Research article

Behavior of class-level landscape metrics across gradients of classaggregation and area

Maile C. Neel1,2,*, Kevin McGarigal1 and Samuel A. Cushman1,3

1Department of Natural Resources Conservation, Holdsworth Natural Resources Center, University ofMassachusetts, Amherst, Massachusetts 01003, USA; 2Current address: Department of Natural ResourceSciences and Landscape Architecture2116 Plant Sciences Building, University of Maryland, College Park, MD20742, USA; 3Current address: USDA Forest Service, Rocky Mountain Research Station, Missoula MT 59807,USA; *Author for correspondence (e-mail: mneel@umd.edu)

Received 15 October 2002; accepted in revised form 18 November 2003

Key words: Connectivity, Fragmentation, Landscape pattern analysis, Neutral landscape models, FRAGSTATS

Abstract

Habitat loss and fragmentation processes strongly affect biodiversity conservation in landscapes undergoing an-thropogenic land use changes. Many attempts have been made to use landscape structure metrics to quantify theindependent and joint effects of these processes. Unfortunately, ecological interpretation of those metrics hasbeen plagued by lack of thorough understanding of their theoretical behavior. We explored behavior of 50 met-rics in neutral landscapes across a 21-step gradient in aggregation and a 19-step gradient in area using a fullfactorial design with 100 replicates of each of the 399 combinations of the two factors to assess how well metricsreflected changes in landscape structure. Metric values from real landscapes were used to determine the extent ofneutral landscape space that is represented in real landscapes. We grouped metrics into three major behavioralclasses: strongly related to focal class area �n�15�, strongly related to aggregation �n�7�, and jointly respondingto area and aggregation �n�28�. Metrics strongly related to class area exhibited a variety of distinct behaviors,and many of these metrics have unique interpretations that make each of them particularly useful in certain ap-plications. Metrics strongly related to aggregation, independent of class area, are particularly useful in assessingeffects of fragmentation. Moreover, metrics in this group exhibited a range of specific behaviors, highlightingsubtle but different aspects of landscape aggregation even though we controlled only one aspect of aggregation.The non-linear behavior exhibited by many metrics renders interpretation difficult and use of linear analyticaltechniques inappropriate under many circumstances. Ultimately, comprehensive characterization of landscapesundergoing habitat loss and fragmentation will require using several metrics distributed across behavioral groups.

Introduction

Because of the fundamental reciprocal relationshipsbetween landscape structure and ecological processes,objectively quantifying spatial landscape structure re-mains an important aspect of landscape ecology�Turner 1989�. A large number of metrics and indiceshave been developed to characterize landscape com-position and configuration based on categorical mappatterns �e.g., McGarigal and Marks 1995; McGari-

gal et al. 2002�. These metrics are used to analyzelandscape structure for a wide variety of applications,including quantifying landscape change over time�O’Neill et al. 1997� and relating structure to ecosys-tem �Wickham et al. 2000�, population and metapo-pulation processes �Kareiva and Wennergren 1995;Fahrig 2002�. Arguably the major application oflandscape structure metrics has been assessing effectsof habitat loss and fragmentation on landscape con-nectivity �e.g., Fahrig and Merriam 1985; With et al.

Landscape Ecology 19: 435–455, 2004.© 2004 Kluwer Academic Publishers. Printed in the Netherlands.

435

1997; Fahrig 1998; Fahrig and Jonsen 1998; Wick-ham et al. 1999; Riitters et al. 2000�.

Fragmentation is a complex phenomenon that canbe seen both as a consequence of habitat loss and asa process in and of itself �McGarigal and McComb1995�. The process of fragmentation of a continuousmatrix habitat begins with reduction in habitat areaand an increase in proportion of edge-influencedhabitat. Initially, the majority of the remaining habi-tat may continue to be connected but will become in-creasingly perforated and incised �Jaeger 2000�.When sufficient habitat is lost, or when the originalhabitat occurs as a patch mosaic rather than a matrix�~ 50-60% of the landscape�, remaining habitat oftenbecomes separated into isolated patches �Jaeger2000�. In random landscapes, patch isolation typicallyincreases most dramatically in the vicinity of the per-colation threshold �Gardner et al. 1987�. As habitatloss continues, some of the isolated patches willthemselves be broken up into varying sized fragmentswith a peak in the number of patches occurring whenthe focal class comprises 15-30% of the landscape.Eventually, some fragmented patches will be lost andothers will shrink, further isolating remnant patches.The point along this gradient at which the landscapeactually becomes fragmented depends on the organ-ism or process of interest. Throughout the fragmenta-tion process, many aspects of landscape compositionand configuration are affected including patch area,number of patches, amount of patch edge, patch shapecomplexity, interpatch distances, and adjacency oflike cells; all of these characteristics affect landscapeconnectivity. Further, they are affected in differentways in different parts of the fragmentation gradient.Given this complexity, it is not surprising that a largenumber of metrics have been used to describe land-scape responses to fragmentation and a number ofmetrics have been developed specifically for the pur-pose of assessing changes in landscape connectivityresulting from fragmentation �e.g., aggregation index�He et al. 2000�; landscape division, effective meshsize, and splitting index �Jaeger 2000�; clumpinessindex �McGarigal et al. 2002�, cohesion �Schumaker1996�, and contagion �Li and Reynolds 1993��.

The diversity of metrics available and the complex-ity of habitat loss and fragmentation effects make itdifficult to choose an appropriate metric or suite ofmetrics for a particular situation. Ultimately, metricselection should be based on the hypotheses beingtested, on aspects of landscape structure that are rel-evant to the organism or process of interest, and on

characteristics of the landscape itself �e.g., whetherthe focal class occurs as disjunct patches or as thematrix� �McGarigal and Marks 1995�. Informed met-ric selection requires thorough understanding of theconceptual and computational basis of each metric.Meaningful interpretation of the metrics also requiresa relevant landscape classification at an appropriatescale for a particular organism or process �Gustafson1998; McGarigal 2002�. Jaeger �2000� has proposedeight criteria to assess metric suitability for assessingfragmentation: intuitive interpretation, low sensitivityto small patches, monotonic reaction to differentfragmentation phases, detection of structural differ-ences, mathematical simplicity, modest data require-ments, mathematical homogeneity, and additivity. Anadditional desirable metric attribute is ability to assesschanges in landscape configuration that are indepen-dent of area. This ability is particularly important forstudies of habitat fragmentation in which disentan-gling effects of loss of habitat area from effects ofchanges in configuration �e.g., aggregation, subdivi-sion, and isolation� of the remaining habitat has beena major goal �e.g., Fahrig and Merriam 1985; Benderet al. 1998; Fahrig and Jonsen 1998; Trzcinski et al.1999; Belisle and Clair 2002�.

