- Email: [email protected]
Comparing forest fragmentation in Eastern U.S. forests using patch-mosaic and gradient surface models
Accepted Manuscript Comparing forest fragmentation in Eastern U.S. forests using patch-mosaic and gradient surface models
Amy E. Frazier, Peter Kedron PII: DOI: Reference:
S1574-9541(17)30143-7 doi: 10.1016/j.ecoinf.2017.08.002 ECOINF 786
To appear in:
Ecological Informatics
Received date: Revised date: Accepted date:
27 May 2017 22 August 2017 23 August 2017
Please cite this article as: Amy E. Frazier, Peter Kedron , Comparing forest fragmentation in Eastern U.S. forests using patch-mosaic and gradient surface models, Ecological Informatics (2017), doi: 10.1016/j.ecoinf.2017.08.002
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ACCEPTED MANUSCRIPT Comparing Forest Fragmentation in Eastern U.S. Forests using Patch-Mosaic and Gradient Surface Models Amy E. Frazier*1,2 and Peter Kedron1 1
Department of Geography, Oklahoma State University, 337 Murray Hall, Stillwater, OK, 74078
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Center for Applications of Remote Sensing, Department of Geography, Oklahoma State University, 337 Murray Hall, Stillwater, OK, 74078
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*Corresponding author: Email: [email protected]; Address: 337 Murray Hall, Stillwater, OK 74078
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ACCEPTED MANUSCRIPT Abstract
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Forest fragmentation is an ongoing threat to forest communities in the eastern United States where a prevailing pattern of dispersed, low intensity urban development continues to expand the wildland urban interface (WUI). Many large scale forest monitoring initiatives rely on pixel-based remote sensing classifications to quantify fragmentation patterns because they fit seamlessly into the patch-mosaic model (PMM) and can be analyzed using conventional landscape metrics (e.g., FRAGSTATS). The PMM has been key to advancing our understanding of patch dynamics, but some argue it may be inconsistent with ecological theory as it ignores the inherent gradient nature of environments. Studies have advocated a shift toward gradient surface models (GSM), but tools for quantifying spatial patterns in continuous gradient surfaces are limited. We introduce an approach for extracting landscape pattern information from gradient surfaces using a thresholding approach to discretize gradient surfaces into multiple discrete maps according to forest cover density. These maps can then be analyzed using conventional landscape metric tools. Metric values are plotted against density thresholds as a scalogram and interpreted to understand the dynamics of landscape spatial structure. By performing a comparative analysis of two forested ecoregions in the eastern U.S. that have undergone development pressures, we demonstrate how information on landscape structure dynamics at various forest cover densities can be extracted from gradient surfaces to provide additional information on the density scales where fragmentation is pronounced in each region. Results indicate there are ecological thresholds at certain forest cover proportions that can potentially inform management decisions.
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Keywords: landscape metrics; spatial pattern analysis; patch-mosaic model; gradient surface model; scalograms
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Introduction
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Forest fragmentation is one of the greatest threats to global biodiversity (Kupfer and Franklin 2009) and is an ongoing threat to forest communities in the eastern United States (Riitters et al. 2012) where most land is privately owned and therefore unprotected (Smith et al. 2009). Fragmentation caused by urban development is of particular interest because it is the main driver of land use and land cover change in the eastern United States (USDA Forest Service, 2011). A prevailing pattern of dispersed, low intensity urban development continues to expand the wildland urban interface (WUI), which is where urban and suburban development intermingle with undeveloped wildland vegetation (Radeloff et al. 2005). As development penetrates the WUI, anthropogenic impacts are introduced deep into intact forest (Theobald et al. 1997; Stein et al. 2009; Riitters et al. 2012), increasing the risk of fire danger, species invasions, and biodiversity loss (Radeloff et al. 2005).
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Regional, national, and international scale initiatives prioritize measurement and monitoring of forest fragmentation at broad spatial scales (Kupfer 2006), where land cover maps derived from remote sensing images are frequently employed. Satellite or aerial images are converted into land cover information through pixel-based classification techniques in which each pixel is assigned a single land cover class. Pixel-based classifications are used extensively in landscape ecological studies because they fit seamlessly into the patch-mosaic model (PMM), where the landscape is conceptualized as a mosaic of discrete patches. The PMM is lauded for its conceptual simplicity (Forman 1995) and the ease with which it can incorporate categorical maps produced from remote sensing classifications into landscape analysis, and many toolsets have been developed explicitly for quantifying PMM spatial patterns from categorical maps (e.g., FRAGSTATS: McGarigal et al. 2012).
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The PMM has no doubt advanced our understanding of pattern-process relationships (Turner 2005), particularly fragmentation (Uuemaa et al. 2013), but it can be inconsistent with ecological theory as it ignores the inherent gradient nature of environments and land covers (McGarigal and Cushman 2005; Cushman et al. 2010). This issue is particularly pronounced at the broad spatial scales commonly adopted in forest fragmentation studies, as pixel-based classifications often underrepresent spatial heterogeneity. Gradient-based classifications have been proposed and debated in landscape ecology for decades as an alternate way of conceptualizing and representing landscape structure (McIntyre and Hobbs 1999; Manning et al. 2004; McGarigal and Cushman 2005; Cushman et al. 2010; Lausch et al. 2015). Gradients are able to capture and represent a greater amount of landscape heterogeneity because pixels can assume ratio values according to the proportion of land cover present in the pixel and therefore are not confined to a single land cover class. However, gradient datasets are not directly compatible with most available spatial pattern analysis tools, which require hard boundaries for metric computations, making it challenging for researchers to incorporate these datasets into their analyses. Surface metrics have emerged as an alternative method for quantifying patterns in gradient datasets. Originally developed for microscopy and molecular physics, surface metrics were recently introduced to landscape ecologists as a means of analyzing gradient landscapes (McGarigal et al. 2009). While there is growing support and increased use of surface metrics in the ecological literature (Moniem and Holland 2013; Scown et al. 2015; Moniem et al. 2016; Frazier 2016), widespread adoption has been hindered by several factors. First, many surface metrics are constructed to evaluate ideal bearing properties of mechanical surfaces, which are defined as being “smooth with relatively deep scratches to hold and distribute lubricant” (Stewart 1990, 1). This concept does not translate flawlessly into ecology, and therefore interpretation of surface metrics is not always intuitive from a landscape perspective. Second, many surface metrics suffer from correlation and redundancy issues similar to those found with conventional landscape metrics and graph approaches. Lastly, widespread adoption of surface metrics 3
ACCEPTED MANUSCRIPT has been hindered by limited access to software, although the upcoming version of FRAGSTATS is expected to contain some of these metrics.
