Measuring habitat fragmentation: An evaluation of landscape pattern metrics

Transcription

1 Methods in Ecology and Evolution 214, 5, doi: /241-21X Measuring habitat fragmentation: An evaluation of landscape pattern metrics Xianli Wang 1 *, F. Guillaume Blanchet 1,2,3 and Nicola Koper 4 1 Department of Renewable Resources, University of Alberta, 751 General Service Building, Edmonton, AB T6G 2H1, Canada; 2 Section of Ecology, Department of Biology, University of Turku, Turku FI-214, Finland; 3 Mathematical Biology Group, Department of Biosciences, Faculty of Biological and Environmental Sciences, University of Helsinki, PO Box 65 (Viikinkaari 1), Helsinki FI-14, Finland; and 4 Natural Resources Institute, University of Manitoba, 317 Sinnott Building, 7 Dysart Rd., Winnipeg, MB R3T 2M6, Canada Summary 1. Landscape patterns influence a range of ecological processes at multiple spatial scales. Landscape pattern metrics are often used to study the patterns that result from the linear and nonlinear interactions between spatial aggregation and abundance of habitat. 2. However, many class-level pattern metrics are highly correlated with habitat abundance, making their use as a measure of habitat fragmentation problematic. 3. We argue that a class-level pattern metric should be (1) able to differentiate landscapes across a range of spatial aggregations, and (2) independent of habitat abundance, if it is to be used to distinguish between effects of habitat amount and fragmentation. 4. Basedonthesecriteria andusingbothsimulated andactual landscapes, we evaluated 64 class-level pattern metrics. These metrics were reclassified into four groups based on their correlation with aggregation and abundance. 5. Among all these metrics, nine were considered robust for fragmentation measurements, which cover most of the characteristics that define pattern, including core area, shape, proximity / isolation, contrast, and contagion / interspersion. 6. Optimal metrics for individual studies will depend on both biological rationales and statistically robust metrics that are appropriate for achieving each study objectives. Key-words: landscape pattern metrics, fragmentation, habitat abundance, simulated landscape, spatial aggregation Introduction Landscapes consist of natural or anthropogenically altered mosaics of patches, and the spatial arrangement of these patchesisreferredtoaslandscape pattern (Turner 1989; Cushman, McGarigal & Neel 28). Landscape pattern can be measured at three levels: patch, class and landscape (McGarigal et al. 22). A single type of habitat patches (e.g. forest, grassland) delineated in a GIS land-use layer is normally defined as a class ( habitat hereafter), which is a unit between patch and mosaic in landscape ecology (Turner 1989). The spatial patterns of a single class have been shown to be important in studies of species conservation (e.g. Murphy & Noon 1992; Villard, Trzcinski & Merriam 1999) and population dynamics (e.g. Fahrig 1997, 1998; Flather & Bevers 22; With 22) due to their high correlations with various ecological processes. For this reason, class-level spatial pattern may be a major interest in many ecological studies (Neel, McGarigal & Cushman 24; Cushman, McGarigal & Neel 28). *Correspondence author. xianli@ualberta.ca Class-level spatial pattern metrics were developed to measure the spatial arrangement of a focal habitat within a landscape. They allow ecologists to quantify average patch shape, size, interpatch distance and patch connectivity of each habitat, and thus, they have become important tools in ecological research (O Neill et al. 1988; Turner 1989; Li & Reynolds 1993; McGarigal & Marks 1995; Haines-Young & Chopping 1996; Gustafson 1998; He, DeZonia & Mladenoff 2; Jaeger 2). A large body of class-level pattern metrics is available (e.g. McGarigal & Marks 1995), but many of them are highly correlated with habitat abundance (Andren 1994; Riitters et al. 1995; Gustafson 1998; Villard, Trzcinski & Merriam 1999; With & King 21; Neel, McGarigal & Cushman 24; Koper, Schmiegelow & Merrill 27; Cushman, McGarigal & Neel 28; Fraterrigo, Pearson & Turner 29; Wang & Cumming 211). Confounding habitat pattern with habitat amount may make it impossible to understand whether it is habitat amount or habitat pattern that drives variation in a changing landscape. The dynamics of habitat pattern within a landscape are normally defined as habitat fragmentation (e.g. Villard, Trzcinski & Merriam 1999; Cumming & Vernier 22), a process whereby a contiguous patch of habitat is transformed into a 214 The Authors. Methods in Ecology and Evolution 214 British Ecological Society

2 An evaluation of landscape pattern metrics 635 number of smaller, convoluted and/or disjunct patches, isolated from each other by a matrix of habitat unlike the original (Wilcove, McClellan & Dobson 1986; Andren 1994; Fahrig 1997; Schmiegelow & M onkk onen 22; Betts et al. 26). Habitat pattern metrics are therefore commonly used measurements of habitat fragmentation (e.g. McGarigal & Marks 1995; Fahrig 23; Turner 25; Smith et al. 29). Although habitat loss is a major consequence of conversion of native to non-native habitats, habitat fragmentation has distinct and sometimes influential effects as well (e.g. Franklin & Forman 1987; Turner 1989; Saunders, Hobbs & Margules 1991; Hargis, Bissonette & Turner 1999). For example, patch shape, a measurement of habitat fragmentation, may determine the herbivory and fruit production for Solanum americanum, an herbaceous flowering plant (Evans et al. 212). Patch shape has also been shown to influence grounddwelling arthropod a (species richness) and b (species turnover) diversity (Orrock et al. 211) and to diminish the abundance of the Indigo Bunting (Passerina cyanea, a North American disturbance-dependent bird species) by negatively affecting nest site selection and reproduction success (Weldon & Haddad 25). In addition, corridors have little effect on habitat amount, but usually fragment the landscape, which in turn can increase the dispersal range of individuals and genes