Beyond Mapping III

Topic 9: Analyzing Landscape Patterns



Map Analysis book with companion CD-ROM for hands-on exercises

and further reading


Use GIS to Calculate Nearby Neighbor Statistics  describes a technique that calculates the proximity to all of the surrounding parcels of a similar vegetation type
Use GIS to Analyze Landscape Structure  discusses the underlying principles in landscape analysis and introduces some example landscape indices
Get to the Core of Landscape Analysis  describes techniques for assessing core area and edge characterization
Use Metrics to Assess Forest Fragmentation   describes some landscape indices for determining richness and fragmentation


Note: Most of the processing and figures discussed in this topic were derived using ESRI ArcInfo software.  Some of the processing and figures were derived using MapCalcTM software.  See to download a free MapCalc Learner version with tutorial materials for classroom and self-learning map analysis concepts and procedures. 


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Use GIS to Calculate Nearby Neighbor Statistics    

(GeoWorld, May 1999, pg. 26-27)  

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As GIS approaches it’s fourth decade, some of the early, “ivory tower” procedures are being rediscovered within practical contexts.  Landscape structure metrics fall into this category—their theoretical underpinnings have been around for years but it took a refocusing of resource management and a couple of executive/legislative mandates to move the consideration of shape, pattern, arrangement and fragmentation into an operational context.   


It’s windshield common sense that natural and human induced events are continuously altering the makeup of our landscapes.  Most natural resource applications of GIS have focused on the mapping, geo-query and modeling of independent vegetation parcels.  Summaries used in decision-making typically are generalized aggregations of these data.  However, while two watersheds might have the same overall proportion of white birch (a generalized statistic), their relative grouping of the individual parcels could result in dramatically different ecological interactions. 

Landscape structure analysis provides insight into the spatial context of parcels—the “pieces” to the landscape “jig-saw puzzle.”  Most GIS applications in this arena have focused on implementing traditional approaches based on manual map analysis procedures.  But conforming to the theme of this column, there must be some “wild and crazy approaches beyond mapping” that can help us better understand landscape structure. 


The spacing between neighboring parcels of the same type is an important thread in landscape analysis.  Early vector-based solutions for determining the “nearest neighbor” of a parcel used the Pythagorean theorem to calculate centroid-to-centroid distances to all of its neighbors, then selected the smallest distance.  More realistic approaches use a raster-based “proximity” algorithm for considering edge-to-edge distances. 




Figure 1. Processing steps for calculating Nearby Neighbor metrics.


Both approaches reflect traditional map processing and can be manually implemented with a ruler.  Figure 1, on the other hand, depicts an eight-step spatial analysis procedure without a paper map legacy.  The approach uses proximity surface analysis to identify equidistant “ridges” bisecting a set of forest parcels (steps 1-5), then evaluates the inter-parcel distances along the ridges to determine its nearest neighbor and a host of other “nearby neighbor” statistics (steps 6-8).   

The process begins by identifying the set of polygons defining a class of interest, such as all the white birch stands in this example (Step 1).  A proximity map (Step 2) is generated that identifies the distances from all locations in the study area to the nearest polygon.  This raster-based operation is analogous to tossing a handful of rocks into a pond—splash, splash, splash …followed by series of emanating ripples that continue to expand until they collide with each other.  


The area surrounding each polygon before the “distance-waves” collide identifies a catchment area that is analogous to a watershed’s region of influence.  All map locations within a catchment area are closer to its source polygon than any of the others (Step 3).   


At this point, we know how far away every location is to its nearest polygon and which polygon that is.  Step 4 isolates the ridges that bisect each of the neighboring polygons.  It is determined by passing a spatial filter over the source map and noting the number of different catchments within a 3x3 window—one identifies interior locations, two identifies locations along the bordering ridge, and three identifies ridge intersections.  Once the bisecting ridges have been identified the proximity values for the grid cells comprising the borders are “masked” (Step 5).




Figure 2.  Proximity Surface with draped bisecting ridges.


The 3-D plot of the proximity surface for white birch in figure 2 might help to conceptualize the process.  Note that the polygons in the Class inset align with the lowest points (basins) on the surface—zero away from the nearest polygon. As distance increases the surface rises like the seats in a football stadium. 


The Ridges inset aligns with the inflection points where increasing distance values from one polygon start a downhill slide into another.  A pair of distance values anywhere along a ridge identifies how far it is to both of the neighboring polygons.  The smallest pair (deepest dip in a ridge) identifies the closest point between two neighboring polygons; the largest pair (highest sweep along a ridge) identifies the most distant point. 


