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Landscape and Urban Planning 69 (2004) 137–148

Evaluating the effectiveness of neutral landscape modelsto represent a real landscape

Xiuzhen Lia,∗, Hong S. Hea,b, Xugao Wanga, Rencang Bua,Yuanman Hua, Yu Changa

a Institute of Applied Ecology, Chinese Academy of Sciences, P.O. Box 417, Shenyang 110016, Chinab School of Natural Resources, University of Missouri-Columbia, Columbia, MO 65211-7270, USA

Received 29 April 2003; received in revised form 18 October 2003; accepted 20 October 2003

Abstract

Neutral landscape models are often employed to represent real landscapes as the null hypothesis. They usually have statis-tical characteristics similar to real ones. But the spatial characteristics of the real and generated maps are seldom compared.In this study, the neutral landscape models generated by Rule and SimMap are tested against a real forest landscape in North-eastern China. A set of landscape metrics is used for the comparison. Values of some metrics (total number of patches, totalperimeter, and aggregation index) suggest that some level of agreement between the maps generated by neutral landscapemodels and the real landscape do exist at landscape and class levels. But there are also metrics that do not show any agreementbetween generated maps and the real landscape. Neutral models tend to over-aggregate small classes at higher aggregationlevels. Each neutral model has its own strength in representing the real landscape, though neither is perfect. Some metrics,for example, double-logged fractal dimension, are found to have limited capabilities in differentiating landscape structures.© 2003 Elsevier B.V. All rights reserved.

Keywords: Neutral landscape models; Real landscape; Consistency; Landscape metrics

1. Introduction

A neutral model is one used to generate expectedpatterns in the absence of specific processes (Caswell,1976; Gardner et al., 1987; Nitecki and Hoffman,1987; Wimsatt, 1987; With and King, 1997). Neu-tral landscape models have been used to test againstreal landscapes as a null hypothesis (Gardner, 1999).They can be used as a baseline for comparison withreal landscape patterns, or for evaluating the effectsof landscape structure on ecological processes (With

∗ Corresponding author. Tel.:+86-24-83970350;fax: +86-24-83970351.E-mail address: landscape2001@sina.com (X. Li).

and King, 1997). They have the advantage of avoid-ing influence from complicated factors such as soiltypes, ground water level difference, or predation.Different neutral models have been designed to rep-resent the character of various landscape patterns(Gardner et al., 1987), and to study some ecologicalfunctions at landscape scale (With, 1997; Saura andMart́ınez-Millán, 2000).

Since experiments involving landscapes are of-ten very difficult, and replication at the landscapescale is also unfeasible, neutral landscape models,which can generate many replicable maps with sim-ilar statistical properties, have become a useful toolto study landscape processes and test hypotheses(Keitt, 2000). Then to what extent neutral landscape

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138 X. Li et al. / Landscape and Urban Planning 69 (2004) 137–148

models can represent real landscapes, or how consis-tent neutral models are with real landscapes, becomesa question to be answered before they can be fullyaccepted. This paper will try to answer this questionthrough a series of neutral landscape model gen-erated maps and a landscape map derived from aTM image, using a set of commonly used landscapemetrics.

Rule (Gardner, 1999) and SimMap (http://www.udl.es/usuaris/saura/simmap.htm) and (http://www3.telus.net/rwatson/simmap.htm) (Saura and Martı́nez-Millán,2000, 2001) are two sophisticated models that havebeen used to analyze habitats and landscapes (O’Neillet al., 1992; With, 1997; With and King, 1997). Thesetwo models are selected for this study because theirgenerated maps appear to be explicit models of realspatial patterns. In addition, they also provide somepattern metrics that can be calculated directly withinthe model.

Landscape metrics are mathematical measuresadopted to quantify landscape structure. With the de-velopment of software packages such as FRAGSTATS(http://www.umass.edu/landeco/research/fragstats/fragstats.html) and (http://www.innovativegis.com/products/fragstatsarc/index.html) (McGarigal andMarks, 1995), and APACK (http://landscape.forest.wisc.edu/projects/APACK/apack.html) (Mladenoffand DeZonia, 1997), numerous spatial metrics orstatistics can be calculated. The performance of spa-tial metrics on neutral landscapes has been used to

Fig. 1. Real landscape map from Daxing’anling Forest Region.

help interpret the significance of these metrics whencalculated on real landscapes, by separating the ef-fects of topography, natural disturbances, and humanactivities from the expected behavior in the absenceof such effects (Gardner and O’Neill, 1991; O’Neillet al., 1992; Gustafson and Parker, 1992; Milne,1992; Schumaker, 1996; With and King, 1997; Keitt,2000).