across the landscape (e.g. Tewksbury et al. 22). This can result in an increase in pollination, seed dispersal and plant community diversity (Haddad et al. 211). However, corridors are not always effective in achieving their goals (Simberloff et al. 1992), and in some cases, this may be because species are more sensitive to habitat amount than habitat fragmentation. Understanding whether ecological responses are driven by habitat amount or fragmentation is thus critical to making effective management decisions. Although many studies have attempted to separate measurements of habitat pattern from habitat abundance (e.g. Riitters et al. 1996; Villard, Trzcinski & Merriam 1999; Jaeger 2; Flather & Bevers 22; Remmel & Csillag 23; Betts et al. 26; Koper, Schmiegelow & Merrill 27; Wang & Cumming 29), there are no widely accepted or effective solutions due to the complicated nature of the correlation between the two factors (Smith et al. 29). As stated in Wang and Cumming (211), there are at least two causes of the correlation between metric and habitat abundance: natural correlation and functional correlation. Because some spatial patterns are only evident when a sufficient amount of habitat is present, correlation between certain metrics and habitat abundance is expected (Wang, Hamman & Cumming 212). For example, habitat patches have to be large enough to have core areas to formulate the total core area (TCA) index (McGarigal & Marks 1995). However, metrics that are by design artificially correlated with habitat abundance are of greater concern. For example, the mean nearest-neighbour distance (ENN_MN) (McGarigal & Marks 1995) decreases with the increase in habitat abundance, usually nonlinearly, within its range (Fahrig 23; Wang & Cumming 211), regardless of the spatial arrangement of the patches. Wang and Cumming (211) referred to this as functional correlation. Functional correlation is undesirable because metrics burden by this issue tend to measure variations in abundance instead of landscape pattern. An important potential solution to distinguishing effects of habitat amount and fragmentation is to design experiments a priori to reduce or remove the correlation between habitat amount and fragmentation (e.g. Tewksbury et al. 22; Betts et al. 26). However, this is not always possible, because (i) landscape-scale questions may be addressed post hoc; (ii) even with careful study design, correlations often remain (e.g. McGarigal & McComb 1995); (iii) landscape-scale manipulative experiments are too expensive (e.g. Lindenmayer 29). An alternative is to try to statistically remove correlations between habitat amount and fragmentation (Smith et al. 29). However, statistically eliminating these correlations, either by controlling the total amount of habitat (McGarigal & Marks 1995; With & King 21) or by taking linear or quadratic metric-abundance regression model residuals as the real pattern measurements (Trzcinski, Fahrig & Merriam 1999; Villard, Trzcinski & Merriam 1999; Flather & Bevers 22), are often ineffective. As Koper, Schmiegelow and Merrill (27) have shown, using residuals of the relationship between habitat amount and pattern metrics as an index of fragmentation, to remove their correlation, may bias apparent effects of both habitat amount and fragmentation. Furthermore, landscapes with various levels of spatial aggregation may show different habitat patterns (Fahrig 23; Neel, McGarigal & Cushman 24; Wang and Cumming 211). The residuals used to identify the degree of fragmentation of a landscape are conditional to the sample characteristics and thus cannot be used to predict effects of landscape fragmentation under any other conditions (Wang, Hamman & Cumming 212). We argue that the class-level pattern metric used to quantify habitat fragmentation should be (i) able to discriminate among landscapes when levels of spatial aggregation are different and (ii) independent of habitat abundance, especially at low abundance levels, so that effects of habitat abundance can be separated from effects of habitat fragmentation. Neel, McGarigal and Cushman (24) initiated an important first step in understanding these relationships for class-level metrics and reclassified them according to the correlations each metrics had with abundance and aggregation. However, the metric abundance relationship was quantified using Kendall s s, a rank correlation coefficient unable to capture non-monotonic relationships (Zar 21); consequently, their classification may have overlooked important and influential sources of the metric abundance correlation problem (Wang & Cumming 211). The main objective of this study, therefore, was to devise a more robust metric evaluation procedure that could account for their nonlinear and non-monotonic relationships with habitat amount and aggregation, and re-evaluate the commonly used class-level metrics to determine which are most effective at discriminating among landscapes based on habitat pattern. Using both simulated and actual landscapes, we evaluated how class-level pattern metrics vary with different levels of spatial aggregation and habitat abundance. We used generalized additive models (GAM; Hastie & Tibshirani 199) to