We argue that ecological interpretation of land-scape structure also requires understanding of ex-pected behavior of landscape structure metrics undercontrolled conditions. Expected behavior of a numberof metrics has been examined across gradients in fo-cal class area �Gustafson and Parker 1992; Riitters etal. 1995; Hargis et al. 1997; Gustafson 1998; Hargiset al. 1998�. A subset of these studies have also ex-amined metric behavior under a limited array of dif-ferent types of spatial dispersion �e.g., Hargis et al.1997; Gustafson 1998; Hargis et al. 1998�. Addition-ally, Saura and Martínez-Millán �2000� illustrated thebehavior of four metrics �Cohesion, Number ofPatches, Total Edge, and Area-Weighted Mean ShapeIndex� across gradients of area and levels offragmentation. Despite these efforts, metric behavioracross gradients in both aggregation and area has notbeen explored simultaneously for most metrics. Thepurpose of the present work is to explore behavior of55 class-level metrics �Table 1� for binary neutrallandscapes across a 21-step gradient from low tomaximum class aggregation and a 19-step gradient inclass area. It is essential to note that the only aspectof configuration gradient we explicitly controlled wasthe degree of class aggregation. Thus, evaluation ofthe behavior of metrics designed to measure other as-

436

Tabl

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pects of configuration was constrained by the degreeto which they covaried with aggregation in the neu-tral models. The focus on class aggregation was duein part to practical limitations �i.e., inability to createneutral landscape gradients reflecting other aspects ofconfiguration with available software�, but also to thefact that changes in class aggregation are a majorcomponent, if not the dominant component, of thefragmentation process.

Methods

We used the computer program RULE �Gardner1999� to generate 256�256 cell, binary multi fractalneutral landscapes �Figure 1�. RULE uses themidpoint displacement algorithm �Saupé 1988� togenerate multi fractal maps where H, the degree ofspatial autocorrelation among adjacent cells, controlsthe degree of aggregation in the landscape. We gen-erated landscapes in a full factorial design across a21-step gradient in aggregation �H � 0 � 1 in 0.05increments� and a 19-step gradient in focal class area

Figure 1. Example neutral landscapes representing the range of aggregation and area gradients represented in the study. Gradient orientationis the same as the orientation in graphs representing metric behavior �Figure 3-6�.

439

�P � 5 � 95% in 5% increments� with 100 replicatelandscapes for each of the 399 factor combinations�resulting in a total of 39,900 landscapes�.

Neutral landscape models generate grids of cellsthat are comparable to categorical, raster-based rep-resentations of real landscapes commonly used inlandscape structure analysis. These maps have provenuseful as null models for a wide array of landscapeecological investigations �Gardner et al. 1987�,including developing spatially explicit meta- popula-tion and source-sink models �With et al. 1997; Hay-don and Pianka 1999; With and King 2001� andidentifying fragmentation thresholds �With et al.1997�. A major benefit of neutral landscapes is theability to strictly and independently control both areaincluded in a user-specified number of habitat classesand the degree of spatial aggregation of those classes�Gardner et al. 1987�. Neutral landscapes, however,have their limitations. In particular, they can representonly a limited range of the complex spatial patternsthat are typically found in real landscapes �e.g., theydo not adequately represent linear features such asrivers and the associated riparian habitats� and theydo not provide a way to vary the degree of aggrega-tion of habitat patches, only the degree of aggrega-tion of individual cells. Schumaker �1996� hascriticized neutral landscapes as being too simplistic tobe relevant to structure measurement in real land-scapes. However, his conclusion on this matter wasbased on inappropriate comparisons of spatially ran-dom neutral landscapes with real landscapes. For ourpurposes, the level of control over area and aggrega-tion afforded by neutral landscapes provides insightinto sensitivity of metrics to variation in landscapecomposition and configuration that would otherwiseremain obscured �Gustafson 1998�.

We calculated 55 class-level landscape structuremetrics �Table 1� for each landscape using the com-puter program FRAGSTATS 3.2 �McGarigal et al.2002�. Some of these metrics are calculated based onaggregate properties of the class using all cells of thefocal class without reference to individual patches.Others are calculated for each patch and then valuesfor all patches of the focal class are summarized. Weincluded four formulations for the patch-based met-rics: mean value �MN�, area-weighted mean value�AM�, standard deviation �SD� and coefficient ofvariation �CV�. For organizational purposes, metricshave previously been grouped into classes based onconceptual similarity corresponding largely to the as-pect of landscape structure emphasized, but also to

some degree to similarity in computational approach.These conceptual groups correspond to those de-scribed in FRAGSTATS and include area/density/edge, shape, core area, isolation/proximity, contrast,contagion/interspersion, and connectivity �McGarigalet al. 2002�.

While neutral landscapes have no associateddimensions, we imposed dimensions that allowed usto directly compare results from a set of reallandscapes described below. Metric calculations werebased on a 30 m cell size, a 90 m �i.e., 3 cell� edgedepth, a 500 m search radius, and an eight-neighborrule �for patch delineation�. Landscape boundary wasnot included as edge in calculations where its inclu-sion was optional and no border was specified. Ourchoice of cell size was arbitrary and primarily affectsthe magnitude of the class metrics, not the shape oftheir distributions. The exact value of edge depth wasalso arbitrary but was chosen to fall within the rangeof edge depth effects documented for different organ-isms in forested landscapes �e.g., Chen et al. 1995;Demaynadier and Hunter 1998; Gehlhausen et al.2000�. Edge depth magnitude affects all metrics re-lated to core area. A smaller edge depth value wouldresult in more patches with core areas and more corearea for a given patch size with core, while a largeredge depth value would have the opposite effect. Thesearch radius affects only metrics that are based onthe distribution of patches within a specified distanceof a focal patch; for our purposes, only the proximityindex is affected.

We used the programming language Perl to createinput scripts for RULE and batch files for FRAG-STATS, to manage the RULE and FRAGSTATS out-put files, and to calculate summary statistics �mini-mum, maximum, mean, sample standard deviation,and sample coefficient of variation� for FRAGSTATSresults from replicate samples within each of the 399combinations of aggregation and area. Results wereplotted on three dimensional surface graphs usingMATLAB 6.1�The MathWorks 2001� such that meanvalues for each metric at each H�P combination areindicated by the height of the surface on the Z-axis.

