The adequacy of different landscape metrics for various landscape patterns

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1 Pattern Recognition 38 (25) The adequacy of different landscape metrics for various landscape patterns Xiuzhen Li a,, Hong S. He a,b, Rencang Bu a, Qingchun Wen a, Yu Chang a, Yuanman Hu a, Yuehui Li a a Institute of Applied Ecology, Chinese Academy of Sciences, P.O. Box 417, Shenyang 1116, China b School of Natural Resources, University of Missouri-Columbia, Columbia, MO 65211, USA Received 14 September 24; received in revised form 18 May 25; accepted 18 May 25 Abstract The behavior of several landscape pattern metrics were tested against various pattern scenarios generated by neutral landscape models, including number of classes, scale-map extent, scale-resolution, class proportion, aggregation level RULE, and aggregation level SimMap. The results demonstrate that most of the metrics are sensitive to certain pattern scenarios, yet are not sensitive to others; therefore, none of them is appropriate for all aspects of a landscape pattern. Despite these limitations, some of these metrics are recommended for future use, which include total number of patches, average patch size,, double-logged fractal, contagion, and aggregation index. Special attention should be paid to the relationships between metric values and ecological processes rather than the numbers themselves. 25 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved. Keywords: Landscape pattern; Pattern metrics (indices); Behavior; Neutral model 1. Introduction Landscape metrics are quantitative measures for spatial patterns and are widely used in landscape ecological research. With the availability of GIS technology and landscape pattern calculation software such as FRAGSTATS [1] and APACK [2], it is simple to generate many landscape pattern measurements without understanding the mathematics and the implications of these metrics. Results of these metrics are increasingly interpreted or compared without adequate explanations of whether they can represent the underlying processes. This trend has caused researchers to begin investigating not only the applications and limitations of these indices to adequately characterize landscape heterogeneity, but also the ecological implications of the indices [3 11]. Because patterns are fundamental to many of the spatial-temporal relationships that we seek to discover, it is important to understand the factors that influence the interpretation of any landscape indicator or metric [12]. Corresponding author. Tel.: ; fax: address: landscape21@sina.com (X. Li). Relatively simple metrics such as area, perimeter, relative area, and patch shape are mostly derived from mathematical statistics, while many others are derived from information theory (for example, Shannon-Weaver diversity, dominance, and contagion). In addition, new metrics are still being designed, such as aggregation index [13], splitting index [14], and cohesion index [15]. Since most of the metrics are based on the geometric properties of landscape elements and can provide simple quantitative measurements of a complex pattern, they are frequently adopted in landscape ecological research [16]. However, if their strengths and limitations are not clear to the users of these metrics, interpretation of the results can be misleading [12]. At present, systematic analysis on the spatial implications of landscape metrics is still lacking. Wu et al. examined 19 landscape level metrics [17] and 17 class level metrics [18] based on five data sets. Simple scaling functions, unpredictable behaviors, and staircase relations were found between scale changing factors and metric values. Landscape metrics are more consistent and predictable across changing grain size values than changing extent values. Saura studied the effect of spatial resolution on /$ Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved. doi:1.116/j.patcog

2 X. Li et al. / Pattern Recognition 38 (25) several fragmentation indices; these studies yielded comparable results [19]. We believe scale is an essential factor to consider when describing heterogeneous landscapes; however, other critical factors must be taken into account. This paper evaluates the behavior of some landscape metrics under various map properties, including the number of classes, the proportion and the level of aggregation of each class, and the resolution and extent. To avoid the mixed influence of different factors in real landscapes, random maps are used to test the response of landscape pattern metrics to changes in a single property of the configuration. Neutral landscape models (NLMs) were employed in this study to systematically generate maps with varied map properties. Compared with real landscapes, patterns generated from NLMs are highly