3 636 X. Wang et al. (a) (b) (c) Fig. 1. Illustration of simulated and actual landscapes used in the study. Panels (a) and (b) present simulated landscapes with 25% of habitat abundance, and spatial aggregation levels of % and 1%, respectively. Panel c is an actual landscape (township) in Alberta-Pacific Forest Industries forest management area in Northeast Alberta, Canada. These landscapes are binary maps where black areas are the focal habitat polygons (i.e. old mesic forest). capture linear and nonlinear (including monotonic and non-monotonic) metric abundance relationships and classified metrics by their ability to discriminate landscapes with different aggregation levels and by their independence from habitat abundance. The goals of this study were to develop guidelines explaining the circumstances under which each landscape metric should be used and to highlight the metrics that are more robust to the metric abundance correlation problem. Methods SIMULATED LANDSCAPES 1 Simulated landscapes were constructed as raster maps forming a square grid. We first evaluated the relative effectiveness of each pattern metric in distinguishing among simulated landscapes to ensure that values associated with each metric could be compared against known habitat pattern characteristics. Habitat abundance (p) and spatial aggregation (a measure of spatial autocorrelation; h), the two dominant factors defining most landscapes, were varied among our simulated landscapes. We followed the procedure of Remmel and Csillag (23) for generating simulated landscapes. This landscape simulation method was chosen because it was highly recommended in the literature (e.g. Fortin et al. 23; Remmel & Csillag 23; Turner 25). Each landscape was based on a covariance matrix (C) defined by a spatial aggregation parameter (h) and a contiguity matrix (W) that defines the spatial neighbourhood of influence of each cell. Note that matrix W is a Toeplitz matrix or diagonal constant matrix (Gray 26) because our simulations are performed on a regular grid. C ¼ðI hwþ 1 eqn 1 1 Landscape simulator R script was provided by Dr. Tarmo Remmel, Department of Geography, York University, Toronto, Canada ( The relationship between C and W is defined in eqn 1, where I is an identity matrix and 1 defines a matrix inversion. A fast Fourier transform was then performed on the covariance matrix C resulting in a matrix of complex numbers where the imaginary parts were discarded and the real parts conserved. Gaussian noise was then added to obtain an independent realization of simulated landscapes. In the simulated landscape, the spatial aggregation (h) ranges from (pixels are randomly distributed on the landscape) to 1 (pixels are all aggregated into few isotropic large patches). Each simulated landscape was then used to generate 99 binary landscapes where habitat amount ranged from 1% to 99% (see Fig. 1a and b). In our simulation, the contiguity matrix describes a rook pattern; that is, a cell is influenced by its four direct neighbours. For this reason and because our simulation procedure is isometric, the influence from each neighbour cell could not exceed 25%; otherwise, the cumulative spatial aggregation level would exceed 1% (see Remmel & Csillag 23). In our simulations, we generated binary landscapes with nine different levels of spatial aggregation: 1% (25% for each neighbouring cells), 99% (2475%), 97% (2425%), 95% (2375%), 85% (2125%), 75% (1875%), 5% (125%), 25% (625%) and %. For each of these spatial aggregation levels, 1 landscapes were simulated, to be consistent with the sample sizes of similar studies (Fortin et al. 23; Remmel & Csillag 23). In summary, 9 suites (spatial aggregation levels) of landscapes were generated, making a total of 89,1 simulated landscapes used in the study. The simulated landscapes were also constructed as raster maps of and squares to assess the effects of different spatial extents (Shao & Wu 28). Because they yield the same conclusions as from the grids, only the maps constructed at the highest resolution were presented. ACTUAL LANDSCAPES Actual landscapes were also used to evaluate the class pattern metrics to ensure they are also robust measurements of habitat fragmentation for real landscapes. We selected actual landscapes with a wide range of habitat (forest) amounts that were fragmented by both anthropogenic (e.g. harvesting) and natural (e.g. fire) disturbances (Wang & Cumming 29). The actual landscapes were chosen from a ~8 588 km 2 area in Northeast Alberta, Canada, (55 N, 117 W; 58 N, 11 W), a region dominated by managed boreal forest. Landscape

4 An evaluation of landscape pattern metrics 637 units of approximately 9 ha were determined aprioriby digital forest inventory maps, and were square in shape. 2 We adopted a classification of this inventory to delineate old mesic forest, the habitat for a group of vulnerable and declining songbird species such as blackthroated green warblers (Setophaga virens) and olive-sided flycatcher (Contopus cooperi) (see also Cumming & Vernier 22; Vernier et al. 28), which we used as the focal habitat to test the metrics in the study. This forest type is dominated by different combinations of trembling (or quaking) aspen (Populus tremuloides (Michx.)) and white spruce (Picea glauca (Moench) Voss) with an estimated canopy age greater than 9 years (see also Cumming & Vernier 22). Other cover types include young mesic forests, black spruce forests, pine forests, muskegs, water bodies, anthropogenic areas, recently burned (<3 years) areas, old burned forests, recently harvested forests (<3 years) and old harvested forests. These multiple cover types are critical for the computation of some landscape pattern metrics (see the next section). Altogether, 713 actual landscapes were used in this study (an example of actual landscape is given in Fig. 1c). LANDSCAPE METRIC COMPARISON From the available pool of class-level metrics, 64 metrics representing seven pattern aspects (McGarigal et al. 22; Neel, McGarigal & Cushman 24; Cushman, McGarigal & Neel 28) were tested (Table 1). These include all class-level pattern metrics available in FRAGSTATS, the most widely used program for calculating pattern metrics, and almost all available class-level metrics. They were calculated for each individual landscape (whether simulated or actual) using FRAGSTATS 3. (McGarigal et al. 22). Certain metrics (e.g. Total Edge Contrast Index (TECI) or Mean Edge Contrast Index (ECON_MN)) require the user to choose contrast levels ranging between (low) and 1 (high) among cover types. For simulated landscapes, we set the contrast level as 5 between the two cover types as they are binary. For actual landscapes, contrast levels between water bodies and forested areas were set as 1, newly burned areas and pine forests were given a contrast of 75, pine and aspen forests were set as 5, and old and young aspen forests were given a contrast level of 25. If