This paper tests the consistency between patternsgenerated from neutral landscape models and a reallandscape with the help of selected metrics. The pur-pose of this study is to evaluate to what extent neutralmodels can be used to represent a real landscape. Theresult will provide ideas for using neutral models inlandscape ecological planning.

2. Methods

A land cover map from Daxing’anling Forest Re-gion in Northeastern China was delineated from theclassification of TM image dated 14 September 2000(Fig. 1). The selected area is located at the centralpart of Tuqiang Forest Bureau, one of the northernmost administrative units in China. The climate iscold-temperate monsoon. Winter is long, cold and dry;while summer is short, warm, and rainy. This regionis of interest to researchers and land managers owingto the devastating forest fire which occurred in 1987,and which consumed more than one million hectares

X. Li et al. / Landscape and Urban Planning 69 (2004) 137–148 139

of forest. After more than 15 years of tree planting andnatural succession, coniferous forest or mixed foresthas been restored successfully on most of the hills.Apart from birds, wild animals including bears, wildboars, roe deer, and foxes have started to recolonize.New management strategies relating to tree speciescomposition and tree density has begun to affect thestructure of forest stands, as well as the habitat of for-est animals. Further modeling and monitoring of theforest landscape will be of major importance scientif-ically and economically.

The selected area (Fig. 1) covers about 30 km×30 km, or 1024×1024 cells with 30 m resolution, sinceneutral models Rule and SimMap cannot support mapswith irregular boundaries as real landscapes. Thissmall area was mainly covered by coniferous forest(more than 40%) dominated by larch (Larix gmelini)and Pinus sylvestris var. mongolica. Broad-leavedforest (nearly 30%) was dominated by birch (Bertulaplatyphylla) and Populus davidiana. Wetlands arelocated along riverbed, covered by shrubs likeVac-cinum uliginosum and herbs such asCarex spp. Thereare also other land cover types, including bare land,built-up area, and river bed (Table 1).

According to the percentage allocation in the reallandscape map, the same area percentage was assignedfor each corresponding class in the neutral models.Different aggregation levels were designed in Ruleand SimMap, with selected landscape pattern metricscalculated using APACK (Mladenoff and DeZonia,1997).

In Rule, multifractal maps are generated by a mid-point displacement algorithm which creates a map ofreal numbers by successive division, interpolation andrandom perturbation (Gardner, 1999). In this study,

Table 1Absolute and relative area of different classes in the real landscapemap of Daxing’anling Forest Region

Classid Classname Area (km2) Percent

1 Coniferous forest 393.31 41.682 Broad-leaved forest 271.59 28.783 Wetland 225.17 23.864 Bare land 32.29 3.425 Built up 17.35 1.846 River 4.01 0.43

Total 943.72 100

a series of multi-fractal random maps at the size of1024×1024 (210×210) cells were generated in Rule.The percentage for each class was assigned accordingto Table 1, with eight neighborhood rules. Nine aggre-gation levels were simulated, withH = 0.01, 0.1, 0.2,0.3, 0.4, 0.5, 0.6, 0.7, and 0.8, respectively.H is aninternal parameter of the program describing the cor-relation between points. Adjustment of the value ofHbetween 0.0 and 1.0 results in maps ranging from ex-tremely fragmented to highly aggregated. The genera-tion results at all aggregation levels showed that someclasses were always neighbored with each other, whileothers were seldom connected (Fig. 2). This might beconsistent with real landscapes that have spatial gra-dients such as relief. Nevertheless, the generated pat-terns inFig. 2 are not common in reality because it isdifficult to control which class should be neighboredby another.

In SimMap, a series of maps at seven aggregationlevels were designed, with the map size of 1024×1024cells as well (Fig. 3): p = 0.05, 0.1, 0.2, 0.3, 0.4, 0.5,and 0.58, wherep is initial probability which controlsthe fragmentation of the simulated landscapes (Sauraand Mart́ınez-Millán, 2000). The higherp is (up toan upper limit ofpc = 0.5928), the bigger and lessnumerous the patches are, and hence the more aggre-gated are the resulting patterns. The relative area ofeach class was also allocated according toTable 1. Theoriginally generated “bit-map” (bmp) files were firstimported into Erdas (Imagine) and then reclassifiedinto six categories, according to the “bmp” file. Theclassified maps were exported into Erdas file (“gis”format) for metrics calculation with APACK.