Step 6 in the process identifies an individual polygon, then “masks” the set of ridge proximity values surrounding that polygon (Step 7).  The smallest value along the ridge represents the polygon’s traditional Nearest Neighbor Distance— [[2 * Min_Value] + .5 * CellWidth].  Step 8 finalizes the process by summarizing the values along the proximity ridge and stores the resulting indices in a database table that is inherently in the GIS by the polygon’s ID number.  At this point, the process loops to consider the other polygons in the class (Steps 6-8), then recycles to Step 1 to select another set of polygons defining the next class to investigate.   


There are a couple of things to note about this somewhat unfamiliar approach to deriving the very familiar metric of NN distance.  First, it’s a whole lot faster (not to mention more “elegant”) than the common brute force technique of calculating distances from each polygon and checking who’s closest—bunches of separate polygon distance calculations versus just one per class.  


More importantly, NN distance is only a small part of the information contained in the proximity ridges.  The proximity values along the ridges characterize all of the distances to the surrounding polygons—Nearby Neighbors instead of just the nearest neighbor.  The largest value identifies how far it is to the most distant surrounding neighbor.  The average indicates the typical distance to a neighbor.  The standard deviation and coefficient of variation provide information on how variable the connectivity is.  


If animals want to “jump ship” and move from one polygon to another, they rarely know at the onset the closest edge cell for departure and the distance/bearing to the nearest neighbor.  Characterization of the set of linkages to all surrounding neighbors provides a more realistic glimpse of the relative isolation of individual polygons. 


It also provides a better handle for assessing changes in landscape structure.  If one of the polygons is removed (e.g., by timber harvesting or wild fire), the nearest neighbor approach only tracks one of the myriad effects induced on the matrix of interconnected neighbors.  The nearby neighbors approach not only contains information on traditional NN_distance but a wealth of extended metrics summarizing the connectivity among sets of interacting polygons. 


By thinking spatially, instead of simply automating an existing paper-map paradigm, an approach that is both efficient (much faster) and effective (more comprehensive information) is “rediscovered” by implementing general GIS theory on proximity surface analysis developed a couple of decades ago.  I wonder whether Nearby Neighbor metrics might be useful in Competition Analysis among super stores scattered throughout a city?  Now that’s a mind blower to think animal habitat analysis might be analytically linked to shopper habitat!

Author’s Note: A PowerPoint presentation describing this approach in more detail is available.  Nearby Neighbor metrics plus numerous other indices of landscape structure are contained in FRAGSTATS*ARC software used in preparing this column. Both the presentation and a description of the software can be reached via links posted at, select “Column Supplements.”



Use GIS to Analyze Landscape Structure    

(GeoWorld, June 1999, pg. 26-27)  

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Last month’s column described an interesting processing approach for calculating statistics about neighboring polygons.  The technique used proximity ridges to identify all of the surrounding polygons of the same type as a given polygon, then summarize the minimum, maximum, average and variation of the distances.  The result was a set of metrics that described the “isolation” of every polygon to its nearby neighbors.  Further summary provides insight into the relative isolation of each polygon to others in its class and, at another level, the isolation occurring within one vegetation type compared to that of other types.  


In practice, this information can help resource professionals better understand the complex ecological interactions among the puzzle pieces (forest polygons) comprising a forested landscape.  There is growing evidence that habitat fragmentation is detrimental to many species and may contribute substantially to the loss of regional and global biodiversity.  How to track and analyze landscape patterns, however, has been an ecological problem—but an ideal opportunity for GIS technology.


Although the “nearby neighbors” technique is interesting in its own right (techy-types revel in the elegance of the bazaar logic), it serves as a good introduction to an entire class of map analysis operations—landscape structure metrics.  Many of the structural relationships can be expressed by indices characterizing the shape, pattern and arrangement of landscape elements, spatially depicted as individual patches (e.g., individual vegetation polygon), classes of related patches (e.g., polygons of the same type/condition), and entire landscape sets (e.g., all polygons within an area).  


Two additional concepts relating to map scale complete the systematic view of landscape elements—extent and grain (see figure 1).  Extent refers to the overall area used in an analysis.  Grain refers to the size of the individual patches.  It is important to note that these criteria define the resolution and scale-dependency of a study.  