these contrasts were estimated differently, the metric values will consequently change; however, because the contrasts were applied to all landscapes, the overall trend of the metric value changes across habitat abundance levels would be consistent. Analysis We performed two tests to study the metrics: (i) the landscape differentiability test, to assess how aggregation influences pattern metrics, and (ii) the habitat abundance dependency test, to evaluate how independent a metric is to varying habitat abundance. In general, a lower correlation with habitat abundance and higher correlation with aggregation would be considered optimal for a class-level pattern metric. LANDSCAPE DIFFERENTIABILITY TEST The landscape differentiability test compared each class metric among various aggregation levels. In this test, more emphasis was given to the simulated landscapes because they were 2 Provided by Alberta-Pacific Forest Industries, Edmonton, Canada ( designed (and thus known) to be different at different spatial aggregation levels. Note that habitat in actual landscapes is usually highly aggregated (e.g. Fortin et al. 23; Remmel & Csillag 23), which reduces their range of spatial aggregation levels. Simulated landscapes were compared using 95% confidence ranges(the metric value range between its 25th and 975th percentiles) at each abundance level. We considered the metric values at different aggregation levels to be significantly different if confidence ranges at these aggregation levels did not overlap. In this test, we used actual landscapes to evaluate differentiability by assessing whether the spread of the metric values was wider than that of a single aggregation level of the simulated landscapes. The differentiability of a metric was evaluated using landscapes with less than 5% of habitat. We used a 5% threshold because some evidence suggests that pure pattern effects are detectable only at lower levels of habitat abundance, either between 2 and 3% (Andren 1994; Fahrig 1998) or 3 5% (Flather & Bevers 22). The actual landscapes were used to verify whether the differentiability found with the simulated landscapes was also relevant for actual landscapes. HABITAT ABUNDANCE DEPENDENCY TEST Some pattern measurements are sensitive to both landscape extent and habitat abundance. For example, a landscape with small patches or very low abundance will probably have zero total core area (TCA). On the other hand, same habitat patches in landscapes of different extents may have different pattern measurements, for example, mean nearest-neighbour distance (ENN_MN) (see Wang & Cumming 211). For this reason, we performed the habitat abundance dependency test for the simulated and actual landscapes separately, as their extents were notably different. The habitat abundance dependency test was carried out in three steps. First, a series of subsets of landscapes were selected. The subsets were selected such that habitat abundance is below 1%, 2%,..., 1% at increments of 1. For simulated landscapes, this step was performed over the nine suites of simulated landscapes pooled together. Next, we fitted a generalized additive model (GAM) between each candidate metric and habitat abundance for each selected subset of landscapes. GAMs were used because they account for the functional nonlinear relationships between metrics and habitat abundance without having to be explicitly specified (Wang & Cumming 211). Finally, we determined the strength of the metric abundance relationship with the GAM s adjusted coefficient of determination (R 2 adj ). A metric was considered to have low correlation with habitat abundance if at least the first three sequential GAM R 2 adj values, from 1% to 3% of habitat abundance (Andren 1994), were less than a predefined R 2 adj threshold. The more habitat abundance levels where the correlations were low, the better the metric is considered. To ensure that our results were not driven by our selection of an arbitrary R 2 adj threshold, we considered a range of threshold R 2 adj values, from 1to9by 1-unit increments. Although we discussed the results

5 638 X. Wang et al. Table 1. Class-level pattern metrics compared in this study. These metrics were organized into four categories (where p = habitat abundance, h = aggregation level, and the subscript H and L stand for high and low, respectively): p H h H = highly correlated with both habitat abundance and spatial aggregation; p H h L = highly correlated with habitat abundance but weakly correlated with spatial aggregation; p L h H = weakly correlated with habitat abundance but highly correlated with spatial aggregation; p L h 1 L = weakly correlated with both habitat abundance and spatial aggregation, but could not distinguish between any landscape types; p L h 2 L = weakly correlated with both habitat abundance and aggregation, but could differentiate between actual and simulated landscapes. R 2 adj -simulated and R2 adj-actual are the generalized additive model (GAM) adjust coefficients of determination for metric abundance at p = 3%. In addition, sequential R 2 adj 5 for p 3% are highlighted with *, sequential R 2 adj 5 for p 4% are marked with **, and sequential 5 for p 5% are identified with ***. Metric Abbreviation Full Name Aspect R 2 adj -simulated R2 adj -actual p H h H AREA_CV Coefficient of Variation of Mean Patch Area AREA/EDGE/DENSITY 19* 63 COHESION Patch Cohesion Index CONNECTIVITY CONTIG_AM Area Weighted Mean Contiguity Index SHAPE 5* 57 CONTIG_MN Mean Contiguity Index SHAPE 79 11*** CPLAND Core Percentage of Landscape CORE AREA 28*** 88 CWED Contrast Weighted Edge Density CONTRAST DCAD Disjunct Core Area Density CORE AREA ED Edge Density AREA/EDGE/DENSITY 86 9 ENN_CV Coefficient of Variation of Euclidian Nearest PROXIMITY/ISOLATION 63 14*** Neighbour Index ENN_SD Standard Deviation of Euclidian Nearest PROXIMITY/ISOLATION 7 3*** Neighbour Index FRAC_AM Area Weighted Mean Fractal Dimension Index SHAPE FRAC_CV Coefficient of Variation of Mean Fractal SHAPE 89 43*** Dimension Index FRAC_MN Mean Fractal Dimension Index SHAPE 89 16*** FRAC_SD