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With these limitations, researchers are tasked with finding alternative approaches to incorporate continuous, gradient surface models into landscape investigations and bridge the gaps between the patchmosaic and the gradient surface paradigms. In this study, we introduce an approach for extracting increased landscape pattern information from gradient surfaces using a common toolset (i.e., FRAGSTATS). Specifically, we demonstrate how a thresholding approach can be used to discretize gradient surfaces into multiple discrete maps that can then be analyzed as patch-mosaic models. We create scalograms of these multiple metric values showing metric change across a continuum of forest density scales and compare them to single-value metrics computed for patch-mosaic landscapes to illustrate how the additional information can be analyzed in an ecological context. We frame our study around a comparison of forest fragmentation in two ecoregions in the eastern U.S. Study Area and Data
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With a lack of comparative regional assessments of forest fragmentation noted in the literature (Riitters et al. 2012), we elected to compare two ecoregions that differ in their level of urban development: (1) the Southeastern USA Plains (SEP) nested within the Eastern Temperate Forests ecoregion, and (2) the Atlantic Highlands (AH) nested within the Northern Forests ecoregion (Omernik 1987). The SEP includes several major development corridors (I-85, I-95, etc.) and comprises major cities such as Baltimore, M.D., Charlotte, N.C., and Atlanta, G.A. It also includes several rapidly developing Midwest cities that have experienced sprawling urban growth in recent decades, such as Nashville, TN, as well as urban fringes of developing cities in Texas including Dallas/Fort Worth, Houston, Austin, and San Antonio (Fig. 1). The SEP region contains over 250,000 km2 of total WUI (Radeloff et al. 2005), amounting to about 25% of the region. In comparison, the AH region is located in the Northeast U.S. and comprises portions of Pennsylvania, New York, and New England. The AH does not contain any major cities over 500,000 people or large development corridors. However, proportionally the region contains approximately the same amount of WUI with 40,000 km2, also about 25% (Radeloff et al. 2005). The similarities in the amount of WUI and differences in the likely proximate causes of fragmentation between the two regions provides an ideal case for examining forest cover patterns.
Figure 1. The two study regions for comparative analysis: the Southeastern USA Plains and the Atlantic Highlands 4
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The National Land Cover Database (NLCD) developed by the Multi-Resolution Land Characteristics Consortium (MRLC) is the primary source of land cover data in the United States (Wickham et al. 2010). The MRLC produces several products including a seamless, 16-class thematic, land cover map commonly referred to as the ‘NLCD’ and a seamless, gradient surface representing percent tree canopy cover (TCC) across the continuous United States. Both datasets are based on Landsat images over the same time period and have the same nominal spatial resolution (30m) (Xian et al. 2011; Coulston et al. 2012, 2013; Tipton et al. 2012; Homer et al. 2015), thereby offering a unique opportunity to examine forest cover from both a patch-based and gradient perspective. We downloaded the 2011 NLCD and TCC rasters for the conterminous U.S. from the MRLC (http://www.mrlc.gov/) and thematically aggregated the NLCD into eight classes (Water, Developed, Barren, Forest, Shrubland, Herbaceous, Planted/Cultivated, Wetlands). This aggregation produced a single forest class, which included ‘Deciduous Forest’, ‘Evergreen Forest’, ‘Mixed Forest’, and ‘Woody Wetlands’ following Riitters et al. (2012), that could be compared to the TCC. The TCC dataset consists of pixels with values ranging from 0 to 100 according to the percent tree canopy cover as a continuous variable, providing a complementary forest cover dataset in gradient surface format to analyze and compare to the NLCD forest class.
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We next generated a fishnet sampling grid covering each ecoregion, where each grid square was approximately 20x20km to standardize the extent and shape of sample area units. While some landscape metrics are impacted by the size and shape of the landscape, the 20x20km extent with 30m resolution provided a sufficient grain-to-extent ratio to minimize boundary effects. Any grid squares intersecting the boundary of the ecoregion were discarded to ensure only sample areas fully contained in the ecoregion were utilized. To reduce sampling bias in heavily urbanized areas, we removed grid squares comprising all or part of an urbanized area greater than 500,000 people (as determined by the 2014 cartographic boundary file from the U.S. Census). All remaining grid squares were considered eligible candidates for sampling. We then randomly selected 125 squares from each ecoregion for analysis (Fig. 1). This number is sufficient to develop statistical summaries and comparisons across the two regions. For each of the 125 selected grid squares, we clipped the aggregated NLCD and TCC datasets (Fig. 2) and processed the data according to the methods described below.
Figure 2. Examples of the two datasets: (a) the NLCD patch-mosaic reclassified into eight thematic classes (only forest class analyzed in this study), and (b) the same area showing the tree canopy cover (TCC) gradient surface product 3.
Methods
Methods have been developed previously within remote sensing to discretize gradient data produced by sub-pixel classification techniques (e.g., spectral unmixing) for spatial analysis of continuous datasets (Arnot et al. 2004; Walsh et al. 2008; Frazier and Wang 2011). Essentially, these methods ‘slice’ a gradient surface into a set of multiple discrete maps that can then be analyzed as binary land cover maps. These ‘slicing’ approaches fall into two categories: (1) the range approach, where different ranges of the 5
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continuous value are analyzed as discrete maps, and (2) the threshold approach where a continuum of thresholds is set and pixels are discretized at each step based on whether their value falls above or below the given threshold. In both scenarios, multiple, categorical maps are created from a single gradient surface (Fig. 3). By applying these slicing methods to segment gradient surfaces in a landscape ecological context, it is possible to produce discrete maps that represent different forest cover densities yet still adhere to the patch-mosaic paradigm, thus allowing landscape structure to be quantified for each map using conventional landscape metric tools (e.g., FRAGSTATS). Since multiple maps are created from each gradient surface, multiple metrics can be computed for a single landscape and compared across ranges or thresholds through scalograms (discussed below). The primary benefit of these approaches is that the tools and techniques familiar to landscape ecologists can be applied directly to the transformed maps, thereby extending decades of disciplinary progress in spatial pattern analysis to the gradient realm.