We also investigated relationships between metricvalues realized in neutral landscapes with those fromall classes in 428 real landscapes �2727 landscape xclass combinations� from three disjunct regions ofNorth America. The first region included an approxi-mately 15,000 km2 portion of western Massachusettsthat is dominated by northern hardwood forests andcharacterized by rolling hills, agricultural valleys and

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scattered urban and residential development. Thelandcover map used in this analysis was created from1999 aerial photography with a minimum mappingunit of 0.1 acre for MassGIS, an office of the Massa-chusetts Executive Office of Environmental Affairs.We converted the original vector coverage into a gridwith a 30 m cell size and reclassified it into sevencover classes to ensure adequate distribution ofclasses across sub-landscapes �see below�. The sevenclasses included forest, water, grassland, cropland,urban, high-density residential, and low-density resi-dential.

The second region was the 8,480 km2 San JuanNational Forest in southwestern Colorado. Thismountainous landscape has rugged topography andextreme elevational relief. The landcover is zonal,with Ponderosa pine �Pinus ponderosa� forest in thelower elevations, mixed-coniferous and aspen �Popu-lus tremuloides� forest in the middle elevations, andspruce-fir forest �primarily Picea engelmannii andAbies lasiocarpa� and treeless alpine communities atthe highest elevations. The landcover map used in thisanalysis was derived from the USDA Forest ServiceIntegrated Resources Inventory �IRI� and ResourcesInformation System �RIS� database. The landcovermap was developed by the Forest Service from acombination of information sources and processes,including the existing RIS polygon boundaries, aerialphoto interpretation �1993, 1:24000 natural color�,digital image analysis of Landsat Thematic Mapperimagery, and logic written into a C program to delin-eate and attribute polygons. We converted the vectorcoverage into a grid with a 25 m cell size and reclas-sified it into four cover classes to ensure adequatedistribution of all classes across sub-landscapes �seebelow�. The four classes included forest, water, ripar-ian, and non-forested.

The third region was an approximately 20,000 km2

area of central Idaho. This region is also mountain-ous with zonal landcover. The landcover map used inthis analysis was developed by the Idaho Gap Analy-sis project with 30 meter pixels. We reclassified themap into five cover classes, including forest, rock, ri-parian, grass, and shrub with the same goal of ensur-ing adequate distribution of all classes acrosssub-landscapes �see below�.

We clipped non-overlapping sub-landscapes eachof the three regional landcover maps using a squaregrid 256 cells per side. This process resulted in 155sample landscapes for western Massachusetts, 152

sample landscapes for the San Juan National Forest,and 221for central Idaho.

Results from real and neutral landscapes could notbe compared directly because, while there is a valueof P for both types of landscapes, real landscapeshave no value of H. To assess the range of H occu-pied by real landscapes, we superimposed metric val-ues from both landscapes types �Figure 2�. Within theneutral landscape space, we recorded the range of Hvalues associated with metric values from real land-scapes at each value of P. In several cases the major-ity of values from real landscapes occupied arestricted part of the H gradient while a relativelysmall proportion of landscapes occupied a broaderrange. We noted the portion of the H gradient withhigh densities of real landscape values separatelyfrom areas with only a few landscapes to be conser-vative in assessing application of our results in reallandscapes. The levels of aggregation represented byboth high and low densities of real landscapes werethen plotted on the surface of the three-dimensionalgraphs of metric behavior. This plotting format allowssimultaneous illustration of the general magnitude ofall metrics across H�P space and assessment of theportion of that space found in real landscapes. Wealso examined the nature of overlap between real andneutral landscapes. Our comparisons of real and neu-tral landscapes yielded five types of relationships: 1�real and neutral landscapes mostly overlapping; 2�real and neutral landscapes partially overlapping; 3�neutral landscapes being a subset of real landscapes;4� real landscapes being a subset of neutral land-scapes; and 5� real and neutral landscapes not over-lapping. Five metrics �FRAC_MN, PARA_MN,PARA_CV, SHAPE_MN, and CAI_CV� fell into thislatter category and were eliminated from furtheranalysis yielding a total of 50 metrics examined indetail.

We calculated pair-wise Pearson product momentcorrelation coefficients among all pairs of metrics us-ing PROC CORR in the computer program SAS�SAS Institute 1999� to compare the degree of simi-larity among metric surfaces across the aggregationand area gradients �Robinson and Bryson 1957�. Bycorrelating metric values at each of the sampledpoints on each surface, we were able to estimate ofthe degree of correspondence or overall similarity be-tween the surfaces. Some authors �Robinson 1962;Merriam and Sneath 1966� have suggested a slightmodification of the Pearson’s correlation coefficientto account for dependencies among points on a grid.

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We used both approaches to calculate correlationsbetween a subset of metrics and found the results tobe identical so we used Pearson product-moment cor-relation for computational simplicity. Correlation co-efficients were squared and subtracted from 1 toconvert them to pairwise distances. The matrix ofpairwise distances among all metrics was used in ahierarchical agglomerative cluster analysis usingWard’s linkage method in PROC CLUSTER �SASInstitute 1999�. We then used the results from thecluster analysis and visual inspection of the surfacesto assign metrics to behavioral groups. We usedPROC CORR to calculate Kendall’s � correlation co-efficients between each metric and the H and P gra-dients.

Results and discussion

We recognized three broad behavioral groups of met-rics: �1� metrics that were primarily related to P andrelatively independent of H �n � 15�, �2� metrics thatwere primarily related to H and relatively indepen-dent of P �n � 7�, and �3� metrics that were related tothe interaction between H and P, many with dramati-cally nonlinear behavior at extreme values of P or H�n � 28� �Table 1�. This third major group containsfive loosely defined subgroups of metrics based on thenature the interaction between P and H. We used thesegroups to identify general similarities among metricsthat affect their interpretation. There of course is sub-stantial variation within groups so it is still importantto thoroughly understand each metric.

Metric values in real and neutral landscapes weremostly overlapping in 7 metrics and were partiallyoverlapping in 16 metrics �Table 1�. Values in neutrallandscapes were a subset of those in real landscapesfor 14 metrics and real landscape values were a sub-set of neutral landscape values for 13 metrics. �Table1�. As mentioned previously, values in real and neu-tral landscapes did not overlap at all for five metrics.In addition to identifying five types of relationshipsbetween real and neutral landscapes �Figure 2, Table1�, we recognized three categories of overlap withinneutral landscape space itself: 1� neutral metric val-ues not represented in real landscapes; 2� neutralmetric values well represented in real landscapes; and3� neutral metric values represented in relatively fewreal landscapes �i.e., outliers�. While this approachprovides some insight into metric behavior in reallandscapes it is limited in two ways. First, more of

the H�P space would likely be represented if welooked at more real landscapes. Second, we can onlylook in detail at behavior within neutral landscapespace, we have no way to address metric behavior inreal landscapes that falls outside this space.