Standard Deviation of Mean Fractal SHAPE 9 43*** Dimension Index LSI Landscape Shape Index AREA/EDGE/DENSITY NDCA Number of Disjunct Core Areas CORE AREA NP Number of Patches AREA/EDGE/DENSITY 39 48*** PARA_AM Area Weighted Mean Perimeter Area Ratio SHAPE 48* 55 PARA_MN Mean Perimeter Area Ratio SHAPE 74 11*** PARA_SD Standard Deviation of Mean Perimeter Area Ratio SHAPE 54 32*** PD Patch Density AREA/EDGE/DENSITY 39 47*** PLADJ Percentage of Like Adjacencies CONTAGION/INTERSPERSION 48* 56 SHAPE_CV Coefficient of Variation of Mean Shape Index SHAPE 8 6 TCA Total Core Area CORE AREA 28*** 82 TE Total Edge AREA/EDGE/DENSITY p H h L AREA_AM Area Weighted Mean Patch Area AREA/EDGE/DENSITY 9** 57 AREA_MN Mean Patch Area AREA/EDGE/DENSITY 63 12*** AREA_SD Standard Deviation of Mean Patch Area AREA/EDGE/DENSITY 22* 57 DIVISION Landscape Division Index CONTAGION/INTERSPERSION 11** 69 ECON_MN Mean Edge Contrast Index CONTRAST 65 6*** ECON_SD Standard Deviation of Edge Contrast Index CONTRAST 55 *** ENN_AM Area Weighted Mean Euclidian Nearest PROXIMITY/ISOLATION 75 25*** Neighbour Index ENN_MN Mean Euclidian Nearest Neighbour Index PROXIMITY/ISOLATION 77 28*** GYRATE_AM Area Weighted Mean of Radius of Gyration AREA/EDGE/DENSITY 29* 63 Distribution GYRATE_MN Mean Radius of Gyration Distribution AREA/EDGE/DENSITY 89 17*** LPI Largest Patch Index AREA/EDGE/DENSITY 13** 76 MESH Effective Mesh Size CONTAGION/INTERSPERSION 11** 65 PROX_AM Area Weighted Mean Proximity Index PROXIMITY/ISOLATION 22** 53 PROX_MN Mean Proximity Index PROXIMITY/ISOLATION 28** 62 PROX_SD Standard Deviation of Proximity Index PROXIMITY/ISOLATION 12** 65 SHAPE_AM Area Weighted Mean Shape Index SHAPE 41* 64 SHAPE_MN Mean Shape Index SHAPE 92 16*** SHAPE_SD Standard Deviation of Mean Shape Index SHAPE SPLIT Splitting Index CONTAGION/INTERSPERSION 48 2*** p L h H AI Aggregation Index CONTAGION/INTERSPERSION 47* 4*** CAI_AM Area Weighted Mean Core Area Index CORE AREA 16*** 49*

6 An evaluation of landscape pattern metrics 639 Table 1. (continued) Metric Abbreviation Full Name Aspect R 2 adj -simulated R2 adj -actual CAI_CV Coefficient of Variation of Core Area Index CORE AREA 1*** 6*** CAI_SD Standard Deviation of Core Area Index CORE AREA 31*** 28*** CLUMPY Clumpy Index CONTAGION/INTERSPERSION 7*** 21*** CORE_CV Coefficient of Variation of Core Area CORE AREA 9*** 24*** DCORE_CV Coefficient of Variation of Disjunct Core CORE AREA 13*** 48* Area Distribution nlsi Normalized Landscape Shape Index AREA/EDGE/DENSITY 47* 41*** PAFRAC Perimeter Area Fractal Dimension SHAPE 18*** 4*** PROX_CV Coefficient of Variation of Proximity Index PROXIMITY/ISOLATION 2*** 7*** p L h 1 L CORE_AM Area Weighted Mean Core Area CORE AREA 6** 47* CORE_MN Mean Core Area CORE AREA 19** 12*** CORE_SD Standard Deviation of Core Area CORE AREA 1** 48* DCORE_AM Area Weighted Mean Disjunct Core Area CORE AREA 5*** 29*** Distribution DCORE_MN Mean Disjunct Core Area Distribution CORE AREA 13*** 32*** DCORE_SD Standard Deviation of Disjunct Core Area Distribution CORE AREA 7*** 32*** p L h 2 L CAI_MN Mean Core Area Index CORE AREA 35*** 11*** CONNECT Connectance Index CONNECTIVITY 25* 12*** ECON_AM Area Weighted Mean Edge Contrast Index CONTRAST 17*** 9*** TECI Total Edge Contrast Index CONTRAST 25*** 9*** obtained with the different R 2 adj thresholds, we gave more emphasis on the classification obtained for the threshold of R 2 adj = 5. A metric was considered to have minimal dependence on habitat abundance if its values showed the same pattern of low correlations at lower levels of abundance for both the simulated and actual landscape types. We organized all class-level pattern metrics in four categories according to their ability to differentiate landscapes between aggregation values at low levels ( 5%) of habitat abundance (determined by landscape differentiability test) and their correlations with habitat abundance (habitat abundance dependency test). The categories included metrics classified by the cross-combinations of high and low correlations between metrics and habitat abundance, and the high and low ability of metrics to differentiate between spatial aggregation levels. The following labelling system was used in the result: p H = metrics highly correlated with habitat abundance, p; p L = metrics weakly correlated with p; h H = metrics highly correlated with spatial aggregation, h;andh L = metrics weakly correlated with h. The four categories therefore include: p H h H, p H h L, p L h H and p L h L. All analyses were performed using the R statistical language (R Development Core Team 211). The generalized additive models were constructed using the mgcv package (Wood 26). Results The first category defined metrics highly correlated with habitat abundance and aggregation (p H h H ). They varied either monotonically (Fig. 2b) or following a unimodal pattern (Fig. 2a,c and d) along p. They were considered inappropriate for fragmentation measurements because of their high correlations with habitat abundance; however, they would be suitable for distinguishing among landscapes of different spatial aggregation at fixed levels of habitat abundance. Twenty-five metrics belonged to this category (Table 1). Among these, nine metrics showed high correlations (R 2 adj 5) with p in both simulated and actual landscapes, whereas the remaining 15 metrics were highly correlated (R 2 adj 5) with habitat abundance for either simulated or actual landscapes, but not both (Table 1). The second category included metrics highly correlated with habitat abundance but unable to differentiate among landscapes of different aggregation levels (p H h L ;Fig. 3showedtwo examples). They are not recommended to be used for measuring habitat fragmentation. This category included 19 metrics including popular metrics such as the mean nearest-neighbour distance (ENN_MN) and Mean Shape Index (SHAPE_MN) (Table 1). These first two categories included 44 of the 64 studied metrics, all of which were strongly correlated with habitat abundance, making them susceptible to the functional correlation problem (Wang & Cumming 211). The third category encompasses 1 pattern metrics that showed little correlation with habitat abundance but were highly correlated with aggregation (p L h H ). These metrics show the most promise in distinguishing between effects of habitat amount and fragmentation (Fig. 4). Perimeter area fractal dimension (PAFRAC) (Fig. 4a) and Clumpy Index (CLUMPY) (Fig. 4b) were two metrics with low habitat abundance dependency but high landscape differentiability. The resultsobtainedwithclumpy(fig.4b)wereinagreement with Neel, McGarigal and Cushman (24) as well as McGari-