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Figure 3. Example of two approaches for ‘slicing’ gradient surfaces into multiple discrete maps: (a) range approach, and (b) threshold approach
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In this study, we adopt the threshold approach, which has been found to capture heterogeneity better than the range approach (Frazier and Wang 2011). For each of the 125 TCC rasters in each ecoregion, we set thresholds at 10% increments and discretize all pixels with forest cover values greater than or equal to the threshold. Finer threshold increments (i.e., 1%, 5%, etc.) produce greater numbers of output maps and therefore capture greater heterogeneity. However, prior research has determined that a 10% threshold adequately captures most landscape variability (Frazier and Wang 2013). By setting 10% thresholds for each TCC gradient raster and discretizing all values greater than or equal to the threshold, we produced 10 discrete maps for each landscape grid (i.e., ≥0%, ≥10%, ≥20%, ...., ≥90%), generating a total of 2,500 maps for analysis (125 landscape grids x 10 maps per grid x 2 ecoregions). For each map, we computed four landscape metrics measuring fragmentation (Table 1) using FRAGSTATS v4.2 (McGarigal et al. 2012) and plotted the metric values against thresholds in a type of scalogram where the x-axis represents the density scale of analysis and the y-axis represents the metric value. We also computed the same four landscape metrics for the 125 NLCD maps in each region for comparison. The NLCD maps generate conventional, single-value landscape metrics that can be compared across the ecoregions to assess fragmentation and can also be compared to the scalograms from the TCC maps. In all cases, metrics were averaged across the 125 landscapes for interpretation and display of results.
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ACCEPTED MANUSCRIPT Table 1. Landscape metrics measuring aspects of fragmentation
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Number of forest patches divided by total landscape area Percent of landscape covered by largest forest patch Forest edges divided by total landscape area (boundaries not included)
Fragmentation Indicator (-) Smaller MPS typically indicates greater fragmentation (+) Larger PD typically indicates fragmentation (-) Smaller LPI indicates greater fragmentation (+) Larger ED indicates greater fragmentation
Results and discussion Canopy cover distribution in each ecoregion
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Description Average size of forest patches
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Metric Mean patch size/area (MPS) Patch density (PD) Largest Patch Index (LPI) Edge Density (ED)
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Frequency histograms of the overall TCC percentages show that canopy cover varied between the two ecoregions, but the overall trend in distribution was similar (Fig. 4a). The bins represent ranges of TCC percentages (i.e., the ‘0’ bin includes all pixels with percentages from 0-10%, the ‘10’ bin includes all pixels with percentages from 10-20%, etc.). Both regions have relatively few, low density pixels with the majority of pixels (~60%) having greater than 80% tree canopy cover. There is, however, and important distinction between the highest density forest pixels in the SEP and AH regions (Fig. 4a). The distribution of canopy cover within the SEP increases in small increments until the 90 bin where frequency more than triples to where just over 40% of all pixels have between 90% and 100% canopy cover. While the same overall trend of frequency increasing with density is observable in the AH, the number of pixels peaks in the 80 bin, which alone contains over 60% of all forested pixels. In contrast with the SEP, the number of pixels drops precipitously in the 90 bin within the AH, where there are only a few pixels between 90% and 100% forest cover.
Figure 4. (a) Proportional frequency distribution histogram for the TCC data for the Southeast USA Plains (SEP) and Atlantic Highlands (AH), and (b) the proportion of pixels analyzed at each threshold. Applying the thresholding method to the TCC gradients produces a reverse cumulative distribution of the proportion of pixels analyzed at each step (Fig. 4b). For example, the 0 threshold includes all pixels with 7
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Landscape metric results for the patch-mosaic models
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any amount of tree cover (i.e., all pixels) while the 90 threshold includes only those pixels with 90% or more tree canopy cover. The AH region has a slightly higher proportion of pixels compared to the SEP for all thresholds up to, and including, the 80 threshold, but the number drops off precipitously at the 90 threshold with only 1.2% of pixels having values greater than 90%. In comparison, in the SEP region, 44% of pixels contain 90% or greater tree canopy cover. It is not clear why the AH region contains so few pixels with greater than 90% tree canopy cover. The AH region contains different constituent forest communities compared to the SEP, with primarily maple-beech-birch in the AH and predominantly oakhickory or loblolly/shortleaf pine in the SEP (Riitters et al. 2012). It is possible that the different forest community types are modeled differently by the random forests technique used to produce the TCC product. Nonetheless, the two regions are fairly similar in the proportion of pixels at each threshold, and therefore suitable for a comparison of sample scalograms based on density thresholds.
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Landscape metrics computed for the patch-mosaic NLCD rasters suggest that forest fragmentation is comparatively more severe in the SEP compared to the AH region (Table 2). For each metric tested, the value from the SEP was more indicative of fragmentation than the value from the AH. Recall, these metric values represent the average from the 125 samples taken from each region. These findings are not unexpected though, since the SEP region includes major cities and large development corridors along the interstate highway system, while the AH region experiences relatively less population pressure. Based solely on comparison of these single-value, patch-mosaic metrics, a logical conclusion would be that the forests in the SEP are considerably more fragmented than those in the AH. However, beyond a basic comparison of values, it is difficult to make any inferences about the nature of that fragmentation from these metrics.
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Frag. Indicator* (-) (+) (-) (+)
74 ha 1.16 28.4 % 65.0
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Table 2 Comparison of landscape metrics for the patch-mosaic model NLCD landscapes in the Southeastern USA Plains (SEP) and Atlantic Highlands (AH) ecoregions. Values represent the average of the 125 samples.