Metrics primarily related to class area (P)

Fifteen metrics in four conceptual groups were pre-dominantly related to P �Table 1�, although there wasconsiderable variability in behavior among metrics�Figure 3�. Because metrics in this group exhibited avariety of distinct behavioral patterns, it was difficultto clearly distinguish subgroups. Of the metrics in thisgroup, LPI, AREA_AM, GYRATE_AM, DIVISION,and MESH were most strongly and clearly related toP, with Kendall’s � correlations all exceeding 0.93 �p� 0.001 for all� �Table 1�; these metrics were alsohighly correlated with one another �r � 0.95, p �0.001 in all cases�. As such, in many cases these met-rics will not provide substantial information that isnot already provided by PLAND–which is easy to in-terpret. None of the metrics in this group, however,were perfectly correlated with PLAND, and the subtledifferences may be important or enlightening undercertain circumstances. Additionally, many of thesemetrics have unique interpretations that make each ofthem particularly useful.

For example, DIVISION and MESH have intuitiveappeal in that they represent the probability that twoindividuals that are limited to the focal habitat andplaced in different areas of a landscape will find eachother �Jaeger 2000�. Specifically, DIVISION is theprobability that two randomly chosen places in a re-gion will not be found in the same undissected areaand MESH represents the size �m2� of patches thatwould result if a landscape was divided into equalsize patches with the same degree of landscape divi-sion as the measured landscape �Jaeger 2000�.MESH, it turns out, is functionally equivalent to AR-EA_AM at the class level; these two metrics differ inmagnitude as a function of P �McGarigal et al. 2002�which results in only slightly different behavioracross the H�P space. Because DIVISION, MESHand AREA_AM are largely redundant, they would notbe used together; however, each can have utility dueto their different interpretations and units. Similarly,GYRATE_AM �also known as correlation length� isa useful metric for assessing connectivity in that it canbe interpreted directly as the distance that an organ-ism that is placed and moves randomly can traverse

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and remain in the focal habitat �Keitt et al. 1997�. Itis important to note that just because these metrics

were largely redundant with P over the H�P gradi-ents we investigated, it does not mean that these met-

Figure 3. Three-dimensional plots of 6 of the 15 metrics that are primarily related to class area. Surface height indicates the mean metricvalue for 100 replicate runs for each H�P combination. Shading indicates the portion of the neutral gradient represented by values in reallandscapes. The metric surface grids represent each step in the area and aggregation gradients. Full metric names are provided in Table 1.

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rics will always be so redundant when other or morecomplex configuration gradients are sampled in eitherneutral or real landscapes. In addition, even thoughthese metrics were strongly related to P, they exhib-ited distinct but subtle gradient responses to H. Be-cause the magnitude of the H response was very smallcompared to the P response, it was largely unnotice-able in the surface plots �Figure 3�.

Several metrics in this group �AREA_AM, LPI,GYRATE_AM, PROX_MN, and PROX_SD� exhib-ited distinct asymmetry in behavior at low versus highvalues of H across the P gradient, although the de-tails varied. Specifically, they increased more or lesslinearly with increasing focal class area at high H, butexhibited nonlinear behavior associated with the per-colation threshold �0.41� �Stauffer 1985� at low H�Figure 3A, 3C, and 3D�. The percolation thresholdeffect, even at the lowest H level, was dampenedoverall compared with the effect in random land-scapes �Gustafson and Parker 1992; Hargis et al.1998�, and the threshold effect diminished rapidly asH increased. Additionally, we detected a second un-expected transition at approximately the percolationthreshold for these metrics. Below this point, metricvalues for any P were larger at high H than at low H;the trend was reversed above P � ~ 45%. This gra-dient reversal is important to recognize because theinterpretation of these metrics with regards to classaggregation is different when P is above versus be-low the percolation threshold. Three core area met-rics in this group �TCA, CORE_AM, andDCORE_AM� also exhibited asymmetry in behaviorat low versus high values of H across the P gradientsimilar to the metrics described above, but the asym-metry was much more pronounced and the nonlinearbehavior at low H occurred at a much higher P thanthe percolation threshold �e.g., Figure 3F�.

Finally, several metrics in this group �AREA_SD,CORE_SD, GYRATE_SD, PROX_SD, andDCAD_SD� were predominantly related to the P gra-dient over much of their ranges, but exhibited nonlin-ear or, in some cases, erratic behavior at very highvalues of P �e.g., Figure 3E�. The first three of thesemetrics had a distinctly parabolic relationship alongthe H gradient at high P, while the latter three metricshad less straightforward but nevertheless dramaticchanges in behavior at high P �primarily when valuesof H were either � 0.8 or � 0.3�. Most of these met-rics measure variability in the spatial character ofpatches and reflect the increasing variability amongpatches as H and P increase. Specifically, as H

increases and the class becomes more aggregated,some patches become larger and more extensive.However, even at the highest H, some cell clustersremain small and disjunct. Thus, the absolutevariability among patches increases with H. Similarly,as P increases and the class becomes more common,some patches naturally coalesce into larger and moreextensive patches; yet some patches remain small anddisjunct, which increases the absolute variabilityamong patches.

Neutral landscape space was well represented byreal landscapes for ten of these metrics, howeverneutral landscapes represented the range of real land-scape behavior for only two of these metrics�CORE_AM and DCORE_AM� �Table 1, Figure 3A-D�. In all cases where values from real landscapes lieoutside the neutral landscape space the real landscapevalues are larger. It is not possible to assess whetherthe metric behavior outside the neutral landscapespace is the same as that within the space. Values ofthe remaining five metrics from real landscapes oc-cupy only a portion of the neutral landscape space,typically the higher levels of aggregation �Figure 3E-F�.