The simulated patterns from SimMap appear to bemore random than the maps generated by Rule becauseit avoided the class neighborhood problem.

Only a few metrics are chosen, since many land-scape metrics are mutually correlated, or have limitedability in describing landscape patterns (Saura andMart́ınez-Millán, 2001; Tischendorf, 2001). The se-lected metrics belong to three groups: (1) simpleexplicit metrics: total number of patches and averagepatch area (mean patch size); (2) edge metrics: to-tal perimeter, edge distribution evenness (EDV), anddouble-logged fractal; (3) clumping metrics: aggrega-tion index (AI), contagion (Li and Reynolds, 1993),and lacunarity. Most of the metrics can be calculatedfor the whole landscape (landscape level) and for each

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Fig. 2. Multifractal maps generated with Rule (please seeFig. 1 for legend).

class (class level). But some may only be calculatedat landscape level, such as contagion; or at class level,such as lacunarity. Some of the metrics are describedbelow:

2.1. Edge distribution evenness (EDE)

It estimates the evenness (or relative diversity) ofthe distribution of edge types on a landscape (Riitterset al., 1995). It can be calculated as:

EDE = measured diversity

max(possible diversity)

where

measured diversity

= −total classes∑

i=1

total classes∑j=1

ti,j × ln(ti,j).

In which, ti,j is the conditional probability of typeibeing adjacent to typej, multiplied by the area factorthat typei occupied in the total area:

Ti,j =(

Ni,j

Ni

)Ai (%)

whereNi,j is the number of times typei being adjacentto typej, Ni is the total number of adjacencies betweenpixels of patch typei and all patch types (includingpatchi itself), andAi% is the percentage of typei inthe landscape, and maximum possible diversity is:

Max pd1= 2 ln (total classes)(order of adjacency maintained)

Max pd2= ln [(total classes)2 + (total classes)]−ln(2) (order of adjacency ignored)

EDE values range from 0.0 for maps of a sin-gle cover type or whose edge types appear in equal

X. Li et al. / Landscape and Urban Planning 69 (2004) 137–148 141

Fig. 3. SimMap generated maps (please seeFig. 1 for legend).

proportion to 1.0 for maps whose edge type distribu-tion is skewed towards one or more edge types.

2.2. Double-logged fractal dimension

It estimates the fractal dimension of the land-scape using the perimeter/area method as describedin Sugihara and May (1990). The calculation methodcan be described as:

D = 2k

where k is the regression slope of patch area andperimeter:

log2

(l

4

)= k × log2 (s) + c

wherel is the perimeter of each polygon,s is area ofthe same polygon, andc is intercept of the regressionequation.

It is reported for the landscape as a whole as wellas for each attribute class in the input map. The value

for double-logged fractal dimension ranges from 1.0for maps made up of regular (or straight) outlinedpatches to 2.0 for maps made up of very irregularoutlined patches.

2.3. Aggregation index

Aggregation index (AI) is a class specific andcomposition independent index (He et al., 2000). Itassumes that a class with the highest level of aggre-gation (AI = 1) is comprised of pixels sharing themost possible edges. A class whose pixels share noedges (completely disaggregated) has the lowest levelof aggregation (AI= 0).

If ei,j represents total edges of classi adjacent toclassj, for classi of areaAi, aggregation index mea-suresei,i, the total edges shared by classi itself, withfour neighbor cells counted. The level of aggregationof classi is calculated as:

AI i = ei,i

max ei,i

142 X. Li et al. / Landscape and Urban Planning 69 (2004) 137–148

where,

max ei,i = 2n(n − 1), whenm = 0,

or

max ei,i = 2n(n − 1) + 2m − 1,

or

max ei,i = 2n(n − 1) + 2m − 2,

andn is the side of largest integer square smaller thanAi, while m = Ai − n2.

For the overall landscape, a landscape aggregationindex (AIL) can be calculated by summarizing AIi thatis weighted byAi%:

AIL =n∑

i=1

AI i × Ai%

wheren is the total number of classes present in thelandscape.