12,532 ha 0.07 80.3 % 15.4
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*Negative signs indicate that lower values are typically indicative of fragmentation, and positive signs indicate higher values are typically more indicative.
Landscape metric results for the gradient surface models
The scalograms generated from the maps produced by thresholding the TCC gradients show the dynamics of landscape spatial structure across density thresholds (Fig. 5). The solid, black lines represent the average metric value from the 125 landscapes, and the gray envelopes represent one standard deviation of values. The red, dashed lines represent the NLCD metric values (Table 2) and allow for comparison of the two data models. The first characteristic to note is that the metrics computed from the TCC data exhibit non-linear behavior across the density thresholds. While the specific scaling functions of each metric are structurally different, there are some notable similarities in scaling relations across the two ecoregions, suggesting that land cover intensity, or density, may be another form of scale, in addition to grain and extent (Wu 2004), in which there is consistency of scaling relationships across landscapes.
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Figure 5. Scalograms created from the thresholded TCC gradient surfaces at 10% threshold increments. Solid black lines represent average values from the 125 samples, and gray envelopes represent ± one standard deviation. Dashed red lines represent the patch-based, NLCD metrics (Table 2). Values have been extended across entire scalogram for comparison but should not be associated with any single threshold.
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Analysis of the gradient data scalograms for mean patch size (MPS: Fig. 5a) show that while the singlevalue, NLCD metrics indicated there were vast differences in MPS between the two ecoregions (Table 2), the landscape structure dynamics are quite similar between the two regions. In both regions, the scaling relationships inflect at approximately the 30% threshold. The first derivative of a smoothed version of these MPS curves would show that the inflection point, or the point with the greatest rate of change in the loss of patch area, occurs when pixels with around 30% canopy cover are removed from analysis, and the steepest slopes are observed between the 20% and 30% thresholds. Stated otherwise, in both ecoregions, as pixels with 20-30% forest cover are removed from consideration, the greatest losses in patch size occur. From a management perspective, since these densities contribute most to gains in patch size, conservation efforts targeted toward these areas would have the greatest impacts on patch area.
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The scalograms for patch density (PD: Fig. 5b) also show structural similarities but with the scaling relationships in the AH more pronounced than in the SEP. In both regions, PD increases as the density threshold increases and fewer, denser pixels comprise the landscape, which is expected. Also in both regions, there are breaks in the scaling relationships at approximately the 20% threshold and the 70% threshold where the rate of PD gains increases. In other words, as low density pixels (<20%) are removed from consideration, the canopy remains relatively well connected, with only small increases in PD (values remain below 2). Between the 20% and 70% thresholds, the rate of PD increases gradually in both ecoregions, but values remain around 2. However, once the 70% threshold is breached and the landscape being analyzed is comprised only of higher density canopy, PD values increase more rapidly in both ecoregions. The differences between the regions become more pronounced in this high density range as PD values reach a maximum of 5.76 in the AH while they peak at only 3.58 in the SEP. While the NLCD single-value metrics suggested that the SEP region had greater PD and was therefore, more fragmented (Table 2), in fact, the TCC data suggests that for the highest densities of forest cover, the AH region is more fragmented.
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The abrupt change in the rate of increase of PD beyond 70% canopy cover may represent an ecological threshold whereby forest structural changes are occurring more rapidly as these canopy densities are lost. It can be concluded from the scalograms that disproportionately large losses in connectivity occur as the focal class becomes composed entirely of high-density pixels (>70% canopy cover), which explains why PD increases rapidly when pixels below this threshold are removed from analysis. One possible ecological explanation is that core forest stands primarily comprise pixels with greater than 70% canopy cover, and the corridors connecting core areas likely comprise pixels with lower canopy cover proportions. The process of increasing the density threshold “nibbles” away at these connecting corridors but does not actually sever the connection until pixels with greater than 70% canopy cover are removed. At that point, once-connected patches fragment into multiple patches, thus causing the dramatic increases in PD at higher thresholds. The scalograms for largest patch index (LPI: Fig. 5c) show general similarities in the two regions with values declining across thresholds. In the SEP, this decline is more gradual, and there are subtle breaks in slope at the 60% and 70% thresholds. In the AH, the asymptote also breaks abruptly at 60% and more subtly again at the 70% threshold. These results support the findings from the analysis of PD above that there may be an ecological threshold around 70% tree canopy cover beyond which there are rapid increases in fragmentation as denser pixels are removed from analysis. In the SEP, the more gradual declines in LPI suggest that the relationship between tree canopy cover density and the size of the largest patch changes in a more linear fashion. In other words, as low density pixels are removed from analysis, patches are shrinking at approximately the same rate.
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ACCEPTED MANUSCRIPT Lastly, the scalograms for edge density (ED: Fig. 5d) show subtle increases in ED across the density thresholds in the SEP region but an exponential scaling relationship in the AH. The abrupt decline in ED for the 90% threshold in the AH region is likely caused by the relatively small number of pixels with greater than 90% canopy cover (Fig. 4). Here, the number of pixels being analyzed is so small that the edge density value is naturally very small and thus is not necessarily representative of a more connected landscape. Therefore, this result should not be interpreted as an improvement in the fragmentation of the landscape since it is more likely an artifact of the data.
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In sum, the results of the gradient threshold analysis uncover several aspects of landscape structure in the two regions that are not apparent from the single-value metrics computed on the NLCD data. In the SEP, the removal of low density pixels from analysis results in a slower rate of change of the four fragmentation metrics tested compared to the AH. These findings are represented by the more consistent changes in metrics across density thresholds. In the AH, the same process of removing lower density pixels via the threshold approach resulted in more rapid changes in landscape metrics as evidenced by the scalograms. In both regions, there appears to be an ecological threshold around 70% canopy cover, where abrupt changes in fragmentation occur as the landscape being analyzed is composed entirely of the highest density pixels. These changes are especially pronounced in the AH region where the removal of pixels with densities greater than 70% canopy cover results in rapid increases/decreases in fragmentation metrics. Using the method described in this paper for ecological management decisions, it is logical to continue protecting high-density cover areas but also target areas with 30-60% cover as these areas appear to contribute the greatest gains in patch connectivity.