replicable and their parameters can be easily controlled [1]. NLMs are therefore convenient and inexpensive tools compared to large-scale field experiments which are highly impractical. Landscape planners may use them to design different planning scenarios and to study the potential ecological consequences of these scenarios. We used a neutral landscape model, RULE, developed by Gardner et al. [2,21], which can generate maps at different aggregation levels or with hierarchical structures to approximate actual landscapes. At the same time, the model retains the relative proportions among classes in the maps. However, the patterns generated by this model always have some classes adjacent with each other, while other classes are separate; therefore, these patterns are not, in fact, random. Nevertheless, the model can represent to a certain degree the topographical gradients found in real world scenarios. Additionally, we employed SimMap, another neutral landscape model designed by Saura and Martínez-Millán [6,22]. Patterns generated by this model are fully random, while aggregation levels and class proportions can also be designed. This paper conducts a systematic analysis by comparing the behavior of landscape metrics against a full set of variables (or map properties), including number of classes, map extent, map resolution, class proportion, and aggregation levels. The paper analyzes the degree to which landscape metrics can effectively discriminate different spatial patterns, and it further clarifies the practicability and applicability of these metrics in quantifying landscape patterns. 2. Methods The primary factors that affect landscape pattern characters were tested by consecutively altering the values of one parameter at a time while holding other factors constant. Table 1 presents six pattern scenarios designed to analyze the response of selected landscape metrics Scenario 1: number of classes This scenario tested the responses of landscape metrics to different numbers of classes in the landscapes. The total area and map resolution for each map were kept constant at a size of 1 rows 1 columns. Each class had an equal area percentage, and classes were randomly distributed. The numbers of classes assigned were 2, 3, 4, 5, 8, 1, 15, 2, 3, 4, 5, 8, and 1, respectively. The maps were directly generated in the Arc/Info GRID module using the RAND command, as shown in Fig Scenario 2: map extent This scenario tested the responses of landscape metrics to variable sizes in the landscapes. Fig. 2 shows random maps Table 1 Parameters used for different pattern scenarios Scenarios Map size (cells) Resolution Number of Relative class area (cell) classes Randomness Number of classes , 3, 4, 5, 8, 1, Equal Random 15, 2, 3, 4, 5, 8, 1 Map extent 8 8, 16 16, 32 32, 64 64, 1 1 Equal Random , 25 25, 5 5, 1 1 Resolution 1 1 1,.5,.25,.2, 3 Equal Predefined.1,.5,.1 Class proportion %, 5%, 1%, Random 2%, 3%, 4%, 5% Aggregation level: Equal Randomly aggregated RULE at 1 levels Aggregation level: SimMap Equal Randomly aggregated at 9 levels

3 2628 X. Li et al. / Pattern Recognition 38 (25) Fig. 1. Random maps for the number of classes scenario. Fig. 2. Map extent scenario Scenario 3: resolution This scenario tested the responses of landscape metrics to different map resolutions while map extent (size) and number of classes remained constant. The resolution of a 3-class 1 1 cells random map (Fig. 3) was altered by resampling it into smaller cell sizes at.5,.25,.2,.1,.5 and.1 unit, respectively, as shown in Fig. 3. The spatial configuration of the original map did not change during this resample process Scenario 4: class proportion Fig. 3. Resolution scenario. Squares on the right side indicate the cell sizes used to resample the map on the left. at sizes 8 8, 16 16, 32 32, 64 64, , 25 25, 5 5, and 1 1 were generated using the Arc/Info GRID module; each map had 1 arbitrary classes with each occupying 1% of the area. The map resolution remained unchanged at one map unit. Results presented in Section 3 show map sizes which are indicated by the number of cells along a single side of the squared maps. This scenario tested the responses of landscape metrics to different class proportions. If more than two classes occur in a map, many combinations of different class proportions are possible for each. To simplify the scenario, only binary maps were chosen to study the effect of class proportion on landscape metric values. In reality, binary maps are also frequently used for both habitat analysis and built-up area distribution studies [9]. The map extent was set at 1 1 cells, and the proportion of one class was 1%, 5%, 1%, 2%, 3%, 4%, and 5%, respectively. The proportion of the other class was correspondingly 99%, 95%, 9%, 8%, 7%, 6%, and 5%, respectively, as shown in Fig. 4. Re-