Metrics primarily related to class aggregation (H)

Seven metrics in three conceptual groups were pre-dominantly related to H and were mostly independentof class area �Table 1, Figure 4�, although there wasconsiderable variability in behavior among metrics interms of the degree of interaction. These metrics areparticularly useful in assessing the aggregation com-ponent of fragmentation without the need for post-hocanalyses to separate these oft confounded effects. Allof these metrics were highly correlated with the Hgradient with correlation coefficients ranging in mag-nitude from � � 0.73 �p � 0.001� for FRAC_SD to� � 0.93 �p � 0.0001� for CLUMPY. It is notewor-thy that several metrics purported to be measures ofclass aggregation �e.g., aggregation index �He et al.2000�, cohesion �Schumaker 1996�, and landscapeshape index �McGarigal et al. 2002�� did not fall intothis behavioral subgroup.

Except for the clumpiness index �CLUMPY�,which is based on like cell adjacencies, all of themetrics in this subgroup are related to some aspect ofpatch shape complexity �Table 1�. FRAC_SD,FRAC_CV, PAFRAC, and PARA_SD are based onperimeter area relationships. Although often not real-ized by practitioners, the relationship between shape

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complexity based on perimeter-area relationships andclass aggregation is well established �e.g., Bogaert2002� and thus this behavioral similarity is to be ex-pected. However, many other metrics based on classaggregation do not behave similarly. While the coremetrics in this subgroup �CORE_CV, CAI_SD� arenot calculated using like adjacencies or perimeter arearatios, the amount of core area in a patch is stronglyaffected by patch shape, with more convolutedpatches having less core area when size is equal.

The behavior of this group of metrics is well illus-trated by PAFRAC, which is a measure of the rela-tive rate of increase of patch area and perimeter.Shape complexity increases �i.e., patches become in-creasingly plane filling� with decreasing levels of ag-gregation, and this relationship is largely consistent

across all levels of P �Figure 4A�. In fact, PAFRACis relatively unaffected by changes in class area when5% � P � 80%. The abrupt decline in PAFRACacross all levels of aggregation when P � 80% islikely a statistical artifact. Because PAFRAC is cal-culated by regressing the log of patch perimeter ontothe log of patch area, it is sensitive to sample size. AsP increases above 80%, the number of patchesbecomes very small and estimates of the metric be-come unreliable. In landscape ecological studies,PAFRAC has been used primarily as a method forcharacterizing patch shape complexity �Krummel etal. 1987; Milne 1988; Turner and Ruscher 1988;Iverson 1989; Ripple et al. 1991�, not habitat aggre-gation. Specifically, it describes the power relation-ship between patch area and perimeter, and thus

Figure 4. Four of the seven metrics that are primarily related to class aggregation and are relatively independent of class area. Surface heightindicates the mean metric value for 100 replicate runs for each H�P combination. Shading indicates the portion of the neutral gradientrepresented by values in real landscapes. The metric surface grids represent each step in the area and aggregation gradients. Full metricnames are provided in Table 1.

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describes how patch perimeter increases per unit in-crease in patch area. If, for example, small and largepatches alike have simple geometric shapes, thenPAFRAC will be relatively low, indicating that patchperimeter increases relatively slowly as patch area in-creases. Conversely, if small and large patches havecomplex shapes, then PAFRAC will be much higher,indicating that patch perimeter increases more rapidlyas patch area increases–reflecting a consistency ofcomplex patch shapes across spatial scales. If, on theother hand, the relative complexity of patch shapesdiffers substantially between smaller patches andlarger patches, then PAFRAC should be estimatedseparately for each range of patch sizes. The fractaldimension of patch shapes, therefore, is suggestive ofa common ecological process or anthropogenic influ-ence affecting patches across a wide range of scales,and differences between landscapes or scale rangescan suggest differences in the underlying pattern-gen-erating process �Krummel et al. 1987�. Our resultssuggest that PAFRAC also provides a means of ef-fectively discriminating among landscapes on the ba-sis of class aggregation and may therefore have evengreater utility than previously realized. We shouldnote, however, that the program we used to create theneutral landscapes used in this study was designed togenerate fractal landscapes. Thus, perhaps it shouldnot be surprising that PAFRAC behaved so nicely indiscriminating among landscapes with varying fractaldimensions. It should be noted, however, that otherfractal metrics �FRAC_AM, FRAC_SD, andFRAC_CV� did not behave similarly.

CLUMPY �Figure 4C� was designed explicitly as ameasure of class aggregation. Specifically, it mea-sures how aggregated the focal class is by comparingthe observed proportion of like cell adjacencies withthe proportion expected under a spatially random dis-tribution. CLUMPY ranges from 1 �maximallyaggregated� to -1 �maximally dispersed�, with 0 indi-cating a completely spatially random distribution ofthe focal class. Another metric that is in the parabolicgroup, nLSI �Figure 5F�, also was designed to mea-sure class aggregation and is based on a standardizedperimeter-area relationship and is normalized to rangefrom 0 �maximally aggregated� to 1 �maximally dis-persed�. Both metrics are highly correlated with H ��� 0.93, p � 0.0001 for CLUMPY and � � � 0.87,p � 0.0001 for nLSI� and thus hold promise as mea-sures of class aggregation largely independent ofclass area. However, CLUMPY is substantially lessparabolic than nLSI and as a result may be more eas-

ily interpreted �Figure 4�. A detailed description of thetheoretical behavior and application of these metricsis the subject of an ongoing study and will be reportedin a subsequent paper.

Two metrics in this group were coefficients ofvariation and two were standard deviations of metricvalues across all patches �Table 1� and thus their in-terpretation is entirely intuitive but can be useful inproviding information regarding among-patch vari-ability in landscapes. Their interpretation is furthercomplicated by the fact that they behave somewhatinconsistently. For example, variability amongpatches in perimeter-area ratio �PARA_SD� and corearea �CAI_SD� increase with increasing aggregation,whereas variability in patch fractal dimension�FRAC_SD,FRAC_CV� decreases with increasingaggregation �Figure 4�. Because these metrics are allbased directly or indirectly on perimeter-area relation-ships, it is not clear why they should behave differ-ently.

Metrics in this group had a variety of reallandscape-neutral landscape relationships �Table 1�.CLUMPY and PAFRAC were the most interpretablein that values from real landscapes fell completelywithin the range of neutral landscapes values. In thecase of CLUMPY, all real landscapes but one hadvalues comparable to H � 0.30 �Figure 4C�. In con-trast, PAFRAC values in real landscapes tended to beless extreme than in neutral landscapes �Figure 4A�.The entire neutral landscape space was represented inreal landscapes for PARA_SD, FRAC_SD, andFRAC_CV, but patches in real landscapes exhibitedhigher variation then neutral landscapes. This differ-ence is likely a function both of differences in patchshape complexity and in the number of patches in thetwo types of landscapes. Values of the two remainingmetrics �CAI_SD and CORE_CV� partially over-lapped in the two landscape types, but differed in thedirection of the deviation �Table 1�.