Both AIi and AIL are sensitive to spatial resolution,while AIL is also sensitive to landscape extent andcomposition.

2.4. Contagion

It reports the degree to which cover classes areclumped into patches. The calculation method is arelative measure of contagion (O’Neill et al., 1988),modified byLi and Reynolds (1993).

COL = 1.0 +∑total classes

i=1∑total classes

j=1 tij × ln(tij)

2 ln(total classes)

The explanation forti,j is the same as that in edgedistribution evenness.

The possible values for contagion (Li and Reynolds,1993) range from 0.0 for maps with minimal contagionto 1.0 for maps with maximum contagion.

2.5. Lacunarity

It is a measure of image texture, reporting the la-cunariy of a class in the landscape at different boxsizes (Plotnick et al., 1993). Lacunarity is typicallymeasured at various resolutions by overlaying boxesof varying sizes upon the landscape map. It can bedefined as:

LCU = second moment

(first moment)2

where

first moment=(biggest box)2∑

s=1

s × Q(s, r)

and

second moment=(biggest box)2∑

s=1

s2 × Q(s, r)

in which, Q(s,r) is the proportion of boxes of sizercontainings occupied sites.

Lacunarity ranges from 0.0 for a map that is ho-mogeneous to arbitrarily large values for a map thatappears highly textured.

All classes in the real landscape were analyzed, butonly class 1 (coniferous forest, occupying 41.68% ofthe total area) and class 4 (bare land, about 3.42% ofthe total) will be presented since many of the metricshave similar trends for different classes as the aggre-gation level increases.

3. Results

Agreement between real landscapes and neutralmodels can be compared by a series of pattern met-rics, each of which represent one or more aspectsof the landscape structure. The results of indicesare reported below. Since the internal parameterH(0–1) andp (0–0.5928) controlling aggregation lev-els in Rule and SimMap have similar value ranges,the metrics’ values for both model scenarios and thereal landscape can be plotted in the same figures(Figs. 4–10), so that we can depict to which extentthe neutral models can represent the real landscape.

3.1. Total number of patches and averagepatch area

These are two explicit metrics that describe thestructure of landscape mosaics. Given a designatedarea, a greater number of patches or smaller averagepatch area means higher fragmentation that may re-sult in low habitat suitability for interior species whichrequire large and connected patches. These two as-pects of the landscape also affect fire disturbance andpropagule dispersion.

X. Li et al. / Landscape and Urban Planning 69 (2004) 137–148 143

Fig. 4. Total number of patches at landscape level and class level in the real landscape and simulated maps. The horizontal axis representsthe aggregation level of generated maps. For Rule, it is the value of “H,” while for SimMap, it is the value of “p.” The range is 0–1 forH, and 0–0.5928 forp. The maps look more clumped when the aggregation values are higher. The vertical axis represents the calculatedvalues for landscape metrics. The same explanation applies for theFigs. 5–10.

Fig. 5. Average patch area at landscape level and class level in the real landscape and simulated maps.

Fig. 6. Total perimeter and landscapes at different aggregation levels.

144 X. Li et al. / Landscape and Urban Planning 69 (2004) 137–148

Fig. 7. Aggregation index and landscapes at different aggregation levels.

Fig. 8. The behavior of contagion and edge density evenness against real landscape and neutral model generated patterns.

Fig. 9. Fractal double-logged vs. different aggregation levels.

X. Li et al. / Landscape and Urban Planning 69 (2004) 137–148 145

Fig. 10. Lacunarity at box size 6 and different landscape pattern scenarios.

The total number of patches and average patch areafor different scenarios and classes are shown inFigs. 4and 5. The two neutral models generated scenariosthat are consistent with the real landscape on differentpoints at landscape level and class level. At the land-scape level, the real landscape has the same total num-ber of patches and average patch area with SimMapsimulated patterns whenp ≈ 0.43, or with Rule simu-lated patterns whenH ≈ 0.23. Therefore, both neutralmodels can represent the real landscape in terms oftotal number of patches and average patch perimeterat the landscape level.

At the class level, similar results were obtained asthat at the landscape level for total number of patches.The only difference is equivalency points between thereal and simulated patterns.