4 X. Li et al. / Pattern Recognition 38 (25) Fig. 4. Class proportion. Percentages are for the darker class. Fig. 5. Aggregation level RULE scenario. sults presented in Section 3 show only 5% of class one presented for landscape level metrics, since the curve for 5 1% is considered to be symmetrical with that for 5% Scenario 5: aggregation level RULE This scenario tested the responses of landscape metrics to multi-fractal maps at different aggregation levels generated by the RULE model [21]. Grid maps of cells with four classes at the same area proportions (25%) were generated. The internal parameter controlling aggregation levels in the RULE program was assigned H =,.1,.5,.1,.2,.3,.4,.5,.6, and.8, respectively, as shown in Fig. 5. Higher H values correspond to higher aggregation levels. The value range for H is 1. Maintaining stability of the proportions of each class becomes problematic where H> Scenario 6: aggregation level SimMap This scenario tested the responses of landscape metrics to purely random maps at different aggregation levels generated by the SimMap model [22]. Similar to RULE, SimMap can also generate random grid maps that have different aggregation levels resembling real landscapes. However, maps generated by SimMap do not experience class adjacency difficulties, and they appear more random than those generated by RULE. The internal parameter p controls the aggregation levels of generated maps, with a range of As the value of p approaches.5928, the aggregation level of generated maps rapidly becomes higher; consequently, maintaining the proportional stability of each class becomes difficult. In this study, p was assigned,.1,.2,.3,.4,.45,.5,.55, and.57, respectively. Each map has 5 5 cells and four classes, each accounting for 25% (see Fig. 6). Several widely used landscape metrics were selected for the evaluation of their sensitivity to pattern changes: total number of patches, mean patch size, average patch perimeter/area ratio,, double-logged fractal, Shannon-Weaver diversity, Shannon-Weaver evenness, dominance, contagion, and aggregation index. Our study employed the landscape analysis package APACK [2]. Because different metrics reflect different aspects of a given pattern, there is no standard rule to judge whether a metric is adequate to represent a landscape. So as long as a metric can adequately describe the desired aspect of the pattern, it may be considered a useful landscape metric. The

5 263 X. Li et al. / Pattern Recognition 38 (25) Fig. 6. Aggregation level SimMap scenario. behavior of these landscape metrics were evaluated for two aspects: sensitivity and stability. Sensitivity reflects whether the metric generates a detectable response when map properties change. On the other hand, a stable metric should remain relatively constant if the parameter variation does not change the general configuration of the landscape (as in the map extent and resolution scenarios, for instance). 3. Results 3.1. Total number of patches The total number of patches can indicate the fragmentation level of a landscape and is often used in habitat analysis. It functions as both a landscape level as well as a class level index. Fig. 7 shows that at the landscape level, as the other factors (map size, resolution, class proportion, and aggregation level) remain unchanged, the total number of patches in random maps initially increases quickly with the increase of classes (N) where N<2. Where N>2, the rate of increase diminishes. Where the number of classes remains constant and only map size changes, the total number of patches will increase as nearly a second power function of map size, as presented in Figs. 2 and 7(b), respectively. Figs. 3 and 7(c) illustrate that after a map is resampled into smaller cell sizes, the total number of patches in the map remains unchanged. If the map were resampled with greater cell sizes, the results would be comparable to that of changing map size. If the relative area percentage of one class in binary maps is changed, the total number of patches will have a peak when one of the classes reaches 15 2%, as presented in Fig. 7(d). A plausible explanation is that, at this point, too many one-cell patches appear. As Fig. 7(e) and (f) demonstrate, more aggregated patterns have fewer patches. These results comport with our general expectation. At class level, with the change of pattern parameters, the total number of patches scenario shows a trend similar to that of the landscape level for most of the scenarios, with the sole exception of the number of classes scenario. When there are roughly five classes in the random maps, the number of patches for a certain class reaches its peak (see Fig. 7(g)), under the conditions that the area percentage of each class is equal, and total area, resolution, and aggregation level remain