Metrics related to the interaction of class area (P)and class aggregation (H)

Twenty-eight metrics in six conceptual groups wererelated to the interaction between H and P. We recog-nized three loosely defined subgroups based on thenature the interaction. One subgroup was distin-guished by being related to H and having parabolicdistributions along the P gradient �Figure 5�; one sub-group had a trend from high H and P to low H and P�Figure 6A-B�; and the final subgroup exhibited dra-

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Figure 5. Three-dimensional plots of 6 of the 13 metrics with parabolic distributions along the gradient of focal class area. Shading indicatesthe portion of the neutral gradient represented by values in real landscapes. Surface height indicates the mean metric value for 100 replicateruns for each H�P combination. The metric surface grids represent each step in the area and aggregation gradients. Full metric names areprovided in Table 1.

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Figure 6. Six representative metrics from the three strongly non-linear distribution categories. Surface height indicates the mean metric valuefor 100 replicate runs for each H�P combination. The grid on the metric surface represents each step in the area and aggregation gradients.Shading indicates the portion of the neutral gradient represented by values in real landscapes. Full metric names are provided in Table 1.

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matically nonlinear behavior at extreme values of Hand P �Figure 6C-F�.

Parabolic distributions along the P gradientThis subgroup included 13 metrics that share a com-mon distributional pattern of a non-linear increasewith increasing values of P, typically with amaximum at some intermediate value, and then asubsequent decline �Figure 5�. The magnitude of themaximum value of most of these metrics declinedwith increasing values of H. This decreasing magni-tude along the H gradient also provides at least somemeasure of class aggregation that is independent ofclass area. This subgroup of metrics is closely alliedwith the subgroup of metrics which are strongly re-lated to class aggregation �Figure 4�. While the endsof the continuum are distinct, it could be argued thatthe metrics in these two groups represent a singlegroup of metrics primarily affected by the H gradientbut exhibiting a gradient of responses with respect totheir non linearity along the P gradient, ranging fromnearly linear �e.g., PAFRAC� to markedly parabolic�e.g., ED and PD�.

While the 13 metrics in this subgroup share theparabolic shape, the point along the area gradient atwhich maximum values were realized differed �Fig-ure 4�. For example, LSI was maximum at P � 30%;PD was maximum at P � 20% at low H and at P �30% � 40% at higher H; ED was maximum andnLSI was minimum at P � 50%; SHAPE_AM wasmaximum at approximately P � 65%; andDCORE_CV peaks at P � 95%. The value of P atwhich DCAD reaches its maximum will varydepending on the edge depth specified, with maxi-mums at higher values of P as edge depth increases.As edge depth approaches 0, the distribution ofDCAD approaches the distribution of PD.

Non-linear behavior across gradients in area makesinterpretation of these metrics problematic. In gen-eral, they cannot be interpreted alone and requireconcurrent examination of at least one other metric.For example, ED is typically interpreted in conjunc-tion with number of patches or class area. Also, if themetrics are to be used in further analyses that assumelinear relationships �e.g., Pearson product momentcorrelation or principal components analysis�, inclu-sion of these metrics may be inappropriate. However,if the landscapes being analyzed represent a relativelysmall proportion of the total H�P gradient, the sur-face may be approximately planar and thus not vio-late assumptions of linear relationships. Additionally,

parabolic behavior was most pronounced at low Hwhile values in most real landscapes were comparableto those seen for higher values of H �Figure 5B�.

ED �or the equivalent total length of edge� is themost commonly used metric in this group in studiesquantifying effects of fragmentation. Clearly, how-ever, using ED to quantify the amount of edge perunit area in a landscape could be problematic due tothe markedly nonlinear response of the metric. Thus,while edge effects have been demonstrated to be oneof the most important consequences of fragmentation�e.g., Demaynadier and Hunter 1998; Gibbs 1998;Bergin et al. 2000; Boulet and Darveau 2000; Burkeand Nol 2000; Gehlhausen et al. 2000; Mancke andGavin 2000; Euskirchen et al. 2001�, ED may not bethe best way to quantify the effects. Further, recentstudies have shown that edge effects are dependent onlandscape composition and context �e.g., contrast be-tween focal habitat and adjacent patches and amountof like habitat in the vicinity of fragments� �e.g.,Heske et al. 2001�. Thus, beyond the problems asso-ciated with nonlinear behavior, simplistic measures ofamount of edge, such as ED, are likely to be insuffi-cient for assessing edge effects. PD has similarbehavior to ED and thus has similar problems inquantifying the effects of fragmentation.

Trend from high H and P to low H and PFour metrics �PARA_AM, PLADJ, AI, CAI_AM�exhibited a slightly nonlinear trend from high H andP to low H and P �e.g., Figure 6A-B�. Thus, thesemetrics have the interesting property of representingstrong interactions of both H and P. On the one hand,this property makes interpretation of these metricsdifficult, because it is impossible to distinguishwhether a change in the metric is due to a change inH or P, or both. Given the importance of distinguish-ing between habitat area and configuration in thestudy of habitat fragmentation, metrics that confoundthe two gradients may have limited utility. On theother hand, simultaneous assessment of changes in Hand P may be desirable when the distinction betweenarea and configuration is not important. In all cases,real landscapes occupied a subset of neutral landscapespace, typically where H � 0.15-0.35. Thus, the ob-served non-linear behavior is potentially less severein real landscapes but it is still an issue.

Two closely related metrics in this group, PLADJand AI �He et al. 2000�, measure the degree of aggre-gation in a focal class based on like cell adjacencies.The difference between the two metrics is that AI

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standardizes the percent like adjacencies based on themaximum number of adjacencies possible given theclass area. These metrics are redundant �r � 0.99, p� 0.001� and thus would never be used in the samestudy. Although AI is standardized to the maximumamount of aggregation possible in a landscape, themetric provides misleading results at P � 50%because it does not account for the changingminimum amount of aggregation as P increases.When P � 50%, a maximally disaggregated land-scape will have no cells with like adjacencies. WhenP � 50%, minimum aggregation increases linearlywith P and thus the expected aggregation for any Pincreases. Because AI does not account for the adja-cencies that necessarily occur when P � 50%, itoverestimates the relative level of aggregation inthese landscapes. This problem can be avoided by us-ing a normalized version of AI that accounts for boththe minimum and maximum like adjacencies possiblefor any given P �McGarigal et al. 2002�.