For example, both the grain would be coarser and the extent larger for studying a hawk’s territory than that for a finch.  A single mixed-woods patch of 25 hectares as viewed by the hawk might comprise the entire extent for the finch with smaller parcels of wetland, birch and spruce forming its perceived patches.  In turn, the extent for a butterfly might be defined by the wetland alone with its grain identified by patches of open water, reeds and grasses of a fraction of a hectare each.  The “parceling of an area” for a ladybug, ant and aphid would result in even finer-grained maps.




Figure 1.  Elements and concepts in landscape structure analysis.


Well so much for the underlying theory; now for the practical considerations.  While the procedures for calculating landscape metrics have been around for years, direct integration with GIS hasn’t occurred until recently (see author’s note).  The question now is whether resource managers can take advantage of their large investments in detailed, geo-referenced data to better understand forest fragmentation and develop management plans at the landscape level. 


Eight fundamental classes of landscape metrics are generally recognized— Area, Density, Edge, Shape, Core-Area, Neighbors, Diversity and Arrangement.  At the heart of many of the metrics is the characterization of the interior and edge of a patch.  For example, Area metrics simply calculate the area of each patch, the area for each class and the total area of the entire landscape.  These measures can be normalized to identify the percent of the landscape occupied by each class and a similarity measure that indicates for each patch how much of the landscape is similarly classified. 


While area metrics indicate overall dominance, Density measures consider the frequency of occurrence.  For example, patch density is computed by dividing the number of patches in a class by the total area of the class (#patches per square kilometer or mile).  Similarly, the average patch size can be calculated for a class, as well as the variation in patch size (standard deviation).  Density metrics serve as first-order indicators of the overall spatial heterogeneity in a landscape—greater patch density and smaller average patch size indicate greater heterogeneity. 


Edge metrics, on the other hand, quantify patch boundaries by calculating the perimeter of each patch, then summing for the total edge in each class and for the entire landscape.  As with the previous metrics, the relative amount of edge per class and edge density can be computed.  This information can be critical to “edge-loving” species such as elk and grouse. 

However the nature of the edge might be important.  An edge contrast index considers the degree of contrast for each segment of the perimeter defining a patch.  For example, an aspen patch that is surrounded by other hardwood species has a much lower contrast to its adjacent polygons than a similar aspen patch surrounded by conifer polygons or bordering on a lake.  In a sense, edge contrast tracks “patch permeability” by indicating how different a patch is from its immediate surroundings—higher index values approaching 100 indicate more anomalous patches.  




Figure 2.  Results of a geo-query to identify the edge contrast of the small, irregular aspen stands within a landscape.


Shape metrics summarize boundary configuration.  A simple shape index measures the complexity of a patch’s boundary by calculating a normalized ratio of its perimeter to its area— [P / (2 * (pi * A).5)].  As the shape index gets bigger it indicates increasingly irregular patches that look less like a circle and more like an ameba.  More complicated shape measures calculate the fractal dimension for an entire landscape or the mean fractal dimension of individual vegetation classes.  These indices range from 1 (indicating very simple shapes such as a circle or rectangle) to 2 (indicating highly irregular, convoluted shapes).  


Now let’s put some of the landscape metrics to use.  Figure 2 shows a predominately hardwood landscape comprising nearly a township in northern Alberta, Canada.  The map was created by the query 1) select forest type aspen (gold), SP1=Aw, 2) reselect small aspen stands (green), Area<15ha, and 3) reselect small aspen stands that are irregular (red), Shape>2.0.  The table identifies the selection criteria for each of the patches, as well as their edge contrast indices.


Several things can be noted.  First, most of the small, irregular forest parcels are in the northern portion of the landscape (9 out of 10).  Most of the patches exhibit minimal contrast with their immediate surroundings (7 out of 10).  Patch #34, however, is very unusual as its high edge contrast index (83 out of 100) indicates that it is very different from its surroundings.  While all of the patches are irregular (shape>2.0), patches #75 and #279 have the most complex boundary configurations (2.65 and 2.57, respectively). 


Also, note that several of the patches aren’t “wholly contained” within the landscape (4 out of 10).  The introduction of the map border spawns artificial edges that can bias the statistics.  For example, Patch #205 with an area of .35 hectare is likely just a tip of a much larger aspen stand and shouldn’t be used in the analysis. 