constant. These results indicate that the total number of patches can reflect the pattern changes successfully. The peak values detected for the class proportion scenario at landscape level, as well as those for the number of classes scenario at class level, may help readers to better understand and explain related results in their own research is a relatively simple measure of landscape patterns. It is ecologically important because it quantifies the aggregation or fragmentation levels of various landscapes, and it can also be used to compare measurements of different classes in one landscape. At landscape level, mean patch size decreases quickly with the increase of number of classes; however, the rate of decrease declines where N>2. Eventually the mean patch size approaches 1 cell (see Fig. 8(a)). Map size affects mean patch size only where map size is very small, as shown in Fig. 8(b). For random maps with less than 2 classes, mean patch size becomes relatively stable where the map extent is over 1 1 cells. Most real landscape maps have a larger size than this threshold. For a predefined mosaic, where the map resolution becomes finer (see Fig. 3), the mean patch size will not change if it is measured in meters. But if it is measured with number of cells, the mean patch size will become exponentially great, as illustrated in Fig. 8(c). Of course, the mean patch size increases as aggregation level of the landscape maps becomes higher. At class level, mean patch size responds similarly to the parameter changes mentioned in other scenarios. For the class proportion scenario, the effect of relative area on mean patch size is different at both landscape level and class level. At landscape level, the mean patch size has

6 X. Li et al. / Pattern Recognition 38 (25) y =.6356x y = Ln(x) R 2 =.9999 R 2 = (a) number of types (b) map size (c) resolution (cell size) a-f: Landscape level. g: Class level for the number of types scenario. Other scenarios have similar results as landscape level. Total patches is for class 1. (d) y=42458x x x R 2 = number of types (e) (g) H (Rule) (f) p'(simmap) Fig. 7. Behavior of total number of patches against different pattern scenarios. The horizontal axis represents the changing variables in each scenario, while the vertical axis shows metric values calculated for each scenario. Only class 1 is presented at class level, since other classes have the same proportion in the maps, or predictable values in the class proportion scenario. The trend for other classes is easily deduced from that of class 1. This applies for all subsequent figures. 1 cells cells 1 cells 1 y=5.5557x -2 1 R 2 =1 1 1 a-f: Landscape level. g: Class level for the relative area scenario. Other scenarios have similar results as landscape level. MPS is for class 1. (a) number of types (b) map size (c) cell size cells cells H' (Rule) cells p' (SimMap) (d) (e) (f) (g) 1 cells Fig. 8. Behavior of mean patch size against different pattern scenarios. a valley when the total area percentage of a class in the binary map reaches 1 2% (see Fig. 8(d)), while at class level mean patch size is positively correlated with the increase of area percentage of one class (see Fig. 8(g)). The rate of increase is especially high where the relative area is 8 9%. Since mean patch size is at once sensitive to the change of pattern parameters, ecologically significant, and relatively simple, it is a reliable index in the analysis of landscape patterns Average patch perimeter/area ratio The average patch perimeter/area ratio is a widely used index in landscape ecological studies. Chiefly, it describes the shape of different patches and is sometimes used as a substitute for shape index, because the latter has been proved to be a weak, even self-contradictory index [5,6]. In this study, the average patch perimeter (edges)/area (cells) ratio increases rapidly at first, then slowly with the increase of the number of classes where N 3 (see Fig. 9(a)). Average patch parameter/area ratio fluctuates irregularly when the map extent is smaller, but becomes more stable when it is large enough (see Fig. 9(b)). The response of average patch parameter/area ratio to the resolution change is linear, and the relationship is positive (see Fig. 9(c)). While the aforementioned scenarios show similar trends at both landscape level and class level, the responses of average patch parameter/area ratio differs significantly. The curves are not so smooth at either landscape level or class level, as shown in Fig. 9(d) (i). For binary maps at landscape level, where the area percentage of one class reaches about 3% of the total, the average patch parameter/area ratio has a wide valley (see Fig. 9(d)). At class level, it decreases irregularly with the increase of area percentage for one class, as shown in Fig. 9(g).