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Our findings using gradient surfaces support several other studies in the field that have utilized patchmosaic data. For instance, Ritters et al. (2004) found that fragmentation caused by development is relatively small for smaller density forests because non-forest land cover types are more common between roads and forests. Our results similarly show that impacts on fragmentation (measured through landscape metrics) were less severe when low density pixels were included in the analysis as evidenced by the gradual changes in metrics at low thresholds. Furthermore, Riitters et al. (2012) found that the relative importance of fragmentation by developed land increased with forest area density, which can also be supported by our gradient threshold analysis, particularly in the AH where fragmentation metrics changed rapidly when the densest pixels were removed from the analysis. Building on Wu (2004), these findings highlight the need for multiscale analyses when utilizing gradient surfaces. Comparison of metric results across models
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An interesting finding from our investigations was that the patch-mosaic metrics computed from the NLCD dataset varied considerably with the TCC scalogram plots by metric and ecoregion. While the two datasets are developed using different classification techniques, both are based on similar input data, and we therefore expected some degree of consistency in the relationship between the metrics computed for the NLCD datasets and those computed for certain TCC thresholds (Fig. 5). For instance, the NLCD forest classes are described as areas dominated by trees generally greater than 5 m tall and comprising more than 20% of the total vegetation cover (Homer et al. 2015). While the TCC product does not specify height requirements, it would be logical to assume that the metrics computed using the NLCD forest pixels would roughly coincide with the values for the 20% threshold from the TCC dataset. In fact, there was very little consistency in the position of the NLCD line in relation to the TCC scalograms. The NLCD metric (red, dashed lines in Fig. 5) intersected the TCC curve near the 20% threshold in only one instance (Fig. 5b: PD in SEP), and in some instances (e.g., Fig. 5a: MPS in AH), the mean NLCD metric value was more than one standard deviation above the mean for the TCC 0% threshold. Recall that the 0% threshold includes every pixel with more than 0% tree cover, suggesting that the NLCD dataset 11
ACCEPTED MANUSCRIPT produced a mean MPS value that exceeded mean MPS when considering all forested pixels in the TCC raster.
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To investigate this issue further, we extracted the TCC values for every NLCD forest pixel in both regions and computed several basic descriptive statistics (Table 3) to gain a better understanding of the canopy composition within the NLCD forest pixels. The forest NLCD pixels in the SEP region contain, on average, about 85% canopy cover while the NLCD pixels in the AH region contain about 79% canopy cover on average. The ranges of canopy cover for each pixel are rather large, with forest pixels in the SEP comprising anywhere from 1% to 100% canopy cover and pixels in the AH containing from 4-87% canopy cover. While these differences do not fully explain the discrepancies between the TCC and NLCD, they do highlight the variations between the two products across geographic regions in terms of the amount of canopy cover captured within NLCD pixels.
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Table 3. Basic descriptive statistics for percent tree cover canopy (TCC) within the NLCD forest pixels
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Another possible reason for the discrepancies between the metrics computed from the NLCD forest pixels and the TCC is the dissimilar methods used to generate each product. The NLCD is updated based on a change detection algorithm (Xian et al. 2009; Jin et al. 2013) while the TCC (2011 edition) utilized random forest modeling that incorporated finer spatial scale data such as orthoimagery and forest inventory analysis (FIA) plots (Coulston et al. 2012). While both studies report sufficient accuracies for mapping, the TCC pilot study notes pseudo R2 values as low as 0.53. This pilot study also did not include a sampling area the AH region (Coulston et al. 2012), which may also contribute to mapping accuracy in that region. Specifically, the AH is heavily forested in parts, yet the TCC product has surprisingly few pixels with greater than 90% canopy cover (Fig. 4). While we do not know the precise cause of the metric discrepancies seen in this study, researchers should use caution when using these two products in tandem as they are not cross validated. Considerations when using the threshold method
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There are several factors to consider when using the threshold method described in this paper for analysis of gradient surfaces. First, the discretization process invariably collapses some of the heterogeneity captured by gradient datasets. By setting finer threshold increments, users can minimize the loss of heterogeneity. However, there is a tradeoff between increased heterogeneity and additional processing time. In a previous study, Frazier and Wang (2013) found that threshold increments less than 10% did not provide considerable detail to warrant the additional processing time. However, researchers should evaluate their specific objectives and select a threshold increment that best suits their study. Second, the gradient rasters used in this study were produced by the MRLC, providing a straightforward dataset to compare to the NLCD patch-mosaic. In situations where a gradient dataset is not available, spectral unmixing methods (Keshava and Mustard 2002) can be applied directly to remotely sensed images to create gradient datasets of land cover. However, while several studies have investigated the propagation impacts of pixel-based classification errors on landscape metrics (Fang et al. 2006; Huang et al. 2006; Iverson 2007; Burnicki 2012), to our knowledge, no studies have examined the impact of sub12
ACCEPTED MANUSCRIPT pixel gradient classification error on landscape metrics. This is an area in need of future attention. Without a thorough understanding of the impact of gradient classification accuracy on landscape metrics, it is difficult to discern whether apparent ecological thresholds, such as those observed for PD (Fig. 4b), are an artifact of the classification scheme used to create the data. 5.
Conclusions
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In this study, we introduced an approach for extracting increased landscape pattern information from gradient surfaces using a common toolset (i.e., FRAGSTATS) to bridge the gaps between the patchmosaic model and the gradient surface model. Framing our investigation around a comparison of forest fragmentation in two ecoregions in the eastern U.S., we demonstrated how a thresholding approach can be used to discretize gradient surfaces into multiple discrete maps that can then be analyzed as patch-mosaic models. We created scalograms showing metric change across a continuum of forest density scales and compared them to single-value metrics computed for patch-mosaic landscape to illustrate how the additional information can be analyzed in an ecological context. Our results highlight several key findings. First, scalograms are able to depict the dynamics of landscape spatial structure across density threshold in a manner not possible with single-value metrics. The scalograms fostered the identification of ecological thresholds where there were abrupt changes in landscape dynamics at certain land cover proportions, and these thresholds have the potential to be used to target landscape management and conservation decisions.