AI is purported to be an effective measure of classaggregation �He et al. 2000�. The authors assert thatAI is superior to several related metrics �e.g., LSI�because it has linear behavior over gradients of ag-gregation. Our results, however, demonstrate that AIis not linearly related to the aggregation gradient. Themetric is linear along the P gradient under completespatial randomness �results not shown� but is stronglynonlinear across all levels of aggregation, particularlyat low levels of P. Bogaert �2002� has recently criti-cized AI as not providing any information that is notalready provided by LSI or nLSI �the normalizedform of LSI�. Our results show that the He et al.�2000� formulation of AI is not redundant with LSIand is redundant with nLSI only when P � 50%�Figure 5, Figure 6�. If AI is normalized to accountfor adjacencies that necessarily occur when P �50%, it becomes completely redundant with nLSI.

Strongly nonlinear at extreme values of H and PEleven metrics were strongly nonlinear at extremevalues of H and P; three subgroups were distin-guished from one another based on the portion of theH by P gradient in which nonlinear behavior was ex-hibited �Table 1, Figure 6�. Despite obvious differ-ences among subgroups there are several noteworthyobservations common to all groups. First, althoughdistributions of these metrics tend to be relatively flatthroughout much of the H by P space, they exhibitthreshold-like behavior in a small portion of the spaceat extreme values of H or P �Figure 6�. This behavior

can make these metrics difficult to interpret because aunit change in H or P does not yield that same unitchange in the metric value throughout the H by Pgradient space. More importantly, the low variabilityacross much of the H by P gradient space suggeststhese metrics will often be of little use in distinguish-ing among landscapes that actually are quite differentin composition and aggregation. The proportion ofH�P space represented in real landscapes variedamong metrics �Table 1, Figure 6�. All or nearly allof the H�P space was represented for six of the met-rics �Table 1�. For the other metrics the degree ofoverlap varied along the P gradient. For example, reallandscapes existed throughout the H gradient forCAI_MN and CORE_MN at low P, but at high P reallandscapes were restricted to H � 0.5. Areas of prob-lematic metric behavior were represented in reallandscapes for all metrics in this category; however,in some cases the most extreme values were not rep-resented �Figure 6�. It is interesting that five of themetrics in these three subgroups are mean values ofpatch-based metrics: AREA, GYRATE, CORE,DCORE, and ENN that are without doubt the mostcommonly used class-level metrics. This poor per-formance has been noted by others. For example,Schumaker �1996� found that AREA_MN,CORE_MN, and ENN_MN were poor predictors ofmodeled dispersal success for Northern Spotted Owlsin landscapes with different levels of connectivityamong old growth forest patches. This poor perform-ance was attributed to sensitivity to small patches, theeffects of which are clearly demonstrated in the neu-tral landscapes examined here. The other formula-tions of most of these metrics �e.g., area-weightedmeans and measures of dispersion� typically behavein manners that will be much more informative.Similarly, in a review of 74 published papers assess-ing connectivity based on both landscape structureand population level processes, Moilanen and Niem-inen �2002� found that Euclidean nearest neighbordistances were rarely correlated with individualabundance, colonization events, or patch occupancy.Given the relative lack of sensitivity of different for-mulations of the Euclidean nearest neighbor metricsthroughout most of the H by P gradient, this lack ofrelationship is not surprising.

COHESION �a measure of the cohesiveness ofpatches in a landscape based on the ratio between thearea-weighted mean patch perimeter-area ratio andthe area-weighted mean shape index� is anothermember of this group that appears to be relatively in-

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variant throughout most of the H�P space. At low H,COHESION is relatively invariant at P � 0.6; athigher H, COHESION is mostly invariant throughoutthe P gradient. As such, our results suggest that thismetric is not likely to be useful for detectinglandscape changes when P � 0.40. This value coin-cides with the point at which additional habitat lossresults in remaining habitat being broken up intosmall pieces. Interestingly, Schumaker �1996� foundthat COHESION did predict modeled spotted owldispersal and thus was useful in distinguishing amongdifferent levels of landscape connectivity. At first thisresult would seem contrary to the behavior of thismetric; however, the percent of the landscapes thatwere occupied by the focal class in his landscapesranged from 5 � 33.7% �Schumaker 1996� which co-incides with the portion of the H�P gradient in whichCOHESION is sensitive �Figure 6�.

The metrics in this group also illustrate that manyclass-level landscape metrics are not stable, and aretherefore difficult to interpret, at extreme values of Hand especially P. This instability is not necessarily aproblem with the metrics per se, but rather accentu-ates the need to understand what the metrics are de-scribing and to apply them intelligently. For example,when the focal class dominates the landscape andforms a matrix, it is not meaningful to measure land-scape structure with patch-based metrics. Similarly,when the focal class is extremely rare, patch-basedmetrics do a poor job of distinguishing among levelsof configuration. In addition, extremely low values ofH are not typical in landscapes, thus erratic behaviorof metrics under those conditions will most often notbe manifested, but our results comparing real andneutral landscape indicate that problematic conditionsare possible in real landscapes for a number of met-rics �Figure 6�.

Conclusions and limitations

The patterns of behavioral similarities among metricsacross the H by P space supports several of our ex-pectations. First, the similarities among metricswithin each behavioral group suggests that manymetrics are closely related, if not perfectly redundant,and describe similar aspects of landscape structure.This point has been shown previously by others �Ri-itters et al. 1995; Cain et al. 1997� and thus was notsurprising. Interestingly though, the cluster analysisand three-dimensional surface plots revealed several

close behavioral similarities among metrics that werenot intuitively obvious prior to the analysis, despiteour intimate familiarity with these metrics. Second,the number of groups of metrics exhibiting markedlydifferent behavior suggests that there are manyimportant dimensions to landscape structure that can-not be succinctly described with only a few metrics.The high dimensionality of landscape structure weobserved was especially intriguing because weexplicitly varied only two aspects of structure: classarea and aggregation. It is likely that additional land-scape structure dimensions exist and are more promi-nent in real landscapes. While there were a numberof dimensions of landscape structure, the H and Pgradients we imposed in our study design were domi-nant. While this limits the scope of our results, thesetwo gradients are considered to be fundamentally im-portant in real landscapes �Turner 1989; Gustafson1998�.