7 2632 X. Li et al. / Pattern Recognition 38 (25) (a) number of types (b) map size (c) 3.85 R 2 = 1 y = 3.221x cell size av.patch p/a ratio (d) y = x x x x R 2 = (e) H (Rule) (f) p'(simmap) (g) (h) H' (Rule) (i) p (SimMap) Fig. 9. Behavior of average patch perimeter/area ratio against different pattern scenarios: (a) (f) landscape level; (g) (i) class level for the relative area and aggregation level scenarios. Other scenarios have results similar to landscape level. The metric value is for class 1. The response of average patch perimeter/area ratio to different aggregation levels is even more irregular. In the RULE scenario, it shows little change as the aggregation level increases, either at landscape level or at class level (see Fig. 9(e) and (h)). In the SimMap scenario, it has a wide valley where the internal parameter p reaches.4 (Fig. 9(f) and (i)). These results indicate that average patch perimeter/area ratio is not a reliable pattern index; however, it remains relatively stable when changing scales. Furthermore, the patch perimeter/area ratio for single patches is more ecologically significant than its average at landscape and class levels, because the shape of single patches may affect the movement of some species Total edge density The index is based on the ratio between total edges (number of cells at patch boundary) and total area (total cells). It can indicate the fragmentation level of either a landscape or one of its classes. At landscape level, initially increases rapidly; however, the rate slows with the increase of number of classes (see Fig. 1(a)). But as the map extent broadens, it initially decreases rapidly and then slows as in Fig. 1(b). Total edge density tends to approach a stable limit in these scenarios. At class level, however, the behavior of total edge density in these two scenarios is entirely different (see Fig. 1(g) and (h)). The edge density of a class decreases with the increase of number of classes in the maps, as shown in Fig. 1(g). Additionally, it fluctuates acutely as the map extent enlarges at the beginning, and becomes stable where the map extent is larger than 5 5 cells, as shown in Fig. 1(h). The responses of to the other scenarios is relatively predictable, and its behavior at landscape level and class level is similar. With the change of map resolution, it changes linearly (see Fig. 1(c)). With the increase of area percentage of one class in the binary map, the increase in follows a parabola curve, reaching its highest point when the two classes have the same area (see Fig. 1(d)). With the increase of aggregation levels, total edge density decreases at an irregular rate, as shown in Fig. 1(e) and (f). These results indicate that is a strong index in representing different patterns. It is sensitive to the change of most pattern parameters, and it is highly predictable. Additionally, it possesses ecological significance: many wild animals use or avoid edges during movement, and mesh size can affect the home range of some animals [23].

8 X. Li et al. / Pattern Recognition 38 (25) (a) y =.289Ln(x) R 2 = number of types R 2 = y = 41x (b) map size (c) cell size (d) y = x x R 2 = y = x R 2 = (e) H' (Rule) (f) p' (SimMap) (g) number of types (h) map size Fig. 1. Behavior of (edges/cell) against different pattern scenarios: (a) (f) landscape level; (g) and (h) class level for the number of class and map size scenarios. Other scenarios have results similar to landscape level. The metric value is for class Double-logged fractal The double-logged fractal index is used to describe the complexity of a patch boundary, and is more complex than those metrics previously mentioned. Although earlier studies rendered different opinions over its practicability [24 27], most of the conclusions were drawn from specific case studies. In fact, it shows different responses to a change of pattern parameters, and the behavior at landscape and class level is also significantly different. At landscape level, double-logged fractal decreases irregularly as the number of classes increases (see Fig. 11(a)). It remains relatively stable where the map extent is sufficiently large, as in Fig. 11(b), and it remains constant where the map resolution becomes finer, as in Fig. 11(c). In the binary maps, when one of the classes reaches 4%, an obtuse peak appears, yet the change is less significant where the relative area of one class ranges 1 9% (see Fig. 11(d)). It is sensitive to change in aggregation levels, as shown in Fig. 11(e) and (f), and it remains predictable in the RULE scenario (see Fig. 11(e)), since the maps in this scenario were generated with multi-fractal criteria. At class level, it fluctuates irregularly with an increase in the number of classes (see Fig. 11(g)). In the class proportion scenario, it is relatively stable where the relative area of class one is 1 8%. Therefore, this index does have limitations at class level, but shows a trend similar to that for the other four scenarios at landscape level Shannon-Weaver diversity, Shannon-Weaver evenness, and dominance The Shannon-Weaver diversity, Shannon-Weaver evenness, and