7 64 X. Wang et al. (a) (b) (c) (d) Fig. 2. Landscape differentiability test result for ED, TCA, PD and CWED metrics, and they characterize group phhh (metrics highly correlated with both habitat abundance and spatial aggregation). Grey area = 95% confidence ranges of the metric values for the simulated landscapes with spatial aggregation ranging from to 1%. Points = actual landscapes. Overlap between confidence ranges is highlighted with darker shading. Percentages in each panel illustrate the aggregation levels of the simulated landscapes. (a) 1 (b) MESH DIVISION Habitat abundance (%) Habitat abundance (%) (a) (b) % 1 7 1% CLUMPY PAFRAC Fig. 3. Landscape differentiability test result for DIVISION and MESH metrics, which characterize group phhl (metrics highly correlated with habitat abundance and weakly correlated with spatial aggregation). Grey area = 95% confidence ranges of the metric values for the simulated landscapes with spatial aggregation ranging from to 1%. Points = actual landscapes. Overlap between confidences intervals is highlighted with darker shading. 1% 1 5 % Habitat abundance (%) Habitat abundance (%) gal et al. (22) who developed this metric to quantify spatial aggregation independently of habitat area and landscape grain size. Their results also show that variation in the simulation 1 Fig. 4. Landscape differentiability test result for PAFRAC and CLUMPY metrics, which characterize group plhh (metrics weakly correlated with habitat abundance and highly correlated with spatial aggregation). Grey area = 95% confidence ranges of the metric values for the simulated landscapes with spatial aggregation ranging from to 1%. Points = actual landscapes. Overlap between confidences intervals is highlighted with darker shading. Percentages in each panel illustrate the aggregation levels of the simulated landscapes. approaches to generate landscapes has minimal impact on the metrics behaviour, which support our findings. Metrics in this category are reliable measurements for habitat fragmentation

8 An evaluation of landscape pattern metrics dency on habitat abundance for the actual landscapes, although the correlations were low only when the abundance of habitat p 3% in the simulated landscapes. Therefore, they might be suitable for distinguishing between habitat amount and fragmentation for ecosystems where the focal habitat type is rare, such as tall-grass prairie (Samson, Knopf & Ostlie 24). Area Weighted Mean Core Area Index (CAI_AM) and Coefficient of Variation of Disjunct Core Area Distribution (DCORE_CV) showed low correlation with habitat abundance when p 3% in actual landscapes, but were consistently weakly correlated with habitat abundance in simulated landscapes. Overall, nine of the 14 metrics (Table 2, grey) showed consistently low correlation ( 5) with habitat abundance up to 5% in both simulated and actual landscapes (see Table 3 for p > 5%), suggesting that these are more robust fragmentation measurements. These nine class-level metrics from five pattern aspects (McGarigal et al. 22) were therefore deemed suitable for habitat fragmentation measurements as they are only mildly influenced by habitat abundance (Table 2). However, no metrics measuring AREA/EDGE/DENSITY and CONNECTIVITY were chosen in the final selections. With the varying R2adj thresholds in the habitat abundance dependency test, metric selection was relatively insensitive to R2adj thresholds between 3 and 6 (Table 3). With an R2adj threshold of 4, the results of Table 2 were unchanged. When we increased the threshold value to 6, number of patches (NP) and patch density (PD) were the only new metrics added into the final list. By decreasing the R2adj threshold below 3, fewer metrics were selected, and when R2adj = 1, only two metrics, Coefficient of Variation of Core Area Index because they were relatively insensitive to variation in habitat abundance, but were powerful in differentiating landscapes with different spatial aggregation levels. The last category also comprised 1 metrics, which are weakly correlated with both habitat abundance and aggregation (plhl). We further divided this category into two subgroups: one containing metrics not capable of discriminating landscape types (pl h1l, e.g. Fig. 5a,b), while the other could not differentiate simulated landscapes, but was successful in distinguishing the differences among actual landscapes (pl h2l, e.g. Fig. 5c,d). Metrics from the first subgroup are not suitable for fragmentation measurement. Metrics in the second subgroup showed unique qualities. For example, Total Edge Contrast Index (TECI) (Fig. 5c) varied substantially among actual landscapes but not the simulated landscapes. Connectance Index (CONNECT), Area Weighted Mean Edge Contrast Index (ECON_AM) and Mean Core Area Index (CAI_MN) showed a similar feature. This suggested that metrics from the second subgroup might be considered suitable for fragmentation measurements depending on the ecological questions asked (see Discussion). From the classification generated by combining the landscape differentiability test and the habitat abundance dependency test, only the 1 metrics in category plhh qualified as consistently reliable landscape fragmentation measurements. However, if we include the four metrics in pl h2l owing to their power in differentiating actual landscapes, 14 metrics in total could be considered candidates for fragmentation measurement (Table 2). Among these 14 metrics, Normalized Landscape Shape Index (nlsi), Aggregation Index (AI) and Connectance Index (CONNECT) had consistently low depen- (b) DCORE_AM % (d) 7 7 CORE_CV % 5 % 25 % % 75% (c) TECI 1% 1% 99%97% 95% DCORE_MN (a) Fig. 5. Landscape differentiability test result for DCORE_MN, DCORE_AM, TECI and CORE_CV metrics, and they characterize group plhl (metrics weakly correlated with both habitat abundance and spatial aggregation). Grey area = 95% confidence ranges of the metric values for the simulated landscapes with spatial aggregation ranging from to 1%. Points = actual landscapes. Overlap between confidences intervals is highlighted with darker shading. Percentages in each panel illustrate the aggregation levels of the simulated landscapes Habitat abundance (%) 1 2 Habitat abundance (%)