But for average patch area, the result is slightly dif-ferent at the class level for different classes. The aver-age patch area of coniferous forest for real and simu-lated patterns are quite close whenH ≈ p ≈ 0.2. Onthe other hand, the average patch area for bare land hasequivalent points between the real and the simulatedpatterns at much higher aggregation levels (H ≈ 0.43or p ≈ 0.55). This indicates an over-aggregation forsmall classes by neutral models.

3.2. Total perimeter and aggregation index

Total perimeter (or total edges) often affect thespeed of flow across landscape boundaries, while the

aggregation index is based on the adjacency prop-erty among neighboring cells or patches (He et al.,2000). The latter has been proved to be sensitive tothe aggregation level of landscape elements.

Figs. 6 and 7indicate the relative aggregation levelof the real landscape against simulated landscape sce-narios based on total perimeter and aggregation index.At landscape level, the real landscape is equivalent tothe Rule and SimMap generated maps at the aggre-gation level ofH ≈ 0.23 andp ≈ 0.41, respectively,according to both metrics.

Although total perimeter and aggregation index aretwo very different metrics mathematically and ecolog-ically, the results for these metrics and the agreementpoints between the real and simulated landscapesindicated by them were very similar, not only at thelandscape level, but also at the class level (Figs. 6 and7). The curves for these two metrics indicated somekind of negative correlation between each other. Thereason could be that the mathematical methods forthese two metrics are both based on the number ofedges related to each class in the landscape map.

3.3. Contagion and edge distribution evenness

Contagion reports the degree of clumping of thelandscape (defined byLi and Reynolds, 1993). Whenmore cells are “clumped” together forming largepatches, the value of this index is higher. It hasbeen used extensively to summarize the amount of

146 X. Li et al. / Landscape and Urban Planning 69 (2004) 137–148

clumping or fragmentation of patches on raster cate-gorical maps (Schumaker, 1996; Ricotta et al., 2003).Edge distribution evenness estimates the relative di-versity of the distribution of edge types upon a land-scape. Both of these two indices are “entropy based”and are calculated at the landscape level only.

Results are presented inFig. 8a. The contagion in-dex indicated the equivalency point of the real land-scape atH ≈ 0.13 for the Rule generated maps, andp ≈ 0.5 for the SimMap generated scenario.

The behavior of edge distribution evenness is dif-ferent for the Rule scenario and SimMap scenario(Fig. 8b). It is not sensitive to different aggregationlevels in the SimMap scenario and has no equivalencypoint with the real landscape. Therefore, none of thetwo neutral models can represent the real landscapeconsistently in terms of edge distribution evenness.

3.4. Fractal (double-logged)

Double-logged fractal is calculated from thelog–log regression of patch perimeter versus patch ar-eas. It is a measure of the complexity of the perimeterand is often evaluated in scaling and habitat analyses(Milne, 1992; With and King, 1999a,b; With et al.,1999; Mouillot et al., 2000).

The double-logged fractal dimension behaves dif-ferently in the two neutral model scenarios. It hasagreement points between the real landscape and theRule scenario atH ≈ 0.27, 0.13, and 0.37 for totallandscape, coniferous forest and bare land, respec-tively (Fig. 9). Again it indicates an over aggregationof small classes in the Rule generated scenario.

In the SimMap scenario, the double-logged frac-tal behaves unsteadily at the landscape level. Thereal landscape has three equivalent points with theSimMap generated patterns, according to this index.Therefore, it is not a good index at the landscapelevel for describing patterns at different aggregationlevels. At the class level, there is an equivalent pointbetween the real and the simulated landscapes whenP ≈ 0.1 for coniferous forest. For the small classbare-land, double-logged fractal is not sensitive todifferent aggregation levels at all.

Therefore, SimMap might not be suitable to rep-resent the real landscape pattern, if we wish to pur-sue similar spatial characteristics indicated by thedouble-logged fractal index.

3.5. Lacunarity

Lacunarity reports the “holeness” of a landscape atdifferent box sizes, from 1, 6, 11,. . . to 46 cells inAPACK.

Here only the lacunarity index at box size of 6 ispresented, since the value for the real landscape ismuch higher than neutral models generated patterns atbox size 1, while a similar trend at box size 6 is foundwhen the box size is bigger than 6.

The behavior of this index is relatively stable fordifferent classes. The real landscape crosses the “Rulecurve” nearH ≈ 0.2, and the “SimMap curve” nearp ≈ 0.55 for both classes. Therefore, the level of“holeness” is similar for different classes, even thoughthey occupy totally different percent of the study area.