dominance metrics are based on relative area percentage of each class in the map. As long as the relative area of each class remains constant, the value for these metrics will remain constant in spite of pattern differences (e.g., see Figs. 5 and 6). They are often used to describe the heterogeneity or evenness of landscape patterns. But actually they are not at all sensitive to changes in spatial arrangement, and are only sensitive to a change in relative area for each class, as shown in Fig. 12(c). Shannon-Weaver diversity is also sensitive to a change in the number of classes (see Fig. 12(a)), but this might also be attributed to the relative area change caused by an increase in the number of classes. It is sometimes improperly used to indicate heterogeneity, perhaps because the name diversity is misleading. Fig. 12 provides the responses of Shannon-Weaver diversity in different scenarios. Fig. 12(a) shows that Shannon- Weaver diversity increases logarithmically with an increase in the number of classes. In the class proportion scenario, the value is greater where the relative areas of each class are approximate, as illustrated in Fig. 12(c). It remains relatively stable in the other scenarios and does not change with resolution or aggregation level changes. Shannon-Weaver diversity responds only weakly where the map extent is relatively small (see Fig. 12(b)). The behaviors of Shannon-Weaver evenness and dominance are similar to that of Shannon-Weaver diversity. They are even insensitive to a change in the number of classes. So long as the relative areas of each class remain equal to each other, the value for Shannon-Weaver evenness is always 1, and the value for dominance is always. Furthermore, where the relative areas of each class are approximate, the value for dominance decreases, and the value for Shannon- Weaver evenness increases. Shannon-Weaver diversity is not appropriate for comparison of landscapes that have different numbers of classes. Conversely, Shannon-Weaver evenness and dominance are appropriate, since they are not sensitive to number of classes. This group of indices is unfit for landscape heterogeneity comparison. The interpretation for the values of these

9 Shannon-weaver diversity Shannon-weaver diversity Shannon-Weaver diversity 2634 X. Li et al. / Pattern Recognition 38 (25) (a) number of types (b) map size (c) resolution (cell size) (d) y =.155Ln(x) R 2 = (e) y = x R 2 = H' (Rule) (f) p' (SimMap) (g) number of types (h) Fig. 11. Behavior of double-logged fractal against different pattern scenarios: (a) (f) landscape level; (g) and (h) class level for number of classes and relative area scenarios. The metric value is for class y = Ln(x).8 R 2 = (a) (b) (c) number of types map size R 2 =.9997 y = 4.751x x x Fig. 12. Behavior of Shannon-Weaver diversity against different pattern scenarios. The value remains at 5 at any resolution, and at any aggregation level. indices should be based on their behavior in different scenarios, rather than their superficial names Contagion Contagion is a landscape level index that quantifies the degree of clumping of the landscapes [28]. It is among the earliest and most debated of metrics ever used [29 32]. Because of the different formulae [28 31] and calculation methods (four-neighborhood rule and eight-neighborhood rule), different results might be obtained for the same landscape mosaic. For this paper, contagion-li [3] was selected because the range for this index is between and 1, and thus considered more reliable than other methods. Contagion-Li is stable in the number of classes and map extent scenarios (see Fig. 13(a) and (b)). The vertical axes in Fig. 13(a) and (b) were exemplified. In pure random maps, cells of the same class are difficult to merge into patches; therefore, the value for contagion is rather low. Contagion is very sensitive to map resolution changes (see Fig. 13(c)). Where grain size becomes finer, the value for contagion becomes higher. For binary maps (see Fig. 4), where the area percentages of each class are approximate, the value for contagion is lower, and vice versa, as shown in Fig. 13(d). This index is also sensitive to aggregation level change in landscape maps. Highly aggregated landscapes have higher contagion values (see Fig. 13(e) and (f)). Generally speaking, contagion-li is a useful index for representing different landscape patterns. Still, special attention must be paid when using it to compare landscape maps with different resolutions Aggregation index Aggregation index is a newly proposed index [13]. The index value ranges from to 1. It also quantifies the aggregation level of landscapes, and can be calculated at landscape level and class level. Its responses to the aggregation level (RULE and SimMap) and relative area scenarios (see Fig. 14(d) (f)) are similar to those of contagion-li (Fig. 13(d) (f)). Aggregation index is sensitive to change in the number of classes. Initially, it decreases rapidly, and then only slowly with the increase in the number of classes (see Fig. 14(a)). Its relationship with map resolution is linear, as shown in Fig. 14(c).