Our study also provided several new insights intothe behavior and utility of landscape metrics. First,landscape structure metrics have traditionally beenorganized conceptually according to the aspect oflandscape composition or configuration they suppos-edly measure �Table 1�. It is common for practitio-ners to choose metrics from each of the conceptualclasses in order to describe different aspects of alandscape �e.g., Ripple et al. 1991�. Our results showthat it is also important to consider the behavioralgroupings because a number of conceptually differentmetrics have similar behavior and thus are redundant.Similarly, metrics from the same conceptual groupoften exhibit widely varying behaviors indicating dif-ferences in how they respond to attributes oflandscape pattern.

Second, our results provide insight into why it hasbeen difficult to find consistent relationships betweenlandscape structure and ecological processes. For ex-ample, Schumaker �1996� found that fractal dimen-sion was a poor predictor of modeled dispersalsuccess for Northern Spotted Owls. He indicated thatfractal dimension was well behaved in neutral land-scapes but behaved unpredictably and non-intuitivelyin real landscapes. Our results indicate that the lackof relationship between any measure of fractaldimension �PAFRAC, FRAC_AM, FRAC_SD, orFRAC_CV� and modeled spotted owl dispersalshould be expected based on the behavior of thesemetrics in neutral landscapes. Dispersal success wasbest predicted by metrics that exhibit a strong rela-tionship to class to area �e.g., TCA, CORE_AM,

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SHAPE_AM, PARA_AM, and COHESION� over therange of P considered in his study �Schumaker 1996�.None of the fractal dimension metrics show such re-lationships. For example, FRAC_AM is parabolicalong P �Figure 5�, while FRAC_SD �Figure4�,FRAC_CV and PAFRAC are most closely relatedto the aggregation gradient. Thus, results from neu-tral landscapes can help in interpreting patterns foundin real landscapes.

Third, our results suggest that many metrics pur-ported to have a certain behavior may not behave inthe intended manner over the entire H by P space. Inparticular, we found that some metrics purported tobe measures of class aggregation �e.g., AI� con-founded class area and aggregation �Figure 6�. Simi-larly, most metrics exhibited nonlinear behavior,although the magnitude and pattern of non linearityvaried markedly among metrics. Nonlinear behaviorrenders the interpretation of metric values problem-atic because a unit change in the metric does not re-flect that same degree of change in landscapestructure over the range of the metric. Finally, a num-ber metrics exhibit erratic and/or unstable behavior atvery high or very low P and demonstrate that land-scape structure is difficult to characterize at the classlevel when the focal class is either dominant or ex-tremely rare. Fortunately, quantifying configurationmay not be that relevant or interesting in such land-scapes anyway.

Our findings must be interpreted within the contextof several limitations imposed by the use of binaryneutral landscapes in our study design. Most impor-tantly, neutral landscapes differ from real landscapesin many important ways. Thus, the beneficial featuresof neutral landscapes in allowing strict and indepen-dent control of certain aspects of landscape structurealso mean that many aspects of structure are not re-flected. In particular, we evaluated a two-dimensionallandscape structure gradient space where configura-tion was represented solely by class aggregation.Thus, metrics were grouped based on how they be-haved in response to changing class area and aggre-gation, yet many metrics are purported to measureother aspects of landscape configuration. There is nodoubt that many of the metrics reported to be partlyor wholly redundant in this study would reveal uniquebehavior in relationship to other gradients of land-scape configuration. Unfortunately, controlling classconfiguration in neutral landscapes is extremely lim-ited with available software; generating a broader ar-ray of configurations remains an important focus for

future software development. In addition, because weused binary landscapes, many metrics that character-ize important aspects of landscape structure in reallandscape �e.g., edge contrast, similarity, intersper-sion, and diversity� were not relevant and we couldnot adequately evaluate their behavior. Similarly,landscape-level metrics were not meaningful toexamine so our results pertain only to class-levelmetrics. While the binary nature of the landscapeslimited the range of metrics we could evaluate, it doesnot limit the applicability of these results inlandscapes with more than two classes. The class-level metrics we present here pertain to the focal classand ignore the class identities and patterns of the sur-rounding mosaic �i.e., the metrics take an island bio-geographic perspective�. This island biogeographicperspective is commonly used in fragmentation stud-ies because fragmentation is inherently a phenome-non that is relevant in context of a focal class. Furtherdifferences between real and neutral landscapes thatlimit the application of these results that neutral land-scapes tend to have larger numbers patches, particu-larly of extremely small patches, than real landscapeswhile larger patches �especially at higher P values�tend to be more extensive and convoluted than largerpatches in real landscapes. These differences result invalues of many metrics from real landscapes fallingoutside the space occupied by neutral landscapes.Obviously, our results can most reliably be applied toreal landscapes when metric values either mostlyoverlap with values from neutral landscapes oroccupy a subset of values occupied by neutral land-scapes �groups 1 and 4, Table 1�.

Our results are also limited because we examinedonly one scale of observation �i.e., grain and extentwere the same for all neutral landscapes�. Relation-ships of metric responses to varying grain and extentare known to be complex, with both the metric val-ues and distributional shape being affected �e.g.,O’Neill et al. 1996; Saura 2002; Wu et al. 2002�. Forexample, in an investigation involving real land-scapes, Wu et al. �2002� found that metrics fell intothree categories of response to changing scale;responses were predictable in only one of these cat-egories. Thus, while we are aware of the importanceof scale, conducting a multi-scale investigation wasbeyond the scope of the present investigation and thusour results and conclusions are limited to the scale ofour examination.

In conclusion, while landscape metrics have provenuseful for describing landscape structure and hold

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promise for broader application, they are often diffi-cult to interpret. More importantly, links betweenecological processes and landscape pattern as mea-sured by these metrics have sometimes been difficultto demonstrate �Schumaker 1996; Moilanen and Ni-eminen 2002�. We argue that understanding expectedmetric behavior can aid in selecting and interpretingmetrics that are sensitive to changes resulting from aphenomenon of interest.

Acknowledgments

We thank M. Cummings and D. Myers of the Univer-sity of Maryland for assistance with Perl program-ming. This work was supported in part by a David H.Smith Conservation Research Postdoctoral fellowshipto MCN and a GAAN graduate fellowship throughUnited States Department of Education to SAC. Thismaterial is based on work partially supported by theCooperative State Research, Extension, EducationService, U.S. Department of Agriculture, Massachu-setts Agricultural Experiment Station and the Depart-ment of Natural Resources Conservation, underProject No. 3322. This paper is Publication no.DHS2003-05 of the Nature Conservancy’s David H.Smith Conservation Research Fellowship Program.

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