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In this study, all metrics tested generated non-linear scaling relationships across the density thresholds, suggesting that spatial pattern analyses using gradient datasets might also require multi-scale analyses. In particular, the notable similarities in scaling relationships across the two ecoregions suggest that land cover density, or pixel value intensity, may be another form of scale in which consistent and robust scaling laws apply. Two components of scale, grain and extent, have received much attention in the landscape ecology literature for the consistent and robust scaling relationships they produce with respect to landscape metrics. In this study, we show that pixel density may be another scale component with similar relationships. Lastly, when analyzing landscape metrics based on gradient data, research is needed to investigate the impacts of classification accuracy on the derived metrics, as this area has not received much attention to date.
Acknowledgements
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This work was funded, in part, by a grant to A. Frazier and P. Kedron from the National Science Foundation (#SBE-1561021).
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Highlights
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Single-value metrics from patch-based data do not capture landscape dynamics Thresholding gradients produces binary maps to analyze with landscape metrics Scalograms of density thresholds indicate nonlinear landscape structure dynamics Scalograms generated from gradients permit identification of ecological thresholds Density scalograms show consistent and/or robust scaling relationships are possible
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Amy E. Frazier, Peter Kedron PII: DOI: Reference:
S1574-9541(17)30143-7 doi: 10.1016/j.ecoinf.2017.08.002 ECOINF 786
To appear in:
Ecological Informatics
Received date: Revised date: Accepted date:
27 May 2017 22 August 2017 23 August 2017
Please cite this article as: Amy E. Frazier, Peter Kedron , Comparing forest fragmentation in Eastern U.S. forests using patch-mosaic and gradient surface models, Ecological Informatics (2017), doi: 10.1016/j.ecoinf.2017.08.002
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT Comparing Forest Fragmentation in Eastern U.S. Forests using Patch-Mosaic and Gradient Surface Models Amy E. Frazier*1,2 and Peter Kedron1 1
Department of Geography, Oklahoma State University, 337 Murray Hall, Stillwater, OK, 74078
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Center for Applications of Remote Sensing, Department of Geography, Oklahoma State University, 337 Murray Hall, Stillwater, OK, 74078
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*Corresponding author: Email: [email protected]; Address: 337 Murray Hall, Stillwater, OK 74078
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ACCEPTED MANUSCRIPT Abstract
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Forest fragmentation is an ongoing threat to forest communities in the eastern United States where a prevailing pattern of dispersed, low intensity urban development continues to expand the wildland urban interface (WUI). Many large scale forest monitoring initiatives rely on pixel-based remote sensing classifications to quantify fragmentation patterns because they fit seamlessly into the patch-mosaic model (PMM) and can be analyzed using conventional landscape metrics (e.g., FRAGSTATS). The PMM has been key to advancing our understanding of patch dynamics, but some argue it may be inconsistent with ecological theory as it ignores the inherent gradient nature of environments. Studies have advocated a shift toward gradient surface models (GSM), but tools for quantifying spatial patterns in continuous gradient surfaces are limited. We introduce an approach for extracting landscape pattern information from gradient surfaces using a thresholding approach to discretize gradient surfaces into multiple discrete maps according to forest cover density. These maps can then be analyzed using conventional landscape metric tools. Metric values are plotted against density thresholds as a scalogram and interpreted to understand the dynamics of landscape spatial structure. By performing a comparative analysis of two forested ecoregions in the eastern U.S. that have undergone development pressures, we demonstrate how information on landscape structure dynamics at various forest cover densities can be extracted from gradient surfaces to provide additional information on the density scales where fragmentation is pronounced in each region. Results indicate there are ecological thresholds at certain forest cover proportions that can potentially inform management decisions.
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Keywords: landscape metrics; spatial pattern analysis; patch-mosaic model; gradient surface model; scalograms
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Introduction
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Forest fragmentation is one of the greatest threats to global biodiversity (Kupfer and Franklin 2009) and is an ongoing threat to forest communities in the eastern United States (Riitters et al. 2012) where most land is privately owned and therefore unprotected (Smith et al. 2009). Fragmentation caused by urban development is of particular interest because it is the main driver of land use and land cover change in the eastern United States (USDA Forest Service, 2011). A prevailing pattern of dispersed, low intensity urban development continues to expand the wildland urban interface (WUI), which is where urban and suburban development intermingle with undeveloped wildland vegetation (Radeloff et al. 2005). As development penetrates the WUI, anthropogenic impacts are introduced deep into intact forest (Theobald et al. 1997; Stein et al. 2009; Riitters et al. 2012), increasing the risk of fire danger, species invasions, and biodiversity loss (Radeloff et al. 2005).
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Regional, national, and international scale initiatives prioritize measurement and monitoring of forest fragmentation at broad spatial scales (Kupfer 2006), where land cover maps derived from remote sensing images are frequently employed. Satellite or aerial images are converted into land cover information through pixel-based classification techniques in which each pixel is assigned a single land cover class. Pixel-based classifications are used extensively in landscape ecological studies because they fit seamlessly into the patch-mosaic model (PMM), where the landscape is conceptualized as a mosaic of discrete patches. The PMM is lauded for its conceptual simplicity (Forman 1995) and the ease with which it can incorporate categorical maps produced from remote sensing classifications into landscape analysis, and many toolsets have been developed explicitly for quantifying PMM spatial patterns from categorical maps (e.g., FRAGSTATS: McGarigal et al. 2012).