10 Aggregation index Aggregation level Aggregation index Aggregation index Aggregation index Aggregation index Aggregation Index Aggregation index X. Li et al. / Pattern Recognition 38 (25) (a) number of types (b) map size (c) Contagion li Contagion li Contagion li.5.4 y = x x x R 2 = cell size Contagion li (d) y = Ln(x) R 2 = Contagion li (e) H' (Rule) Contagion li (f) y =.69e x R 2 = p' (SimMap) Fig. 13. Behaviors of contagion against different pattern scenarios y = 1.87x -4 R 2 = Number of types map size R 2 =.9994 R 2 =.9999 y = x y=2.45x 2-2.5x cell size (a) (b) (c) (d) (e) y = x x R 2 = H' (Rule) (f) R 2 =.9231 y = 1.119x p' (SimMap) (g) y =.9915x -.12 R 2 = (h) map size Fig. 14. Behavior of aggregation index against different pattern scenarios. At class level, the behavior of aggregation index is similar to that of landscape level for most of the scenarios. However, it is relatively unstable where the map extent is small, as in Fig. 14(h). In the binary maps, it increases linearly with the increase of area proportion for one class (see Fig. 14(g)). Aggregation index is more sensitive to change in pattern properties than contagion, and its calculation method is unique. It is suitable for the comparison of landscapes at landscape and class levels. However, the index does possess limitations and rules for application [13]. 4. Discussion The ecological significance and interpretation of landscape metrics is one of the key topics in quantitative landscape ecology [33]. We also attempted to test the sensitivity of some landscape indices to the ecological process of wetland landscapes [4,34 38]. With the development of improved tools for landscape metrics calculation, more and more papers are using landscape indices to compare landscapes or their changes, while the actual meaning of the indices is ignored. It is critical at this time to make the clarifying point that no landscape index is a magic bullet. One should choose representative and simple indices according to the purpose of the study and the situational context of the study area. Interpretation of the results should be rendered with a clear understanding of both the uses and the limitations of the indices. The metrics chosen in this study possess different capacities in quantifying various aspects of landscape patterns. Some of the indices can describe pattern changes caused by

11 2636 X. Li et al. / Pattern Recognition 38 (25) an increase in the number of classes, but cannot discriminate the difference in aggregation levels (Shannon-Weaver diversity, for example). Most of the indices evaluated in this paper are sensitive to aggregation levels. In fact, any given index can describe only one or two aspects of the spatial pattern, such as complexity or aggregation level. There is no index that can fully describe the pattern. For binary landscapes, apart from average patch perimeter/area ratio (see Fig. 9(a)) and double-logged fractal (see Fig. 11(a)), there are some indices that respond discretely to landscapes having more than two classes (corrected average patch perimeter/area ratio and normalized average patch area, for instance). These were analyzed as well, but not presented in this paper. In habitat studies of wildlife, binary maps are often used instead of real landscapes [39 42]. Discrete metrics such as these are not appropriate for binary maps. Because many metrics are based on statistics for patch perimeter and area, redundancy among them is virtually unavoidable [31]. Consequently, metrics chosen for ecological studies should be independent of one another. No matter what indicator is used for pattern quantification, the ecological meaning of the indicator should be considered first. Rather than the creation of new indicators, what is sorely needed is a serious re-examination and thorough study of the relationships between existing indices and ecological, geographical, and anthropological processes. For example, in studying habitat changes for wildlife, we can relate fragmentation, connectivity and lacunarity indices with population size and growth. When studying the effect of landscape change on catchment hydrological process, we can relate the area and aggregation index of sensitive landscape types to hydrological metrics such as runoff and erosion modulus. Any exploration concerning the relationship between landscape indicators and processes is a contribution to the theoretical dimension of landscape ecology. One limitation of this paper is that all of the maps used were computer generated NLMs. But the cases simulated in this study can account for most of the situations encountered in real landscapes. When we use landscape metrics to quantify the patterns of real landscapes, the results presented in this paper may function as a useful reference. Other studies have explored the limitations