9 642 X. Wang et al. Table 2. Metrics with low correlations with habitat abundance measured by the GAM R 2 adj and high correlation with spatial aggregation by comparing the 95% confidence ranges among the aggregation levels. R 2 adj -simulated and R2 adj-actual are GAM adjust coefficients of determination for metric-abundance at p = 3%. Sequential R 2 adj 5 for p 3% are highlighted marked with *, sequential R 2 adj 5 for p 4% are marked with **, not shown, and sequential R 2 adj 5 for up to p 5% are identified with ***. See Table 1 for metric names Metric (CAI_CV) and Coefficient of Variation of Proximity Index (PROX_CV), were retained. Above 7, many metrics were considered suitable because metrics in group p H h L were reclassified into p L h H. Discussion Habitat abundance dependency test R 2 adj -simulated R2 adj -actual Area/Edge/Density nlsi 47* 41*** Shape PAFRAC 18*** 4*** Core Area CAI_AM 16*** 49* CAI_CV 1 1*** 6*** CAI_MN 35*** 11*** CAI_SD 31*** 28*** CORE_CV 1 9*** 24*** DCORE_CV 13*** 48* Proximity/Isolation PROX_CV 2*** 7*** Contrast ECON_AM 1 17*** 9*** TECI 1 25*** 9*** Contagion/Interspersion AI 47* 4*** CLUMPY 7*** 21*** Connectivity CONNECT 25* 12*** 1 These metrics do not differentiate between simulated landscapes, but are able to separate actual and simulated landscapes. Many metrics are correlated with habitat amount along nonmonotonic patterns (e.g. Hargis, Bissonette & David 1998; Fortin et al. 23; Remmel & Csillag 23; Neel, McGarigal & Cushman 24), making the use of the Kendall s s problematic for distinguishing among fragmentation metrics (cf. Neel, McGarigal & Cushman 24). Because our approach allowed for nonlinear relationships among variables, our results categorized pattern metrics differently than did Neel, McGarigal & Cushman (24). For example, in Neel, McGarigal and Cushman (24), edge density (ED), patch density (PD), disjunct core area density (DCAD), and Landscape Shape Index (LSI) were weakly correlated with habitat abundance but highly correlated with spatial aggregation, while our analyses showed that they are highly correlated with both habitat abundance and spatial aggregation (see Table 3, Fig. 2, and Appendix S1). While Neel, McGarigal and Cushman (24) took the important first step in classifying pattern metrics according to their correlation with habitat pattern and composition, allowing for non-monotonic relationships between pattern metrics and habitat abundance was necessary to more appropriately quantify these correlations. Many metrics considered in this study have non-monotonic relationships with increasing abundance (e.g. Fig. 5d, Fig. I-2, and Fig. I-43); therefore, the confidence ranges of certain metrics may overlap at some habitat abundance levels but not others. The differentiability of such metrics was further examined by considering the full range of aggregation across the full range of habitat abundance. For example, the 1% aggregation level confidence range of CORE_CV overlaps with the confidence ranges of the other aggregation levels for habitat abundance below 3% (Fig. 5d). A careful study of the behaviour of this metric indicates that the overlap was due to its nonlinear relationship with habitat abundance; however, the differentiation pattern is still clearly shown, despite the overlap. For this reason, we considered CORE_CV to be sensitive to variations in aggregation. Metrics that are constrained by habitat amount tend to be sensitive to habitat abundance. For example, the total core area (TCA) metric is constrained by the amount of habitat in a landscape (it is impossible to have more total core area (TCA) than there is habitat in the landscape). Consequently, the difference between metric values at different habitat abundance levels could be due to habitat abundance, rather than habitat pattern. The high correlation between the p H h H metrics and habitat abundance makes this group unsuitable for fragmentation measurement among landscapes with large differences in habitat abundance. However, many of these metrics may still be used to better understand static landscape pattern. For example, the amount of total core area (TCA) in a landscape could determine the carrying capacity of landscapes for edgesensitive species. Further, within a portion of the habitat abundance range, some of the metrics in p H h H are only weakly correlated with habitat abundance, making them useful fragmentation measurement tools within a particular range of abundance. For example, patch density (PD) was weakly correlated with abundance when p ranged from 1 to 3% (Fig. 2c). Similarly, edge density (ED) would be suitable for 3 < p < 7 (Fig. 2a), Landscape Shape Index (LSI) for 2 < p < 6 (Fig. I-5) and contrast weighted edge density (CWED) for 3 < p < 7; (Fig. I-9). Also, the Mean ContiguityIndex(CONTIG_MN,Fig.I-23),MeanFractalDimension Index (FRAC_MN, Fig. I-16), Standard Deviation of Mean Fractal Dimension Index (FRAC_SD, Fig. I-18), Coefficient of Variation of Mean Fractal Dimension Index (FRAC_CV, Fig. I-19) and mean perimeter area ratio (PARA_MN, Fig. I- 2) show good differentiation across most habitat amounts, except between 15% < p < 25%. Therefore, they provide good indices of habitat fragmentation across most values of habitat amount, except somewhere within that narrow range of low moderate amounts of habitat. Pattern metrics highly correlated with habitat abundance but unable to differentiate among landscapes of different aggregation levels (p H h L ) fail to differentiate landscape types and are not useful for distinguishing among landscapes

