disproportionate distribution of patch type adjacencies). IJI is not directly affected by the number, size, contiguity, or dispersion of patches per se, as is the contagion index. Consequently, a landscape containing 4 large patches, each a different patch type, and a landscape of the same extent containing 100 small patches of 4 patch types will have the same index value if the patch types are equally interspersed (or adjacent to each other based on the proportion of total edge length in each edge type); whereas, the value of contagion would be quite different. Like the contagion index, the interspersion 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.
13. Simpson’s Diversity Index.--–FRAGSTATS computes several statistics that quantify diversity at the landscape level. These metrics quantify landscape composition at the landscape level; they are not affected by the spatial configuration of patches. Simpson's diversity index (SIDI) is a popular diversity measure that is less sensitive to the presence of rare patch types and has an interpretation that is much more intuitive than the familiar Shannon's index (Simpson 1949). Specifically, the value of Simpson's index represents the probability that any two cells selected at random would be different patch types. Thus, the higher the value the greater the likelihood that any 2 randomly drawn cells would be different patch types. Because Simpson's index is a probability, it can be interpreted in both absolute and relative terms. All diversity indices are composed of two components: richness and evenness. Richness refers to the number of patch types; evenness measures the distribution of area among patch types. Evenness measures the degree of concentration of area among the existing patch types. The higher the concentration of area among a few patch types, the lower the evenness. There are numerous ways to quantify evenness and most diversity indices have a corresponding evenness index derived from them; we will compute Simpson's evenness index (SIEI). In addition, evenness can be expressed as its compliment--dominance (i.e., evenness = 1 - dominance). Indeed, dominance has often been the chosen form in landscape ecological investigations (e.g., O'Neill et al. 1988, Turner et al. 1989, Turner 1990a), although we prefer evenness because larger values imply greater landscape diversity. Evenness is expressed as the observed level of diversity divided by the maximum possible diversity for a given patch richness. Maximum diversity for any level of richness is achieved when there is an equal distribution of area among patch types. Therefore, the observed diversity divided by the maximum diversity (i.e., equal distribution) for a given number of patch types represents the proportional reduction in the diversity index attributed to lack of perfect evenness. As the evenness index approaches 1, the observed diversity approaches perfect evenness.
Characterization of Landscape Structure Dynamics
To characterize the dynamics in landscape structure under the HRV scenario, we simply plotted each landscape metric over time and then summarized its statistical distribution. We combined data across simulation runs (i.e., ignored separate runs) for a total of 350 observations (5 runs x 70 snapshots at 10-year intervals from 800-year runs, after excluding the first 100 year equilibration period) for each landscape extent (i.e., Forest, District and watershed).