and applications of NLMs [37,43]. Further study should also focus on mathematical explanations for the results. For example, for the number of patches index in the number of classes scenario, why is there a turning point where N 2, as presented in Fig. 7(a)? And at class level, why is there a peak where N 5, as presented in Fig. 7(g)? Similar questions arise in using binary maps: when one of the classes reaches 1 2%, why is the value for mean patch size the smallest, as presented in Fig. 8(d)? Such phenomena require further explanation from a mathematical point of view. For complicated indices such as double-logged fractal, contagion, and aggregation index, the mathematical interpretation of their behaviors against different scenarios will be yet more difficult, requiring further consideration. 5. Summary This study tested the adequacy of several landscape metrics frequently used in discriminating different patterns and in representing different configuration properties. The study was based on pattern scenarios generated by neutral landscape models. The study concluded: (i) total number of patches, mean patch size,, and aggregation index can reflect different patterns successfully at both landscape level and class level; (ii) average patch perimeter/area ratio is not sensitive to changes of map configuration at either landscape or class levels; however, patch perimeter/area ratio may have significant and adequate utility in representing the shape of single patches; (iii) double-logged fractal is a reliable index at landscape level, but is unstable where the number of classes changes at class level; (iv) Shannon-Weaver diversity, Shannon-Weaver evenness, and dominance are three correlated landscape level metrics (In general, these metrics should not be used together, as this may result in information redundancy. Shannon-Weaver diversity is not appropriate for comparing landscapes with different number of classes.); and (v) Contagion-Li is a useful index for representing different landscape patterns, but is not suitable for comparing landscape maps with different resolutions. Acknowledgements This paper is sponsored by the National Natural Science Foundation of China (43318, , 412), 973 project (22CB11156), and the Chinese Academy of Sciences. Many thanks to Ian Montgomery, who made great effort improving the English of this paper. References [1] K. McGarigal, B. Marks, FRAGSTATS, spatial pattern analysis program for quantifying landscape structure. General Technical Report PNW-GTR-351. USDA, Forest service, Pacific, Northwest research station, Portland, [2] D.J. Mladenoff, B. DeZonia, APACK 2. User s Guide. Department of Forest Ecology and Management, University of Wisconsin- Madison, Madison, WI, USA, [3] C.D. Hargis, J.L. Bissonette, J.L. 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King, The use and misuse of neutral landscape models in ecology, Oikos 79 (2) (1997) About the Author XIUZHEN LI received her Ph.D. in 2 from Wageningen University and Research Centre, the Netherlands. She is now a research professor in the Institute of Applied Ecology, Chinese Academy of Sciences. Her research interest is pattern and process analysis of wetland and forest landscapes. About the Author HONG S. HE is a professor at the University of Missouri-Columbia and a research professor at the Institute of Applied Ecology, Chinese Academy of Sciences. He primarily works in the field of landscape ecology and geographical information systems, spatially explicit landscape modeling, and GIS and remote sensing data integration. About the Author RENCANG BU is a Ph.D. candidate and an associate professor in the Lab of Landscape Ecology, Institute of Applied Ecology, Chinese Academy of Sciences. His interests include remote sensing image processing and GIS applications.

13 2638 X. Li et al. / Pattern Recognition 38 (25) About the Author QINGCHUN WEN is a Ph.D. candidate in the Lab of Landscape Ecology, Institute of Applied Ecology, Chinese Academy of Sciences. Her dissertation research is about the effect of landscape boundary networks in a mountainous area of western China. About the Author YU CHANG received his Ph.D. from the Institute of Applied Ecology, Chinese Academy of Sciences in 21. He is now an associate professor in the institute. His research interests involve spatially explicit ecological modeling of forest landscapes. About the Author YUANMAN HU received his Ph.D. from the Institute of Applied Ecology, Chinese Academy of Sciences in He is now a research professor in the institute. His research interests focus on wetland and forest landscapes. About the Author YUEHUI LI received her Ph.D. from the Institute of Applied Ecology, Chinese Academy of Sciences in 23. She is an assistant professor in the institute. Her interest is forest landscape ecology and road ecology.