Although landscape metrics might be interesting, the real issue is “so what.”  Do we want more or less small irregular aspen stands?  Do we like them “contrasty?”  What about the large aspen stands?  What about the other vegetation types?  In the case of landscape structure analysis we have the technological cart ahead of the scientific horse—we can calculate the metrics, but haven’t completed the research to translate them into management action.  At a minimum, we have a new tool that can assess the changes in landscape diversity and fragmentation for alternative scenarios… we “simply” need to understand their impacts on ecosystem function.  Next month we will tackle the other metric classes.  In the interim, see if you can think up some applications for structural analysis in what you do.

Author’s Note: A good reference on landscape analysis is USDA-Forest Service Technical report PNW-GTR-351, 1995, by McGarigal and Marks.  This document plus additional material are online at, select FRAGSTATS*ARC.



Get to the Core of Landscape Analysis    

(GeoWorld, July 1999, pg. 26-27)  

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The past couple of columns identified the fundamental classes of landscape structure metrics— Area, Density, Edge, Shape, Core-Area, Neighbors, Diversity and Arrangement.  As noted, the first couple of classes (Area and Density) contain several indices that characterize the relative dominance and frequency of occurrence of the puzzle pieces (forest polygons) comprising a landscape mosaic.  Changes in these indices indicate broad modifications in the overall balance of landscape elements.  The next couple classes (Edge and Shape) focused on the boundary configuration and adjacency of the polygons.  Changes in these metrics indicate alterations in a polygon’s complexity and its contrast to its surroundings.  


Also recall that the metrics can be summarized for three perspectives of landscape elements—patches (individual polygons), classes (sets of similar polygons) and landscape (all polygons within an area).  At the class level, individual patch indices are aggregated to identify differences and similarities among the various vegetation types.  Landscape indices further summarize structural characteristics for an entire project area, such as a watershed or eco-region. 


Now the stage is set to discuss some of the advanced stuff—assessing landscape edge characteristics.  Core-Area metrics begin to blur the sharp edge of the puzzle-pieces by making a distinction between the edge-influenced area and the interior of a polygon.  In figure 1 the dark green lines identify a buffer of 20 meters around the forest patches.  The light red portions identify the core areas of each patch.  




Figure 1.  Core-Area metrics summarize the interior portions of landscape patches.


Many ecosystem processes respond differently to exterior and interior locations.  In fact with the advent of modern GIS tools, an argument can be made that a new ecological element has surfaced—the patch edge.  For that matter, one could argue that in the vector world of GIS there is a new map feature—points, lines, polygons and polygon edge, or buffered transition...  sort of a “fat” boundary line. 


Information about core areas provides a new perspective of a landscape mosaic.  Many species of flora and fauna (humans included) react differently to the interior and exterior of a forest parcel.  Simple statistics about core area can adjust for effective habitat area.  The inset in figure 1 focuses on a single parcel of 4.5 hectares of excellent habitat type.  But for an interior-loving animal the total geometric area is reduced dramatically to just 1.6 hectares (light red), barely a third of the original polygon’s area.  


That’s important information if you’re a wildlife biologist trying to set aside sufficient habitat to sustain a population of interior-loving things.  Just as important is the knowledge that the interior area is divided into two distinct cores (and almost three).  If individual core areas are so small that no self-respecting organism would occupy such small islands, then the polygon actually contributes nothing to the habitat pool (from 4.5 to 0 hectares).  A simple GIS query for the area of all the candidate habitat parcels can dramatically overestimate the available habitat as database retrieval of the geometric area fails to consider the combined effects of parcel size, shape and buffer extent.  Similarly, management alternatives that simply consider forest type totals could on the surface appear viable, but be rotten at the core.  Core-Area metrics provide a means for adjusting simple geographic area to effective habitat area based on each path’s core area and number of disjoint cores. 


The character of the edge can make a difference as well.  Similar to the edge contrast metrics discussed last time, the nature of the edge changes as you move along it.  If an edge location is mostly surrounded by another type, it is more “edgy” than one that is sounded by similar edge type, or even better, interior locations.




Figure 2.  Analyzing polygon edge characteristics.


Like belly-buttons, the curves along an edge can be categorized as “in-ies” (concave indentation) or “out-ies” (convex protrusion).  The nature of the edge transition is best analyzed in an analysis grid.  As depicted in figure 2, the first step is to “burn” the boundary lines into the grid and assign each cell the condition that dominates it—interior core (light red) or boundary edge (dark green). 