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The PMM has no doubt advanced our understanding of pattern-process relationships (Turner 2005), particularly fragmentation (Uuemaa et al. 2013), but it can be inconsistent with ecological theory as it ignores the inherent gradient nature of environments and land covers (McGarigal and Cushman 2005; Cushman et al. 2010). This issue is particularly pronounced at the broad spatial scales commonly adopted in forest fragmentation studies, as pixel-based classifications often underrepresent spatial heterogeneity. Gradient-based classifications have been proposed and debated in landscape ecology for decades as an alternate way of conceptualizing and representing landscape structure (McIntyre and Hobbs 1999; Manning et al. 2004; McGarigal and Cushman 2005; Cushman et al. 2010; Lausch et al. 2015). Gradients are able to capture and represent a greater amount of landscape heterogeneity because pixels can assume ratio values according to the proportion of land cover present in the pixel and therefore are not confined to a single land cover class. However, gradient datasets are not directly compatible with most available spatial pattern analysis tools, which require hard boundaries for metric computations, making it challenging for researchers to incorporate these datasets into their analyses. Surface metrics have emerged as an alternative method for quantifying patterns in gradient datasets. Originally developed for microscopy and molecular physics, surface metrics were recently introduced to landscape ecologists as a means of analyzing gradient landscapes (McGarigal et al. 2009). While there is growing support and increased use of surface metrics in the ecological literature (Moniem and Holland 2013; Scown et al. 2015; Moniem et al. 2016; Frazier 2016), widespread adoption has been hindered by several factors. First, many surface metrics are constructed to evaluate ideal bearing properties of mechanical surfaces, which are defined as being “smooth with relatively deep scratches to hold and distribute lubricant” (Stewart 1990, 1). This concept does not translate flawlessly into ecology, and therefore interpretation of surface metrics is not always intuitive from a landscape perspective. Second, many surface metrics suffer from correlation and redundancy issues similar to those found with conventional landscape metrics and graph approaches. Lastly, widespread adoption of surface metrics 3
ACCEPTED MANUSCRIPT has been hindered by limited access to software, although the upcoming version of FRAGSTATS is expected to contain some of these metrics.
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With these limitations, researchers are tasked with finding alternative approaches to incorporate continuous, gradient surface models into landscape investigations and bridge the gaps between the patchmosaic and the gradient surface paradigms. In this study, we introduce an approach for extracting increased landscape pattern information from gradient surfaces using a common toolset (i.e., FRAGSTATS). Specifically, we demonstrate how a thresholding approach can be used to discretize gradient surfaces into multiple discrete maps that can then be analyzed as patch-mosaic models. We create scalograms of these multiple metric values showing metric change across a continuum of forest density scales and compare them to single-value metrics computed for patch-mosaic landscapes to illustrate how the additional information can be analyzed in an ecological context. We frame our study around a comparison of forest fragmentation in two ecoregions in the eastern U.S. Study Area and Data
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With a lack of comparative regional assessments of forest fragmentation noted in the literature (Riitters et al. 2012), we elected to compare two ecoregions that differ in their level of urban development: (1) the Southeastern USA Plains (SEP) nested within the Eastern Temperate Forests ecoregion, and (2) the Atlantic Highlands (AH) nested within the Northern Forests ecoregion (Omernik 1987). The SEP includes several major development corridors (I-85, I-95, etc.) and comprises major cities such as Baltimore, M.D., Charlotte, N.C., and Atlanta, G.A. It also includes several rapidly developing Midwest cities that have experienced sprawling urban growth in recent decades, such as Nashville, TN, as well as urban fringes of developing cities in Texas including Dallas/Fort Worth, Houston, Austin, and San Antonio (Fig. 1). The SEP region contains over 250,000 km2 of total WUI (Radeloff et al. 2005), amounting to about 25% of the region. In comparison, the AH region is located in the Northeast U.S. and comprises portions of Pennsylvania, New York, and New England. The AH does not contain any major cities over 500,000 people or large development corridors. However, proportionally the region contains approximately the same amount of WUI with 40,000 km2, also about 25% (Radeloff et al. 2005). The similarities in the amount of WUI and differences in the likely proximate causes of fragmentation between the two regions provides an ideal case for examining forest cover patterns.
Figure 1. The two study regions for comparative analysis: the Southeastern USA Plains and the Atlantic Highlands 4
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The National Land Cover Database (NLCD) developed by the Multi-Resolution Land Characteristics Consortium (MRLC) is the primary source of land cover data in the United States (Wickham et al. 2010). The MRLC produces several products including a seamless, 16-class thematic, land cover map commonly referred to as the ‘NLCD’ and a seamless, gradient surface representing percent tree canopy cover (TCC) across the continuous United States. Both datasets are based on Landsat images over the same time period and have the same nominal spatial resolution (30m) (Xian et al. 2011; Coulston et al. 2012, 2013; Tipton et al. 2012; Homer et al. 2015), thereby offering a unique opportunity to examine forest cover from both a patch-based and gradient perspective. We downloaded the 2011 NLCD and TCC rasters for the conterminous U.S. from the MRLC (http://www.mrlc.gov/) and thematically aggregated the NLCD into eight classes (Water, Developed, Barren, Forest, Shrubland, Herbaceous, Planted/Cultivated, Wetlands). This aggregation produced a single forest class, which included ‘Deciduous Forest’, ‘Evergreen Forest’, ‘Mixed Forest’, and ‘Woody Wetlands’ following Riitters et al. (2012), that could be compared to the TCC. The TCC dataset consists of pixels with values ranging from 0 to 100 according to the percent tree canopy cover as a continuous variable, providing a complementary forest cover dataset in gradient surface format to analyze and compare to the NLCD forest class.
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We next generated a fishnet sampling grid covering each ecoregion, where each grid square was approximately 20x20km to standardize the extent and shape of sample area units. While some landscape metrics are impacted by the size and shape of the landscape, the 20x20km extent with 30m resolution provided a sufficient grain-to-extent ratio to minimize boundary effects. Any grid squares intersecting the boundary of the ecoregion were discarded to ensure only sample areas fully contained in the ecoregion were utilized. To reduce sampling bias in heavily urbanized areas, we removed grid squares comprising all or part of an urbanized area greater than 500,000 people (as determined by the 2014 cartographic boundary file from the U.S. Census). All remaining grid squares were considered eligible candidates for sampling. We then randomly selected 125 squares from each ecoregion for analysis (Fig. 1). This number is sufficient to develop statistical summaries and comparisons across the two regions. For each of the 125 selected grid squares, we clipped the aggregated NLCD and TCC datasets (Fig. 2) and processed the data according to the methods described below.