10 An evaluation of landscape pattern metrics 643 Table 3. The Generalized Additive Models adjusted coefficient of determination (R 2 adj )formetric abundance at p 1%, p 2%,...and p 9% for the simulated landscapes, and p 1%, p 2%,...and 5% for the actual landscapes. Configuration metrics were organized into four categories based on both landscape types: p H h H = highly correlated with both habitat abundance and spatial aggregation; p H h L = highly correlated with habitat abundance but weakly correlated with spatial aggregation; p L h H = weakly correlated with habitat abundance but highly correlated with spatial aggregation; p L h 1 L = weakly correlated with both habitat abundance and spatial aggregation, but could not distinguish between any landscape types; p L h 2 L = weakly correlated with both habitat abundance and aggregation, but could make a distinction between actual and simulated landscapes Simulated landscapes Actual landscapes Landscape Types Habitatabundance(%) p H h H AREA_CV COHESION CONTIG_AM CONTIG_MN CPLAND CWED DCAD ED ENN_CV ENN_SD FRAC_AM FRAC_CV FRAC_MN FRAC_SD LSI NDCA NP PARA_AM PARA_MN PARA_SD PD PLADJ SHAPE_CV TCA TE p H h L AREA_AM AREA_MN AREA_SD DIVISION ECON_MN ECON_SD ENN_AM ENN_MN GYRATE_AM GYRATE_MN LPI MESH PROX_AM PROX_MN PROX_SD SHAPE_AM SHAPE_MN SHAPE_SD SPLIT p L h H AI CAI_AM CAI_CV CAI_SD CLUMPY CORE_CV DCORE_CV

11 644 X. Wang et al. Table 3. (continued) Simulated landscapes Actual landscapes Landscape Types Habitatabundance(%) nlsi PAFRAC PROX_CV p L h 1 L CORE_AM CORE_MN CORE_SD DCORE_AM DCORE_MN DCORE_SD p L h 2 L CAI_MN CONNECT ECON_AM TECI according to their spatial pattern.however,the information they provide about the landscape features they were designed to measure may still be helpful. For example, Mean Euclidean Nearest Neighbour Index (ENN_MN) and Area Weighted Mean Euclidian Nearest Neighbour Index (ENN_AM) may be useful for understanding the ability of species to disperse among habitat patches. Nonetheless, users must be aware of the risk that apparent habitat pattern effects measured by such metrics might be driven by variation in habitat abundance among landscapes. Jaeger (2) developed a number of CONTAGION/ INTERSPERSION indices of fragmentation including MESH, SPLIT and DIVISION. Some of the benefits of these metrics include characterizing the anthropogenic penetration of landscapes based on the distribution function of the remaining patch sizes (Jaeger 2). We found these metrics to be highly correlated with habitat abundance in the actual landscapes (Table 3) and unable to differentiate among landscapes of different aggregation levels (e.g. Fig. 3). These metrics may be useful to measure human penetration impacts (such as the seismic lines in the boreal forest of Alberta, Canada). However, they may not be as effective in reflecting habitat spatial aggregation changes compared with the Clumpy Index (CLUMPY), which was also classified in the CONTAGION/INTERSPER- SION indices group. Metrics that are weakly correlated with habitat abundance but can differentiate among landscapes of different aggregation levels (p L h H ) are the best choices for measuring landscape fragmentation. This is due to their low correlation with habitat abundance and because they are strongly link to spatial aggregation. Although p L h H contains only 1 metrics, it reflects a broad suite of metric types, including Clumpy Index (CLUMPY) for CONTAGION/INTERSPERSION, perimeter area fractal dimension (PAFRAC) for SHAPE, Normalized Landscape Shape Index (nlsi) for AREA/EDGE/ DENSITY and Coefficient of Variation of Proximity Index (PROX_CV) for PROXIMITY/ISOLATION. Among the metrics measuring CORE AREA, Area Weighted Mean Core Area Index (CAI_AM) is perhaps the most intuitive to interpret as it is the only metric that is not a measure of variance. For this reason, we recommend CAI_AM as a broadly appropriate landscape fragmentation measurement index for measuring core area. The last group, p L h L, encompasses some metrics that can differentiate actual and simulated landscape and others that cannot. Metrics in p L h 1 L are generally not well suited to describing habitat fragmentation because they fail to pass the differentiability test. Conversely, metrics within p L h 2 L are able to discriminate landscapes of different aggregation levels. Metrics within p L h 2 L are unusual because they showed variations for actual but not for simulated landscapes (Fig. 5c and 5d and Appendix S1). We suspect part of this phenomenon is caused by the contrast levels we assigned between different habitat classes, a requirement in the computation of these metrics (McGarigal et al. 22). For example, Total Edge Contrast Index (TECI) is defined as: the sum of the lengths (m) of each edge segment involving the corresponding patch type multiplied by the corresponding contrast weight, divided by the sum of the lengths (m) of all edge segments involving the same type, multiplied by 1 (to convert to a percentage) (McGarigal & Marks 1995). Because the contrast weight was set to 5 inthe binary simulated landscapes, Total Edge Contrast Index (TECI) values for all simulated landscapes should be close to 5%, which is consistent with our results (Fig. 5c). Because these metrics rely, at least partially, on prior information of users and the number of habitat classes in the landscapes, variation reflects some aprioriassessments of the relationships among habitat classes. Such metrics should be used only in situations where there is no ambiguity as to how contrast levels are assigned among habitat classes. It is well known that the characteristics of the habitat define species niches (Hutchinson 1957). When choosing a landscape pattern metric, the particularities of the niche of the studied species should be considered. For example, a metrics