Depending on cell-size, the edge locations have three possible conditions in terms of the surrounding cells—some interior, some edge and some other type.  One summary procedure moves a 3x3 window around the edge cells and counts the number of “other cells.”  A large edgy index means things around it are fairly different; a small one means it has a bunch of very similar things.  


The inset in figure 2 shows “a fairly edgy out-ie” as half of its surroundings are something else.  However, the edge cell directly below it isn’t very edgy as just 1 of its 8 neighbors is something else.  The edge cell below that is even less edgy as its neighborhood doesn’t have any “something else” and even has 1 interior cell.  


Now imagine moving the 3x3 window around all of the light green cells.  Combinations range from nearly all interior cells (very amiable in-ies) to nearly all something else (very edgy out-ies)—that’s the stuff indices are made of.  At this point the spatial distribution of edgyness is mapped and areas of high or low transition can be identified. 


This information can be summarized by edge-type, individual patches, and at the class and landscape levels.  An extension takes a cue from edge contrast and extends the edgy index to a weighted edgy index by applying weighting factors to each of the vegetation type combinations—“…a little edgy around that type, but really edgy around that other type.” 


All this might run contrary to conventional cartography and ecological precedent, but heck, that’s the way it is in the reality of the wilderness far from human engineering and surveying.  The discrete lines just aren’t there (reports of foresters tripping over them have been greatly exaggerated).  Transitional gradients (patch edge) with undulating shapes that continuously change relationships are the norm.  Instead of “force-fitting” metrics to past simplifying theories we need to use spatial reasoning and GIS processing to make the metrics fit reality whenever possible.  Certainly in landscape analysis this is true, but the kernel of wisdom might be pertinent in other GIS applications.

Author’s Note: see A good reference on landscape analysis is USDA-Forest Service Technical report PNW-GTR-351, 1995, by McGarigal and Marks.  This document plus additional material are online at, select FRAGSTATS*ARC.



Use Metrics to Assess Forest Fragmentation   

(GeoWorld, August 1999, pg. 20-21)   

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The past few columns have investigated several metrics used to characterize landscape structure.  The first column in the series looked at Nearby Neighbor indices that describe the relative isolation of vegetation parcels.  The next investigated the basic metrics of Area, Density, Edge and Shape that are conceptually simple, but a bit of a struggle as a bunch of equations. Last month's column focused on Core-area measures that introduced "buffered edges" around each polygon as a new map feature.  This time we'll flounder in more advanced stuff-- metrics assessing Diversity and Arrangement.  


Recall that there are three levels of landscape metrics (patch, class and landscape) depending on whether the focus is on a single vegetation parcel, a set of similar parcels or all of the parcels within an area.  Traditionally, diversity metrics are only calculated at the landscape level, since by definition more than one class is needed.  


The indices are influenced by two components-- evenness and richness.  Richness identifies the number of classes or patch types.  A landscape composed of twelve cover types is considered much "richer" than one containing only three.  Evenness, on the other hand, refers to the distribution of the area among the different vegetation types.  A landscape where the classes are fairly equally distributed is considered much more "even" than another that has just a couple of types dominating the area.  Note that richness and evenness are not directly related.  Landscapes that are "rich" but "uneven" often contain rare types (infrequently occurring) that are ecologically important.  


So how does the computer reduce diversity to a bunch of numbers?  The simplest is a direct measure of richness that just counts the number of patch types in a landscape.  Relative patch richness translates the count to a percent by considering the maximum number of classes as specified by the user-- [((#Patch Types / Max #Patch Types) * 100)].  This enables users to easily compare the richness among different landscapes in a region.  Patch richness density standardizes the count to an intuitive per area basis-- [(#Patch Types / Area)].  An area with 4.25 types per square mile is considered richer than one with only 1.73 types. 


A somewhat more sophisticated and frequently used measure is Shannon's diversity index that considers the proportional abundance of each vegetation type-- [-SUM((Pi) * ln(Pi)), where Pi= Areai / Total Area].  The index is zero if the landscape has only one type and increases as richness increases or the proportional distribution of the area among patch types becomes more even.  Since it considers both richness and evenness it is a popular metric and is frequently used as a relative measure for comparing different landscapes. 


Simpson's diversity index is another popular measure based on proportional abundance-- [1 - (SUM( (Pi)2 )].  Simpson's index is less sensitive to the presence of rare types and represents the probability that any two patches selected at random will be different types.  The index ranges from 0 to 1 with higher values indicating greater diversity. 