4. Discussion

The above results demonstrate that neutral land-scape models have difficulty capturing all the patterncharacteristics of a real landscape by approximatingthe landscape and class level metric values. If an areadesigned with neutral landscape models is to replacethe real landscape with maximum interior area (highAI value), it would lose the character of other as-pects, such as edge distribution evenness and numberof patches, and thus, may lose the considered edgespecies that demand more than one type of land cover.

But neutral models at different aggregation levelscan represent the spatial pattern of real landscapes tosome extent. The aggregation level identified for thereal landscape is different for various landscape met-rics, probably because they describe or quantify differ-ent aspects of the landscape patterns. We have testedsome other real landscapes, and the identified aggrega-tion levels (or agreement points between the real andneutral models) also changed with different metrics.But the general trend of the results did not change.

The aggregation level of different classes can be dif-ferent in real landscapes, while in the neutral models,the aggregation levels are pre-defined for the wholelandscape and also for each class. This could be thereason why the equivalent points are different for thelandscape and for each class identified by the same in-dex, such as those indicated by total perimeter, num-ber of patches and aggregation index.

X. Li et al. / Landscape and Urban Planning 69 (2004) 137–148 147

The landscape metrics selected in this study donot represent all those that are included in theFRAGSTATS and APACK packages. But most ofthose metrics have correlations or have certain kindof limitations, according to earlier research (Li, 2000;Saura and Martı́nez-Millán, 2001; Tischendorf, 2001).There is no single index that can unambiguously dif-ferentiate all shapes (Haines-Young and Chopping,1996). That is why we selected a group of metricsinstead of only one or two. If another group is chosenfor this study, similar results would be anticipated.

Any pattern in a landscape is related to certainprocesses. Pure stochastic pattern scenarios like thosegenerated by SimMap may show the process of landaggregation caused by human land use planning.But human activities often focus on one or two re-sources and in the mean time cause fragmentation onother landscape components, which might be impor-tant habitats for wild animals. None of these neutralmodels mentioned in this study can simulate the ag-gregation/fragmentation level differently for differentclasses. For example, residential area tends to beaggregately distributed, while bare land is scatteredamong other types. The aggregation level for thesetwo types should be different in the real landscape,but it is difficult to simulate in neutral models. Asa result, over aggregation or over fragmentation ofsome classes is unavoidable.

The multi-fractal maps generated by Rule seems tobe less “stochastic” than the SimMap scenario. But itis difficult to control which class should be always ad-jacent with another, or avoid another. It is also difficultto “mix” some of the classes and keep some others tofollow certain kinds of “adjacency rules.”

The two neutral models adopted in this study alsoshow some kind of consistency with each other, espe-cially when the aggregation level is very low or veryhigh, as indicated inFigs. 4–10. Since they follow dif-ferent aggregation rules in the simulation, the patternsgenerated are often different. But some aspects shouldbe comparable with each other, as detected by somelandscape pattern metrics.

Another point is that the spatial distribution ofdifferent classes in the real landscape was largelyassociated with topographical factors. For example,wetlands and river bottomland are always distributedalong rivers, and rivers are always linearly connected.But in the maps generated by neutral models, all the

classes were allocated randomly, with only relativearea and number of classes retained. The rivers mightbe broken into pieces and appear in the area adjacentto forest or residential area, while residential areamight be scattered everywhere, even in the wetlandsand rivers. Therefore, the geographical characteristicsof the real landscape could not be represented logi-cally with either of the neutral models. It is possibleto improve neutral models so that they can followsome “rules” and generate more “reasonable” maps(Johnson et al., 1999; With and King, 2001). Butonce they are “trained” with more conditions, theywill not be “neutral” any more, and new limitationsmay arrive with their potential use.

In spite of all the limitations of neutral landscapemodels, they never the less can be an important toolin landscape planning owing to their high repeatabil-ity. Once the agreement thresholds for the aggregationlevels in the landscape have been identified, additionalmaps showing different scenarios can be readily gen-erated. This ability to generate alternate scenarios isthe strength of neutral landscape models for landscapeplanning.

Acknowledgements

This paper is sponsored by the Chinese Academyof Sciences, National Natural Science Foundation ofChina (40331008, 30270225, 40001002), and National973 Project (2002CB111506). Special thanks for theanonymous reviewers for their valuable comments toimprove the manuscript.

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