Another class of metrics focuses on the "evenness" aspect of diversity.  Both Shannon's evenness index— 


[( (-SUM((Pi) * ln(Pi)) ) / (ln(Max #Patch Types)) )]


and Simpson's evenness index— 


[( (1 - (SUM( (Pi)2 ) ) / ( 1- ( 1 / ln(Max #Patch Types)) )]


…isolate the effect of the distribution of the total area among vegetation types.  Both measures range from 0 (very uneven distribution) to 1 (perfectly even distribution).  


In addition to the diversity measures, arrangement metrics provide insight into landscape configuration and fragmentation.  While the measures are far too complex for detailed discussion in this column (see author's note), they are fairly easy to conceptualize.  They involve some fairly unfamiliar terms-- contagion, interspersion and juxtaposition-- that might need explanation.  "Contagion," like its more familiar usage as contagious, implies contact.  The contagion index is based on raster cell adjacencies and reports the probability that two randomly chosen adjacent cells belong to a particular pair of vegetation types.  The index ranges from 0 to 100, where 100 indicates that all vegetation types are equally adjacent to all other types (even distribution of adjacencies).  Lower values indicate landscapes with uneven adjacencies indicating a clumping bias in the distribution of vegetation types. 


"Interspersion" means scattering and "juxtaposition" means side-by-side positioning.  The interspersion and juxtaposition index is similar to the contagion index except it measures entire "patch" adjacency (vector) and not individual "cell" adjacency (raster).  It evaluates each patch for the vegetation types surrounding it then summarizes the data at the class and landscape levels.  Higher values indicate well-interspersed landscapes (types are equally adjacent to each other), whereas lower values characterize landscapes clumping (disproportionate patch type adjacencies). 


Whew!!!  That's a lot of theory and a wrath of intimidating equations presented in this and the past few columns.  The bottom line is that linking GIS-based forest maps to these calculations provides an operational tool for expressing important ecological concepts, which until now, were locked in the realm of the eco-scientists and doctoral dissertations.  Resource managers now can easily assess the structure of different landscapes, or the same landscape at different times or under different management alternatives.  In light of increasing pressure to consider spatial context in resource planning and management, this information should prove invaluable. 


However, the contribution of GIS isn't solely an expedient for practical expression of existing theory.  It provides a foothold for extending that that theory.  


For example, consider figure 1.  The bottom layer is a typical forest map locating the various vegetation types in the area.  The richness surface is derived by first rasterizing the type map, then moving a window over the grid that counts the number of different vegetation types.  The red clumps on the richness surface locate highly diverse areas with seven vegetation types within the half-kilometer radius of the window. 




Figure 1.  A "richness" surface identifies the number of different vegetation types within the vicinity of each grid cell (brighter tones indicate more diverse areas).


In effect, the roving window serves as a temporary "mini-landscape" definition and can be summarized for most of the existing landscape metrics-- the concept of the grid "cell" being substituted for the polygonal "patch."  As with traditional measures, the "extent" (window size) and "grain" (cell size) are important considerations in mapping the indices as surfaces.


The top pair of circles in Figure 2 shows local conditions for a "richness" index of 1 on the left and 3 on the right.  The next pair of windows has the same richness value of 3, but show alignments with different "evenness" measures.  The bottom pair has the same richness (number of different types) and evenness (same proportional areas), but the one on the right is more "interspersed."  


The surface maps of the indices show the actual spatial distribution of landscape structure concepts— e.g., "more diverse over here, but a real mono-culture over there, though it's just moderately diverse overall."  The cell values occurring within each patch can be summarized then aggregated at the class and landscape levels.  The extended procedures provide new insight into the localized effect of management alternatives.  



Figure 2.  Roving window configurations for various landscape richness, evenness and interspersion conditions.


Also they demonstrate the potential for applying GIS and spatial reasoning for more than simply packaging data and displaying traditional landscape structure indices.  In the next decade watch for more realistic, useful and practical applications of "map structure analysis" being applied to a host of new disciplines-- the marriage of ecological theory and GIS technology has been consummated with innovation the offspring.

Author’s Note: An extended discussion of Diversity and Interspersion/Juxtaposition metrics and an online copy of Topic 5, "Assessing Variability, Shape and Pattern of Map Features," from Beyond Mapping by Joseph K. Berry are available via the Internet at, select “Column Supplements.”


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