Figure 2. Examples of the two datasets: (a) the NLCD patch-mosaic reclassified into eight thematic classes (only forest class analyzed in this study), and (b) the same area showing the tree canopy cover (TCC) gradient surface product 3.
Methods
Methods have been developed previously within remote sensing to discretize gradient data produced by sub-pixel classification techniques (e.g., spectral unmixing) for spatial analysis of continuous datasets (Arnot et al. 2004; Walsh et al. 2008; Frazier and Wang 2011). Essentially, these methods ‘slice’ a gradient surface into a set of multiple discrete maps that can then be analyzed as binary land cover maps. These ‘slicing’ approaches fall into two categories: (1) the range approach, where different ranges of the 5
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continuous value are analyzed as discrete maps, and (2) the threshold approach where a continuum of thresholds is set and pixels are discretized at each step based on whether their value falls above or below the given threshold. In both scenarios, multiple, categorical maps are created from a single gradient surface (Fig. 3). By applying these slicing methods to segment gradient surfaces in a landscape ecological context, it is possible to produce discrete maps that represent different forest cover densities yet still adhere to the patch-mosaic paradigm, thus allowing landscape structure to be quantified for each map using conventional landscape metric tools (e.g., FRAGSTATS). Since multiple maps are created from each gradient surface, multiple metrics can be computed for a single landscape and compared across ranges or thresholds through scalograms (discussed below). The primary benefit of these approaches is that the tools and techniques familiar to landscape ecologists can be applied directly to the transformed maps, thereby extending decades of disciplinary progress in spatial pattern analysis to the gradient realm.
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Figure 3. Example of two approaches for ‘slicing’ gradient surfaces into multiple discrete maps: (a) range approach, and (b) threshold approach
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In this study, we adopt the threshold approach, which has been found to capture heterogeneity better than the range approach (Frazier and Wang 2011). For each of the 125 TCC rasters in each ecoregion, we set thresholds at 10% increments and discretize all pixels with forest cover values greater than or equal to the threshold. Finer threshold increments (i.e., 1%, 5%, etc.) produce greater numbers of output maps and therefore capture greater heterogeneity. However, prior research has determined that a 10% threshold adequately captures most landscape variability (Frazier and Wang 2013). By setting 10% thresholds for each TCC gradient raster and discretizing all values greater than or equal to the threshold, we produced 10 discrete maps for each landscape grid (i.e., ≥0%, ≥10%, ≥20%, ...., ≥90%), generating a total of 2,500 maps for analysis (125 landscape grids x 10 maps per grid x 2 ecoregions). For each map, we computed four landscape metrics measuring fragmentation (Table 1) using FRAGSTATS v4.2 (McGarigal et al. 2012) and plotted the metric values against thresholds in a type of scalogram where the x-axis represents the density scale of analysis and the y-axis represents the metric value. We also computed the same four landscape metrics for the 125 NLCD maps in each region for comparison. The NLCD maps generate conventional, single-value landscape metrics that can be compared across the ecoregions to assess fragmentation and can also be compared to the scalograms from the TCC maps. In all cases, metrics were averaged across the 125 landscapes for interpretation and display of results.
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Number of forest patches divided by total landscape area Percent of landscape covered by largest forest patch Forest edges divided by total landscape area (boundaries not included)
Fragmentation Indicator (-) Smaller MPS typically indicates greater fragmentation (+) Larger PD typically indicates fragmentation (-) Smaller LPI indicates greater fragmentation (+) Larger ED indicates greater fragmentation
Results and discussion Canopy cover distribution in each ecoregion
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Description Average size of forest patches
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Metric Mean patch size/area (MPS) Patch density (PD) Largest Patch Index (LPI) Edge Density (ED)
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Frequency histograms of the overall TCC percentages show that canopy cover varied between the two ecoregions, but the overall trend in distribution was similar (Fig. 4a). The bins represent ranges of TCC percentages (i.e., the ‘0’ bin includes all pixels with percentages from 0-10%, the ‘10’ bin includes all pixels with percentages from 10-20%, etc.). Both regions have relatively few, low density pixels with the majority of pixels (~60%) having greater than 80% tree canopy cover. There is, however, and important distinction between the highest density forest pixels in the SEP and AH regions (Fig. 4a). The distribution of canopy cover within the SEP increases in small increments until the 90 bin where frequency more than triples to where just over 40% of all pixels have between 90% and 100% canopy cover. While the same overall trend of frequency increasing with density is observable in the AH, the number of pixels peaks in the 80 bin, which alone contains over 60% of all forested pixels. In contrast with the SEP, the number of pixels drops precipitously in the 90 bin within the AH, where there are only a few pixels between 90% and 100% forest cover.
Figure 4. (a) Proportional frequency distribution histogram for the TCC data for the Southeast USA Plains (SEP) and Atlantic Highlands (AH), and (b) the proportion of pixels analyzed at each threshold. Applying the thresholding method to the TCC gradients produces a reverse cumulative distribution of the proportion of pixels analyzed at each step (Fig. 4b). For example, the 0 threshold includes all pixels with 7
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Landscape metric results for the patch-mosaic models
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any amount of tree cover (i.e., all pixels) while the 90 threshold includes only those pixels with 90% or more tree canopy cover. The AH region has a slightly higher proportion of pixels compared to the SEP for all thresholds up to, and including, the 80 threshold, but the number drops off precipitously at the 90 threshold with only 1.2% of pixels having values greater than 90%. In comparison, in the SEP region, 44% of pixels contain 90% or greater tree canopy cover. It is not clear why the AH region contains so few pixels with greater than 90% tree canopy cover. The AH region contains different constituent forest communities compared to the SEP, with primarily maple-beech-birch in the AH and predominantly oakhickory or loblolly/shortleaf pine in the SEP (Riitters et al. 2012). It is possible that the different forest community types are modeled differently by the random forests technique used to produce the TCC product. Nonetheless, the two regions are fairly similar in the proportion of pixels at each threshold, and therefore suitable for a comparison of sample scalograms based on density thresholds.
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Landscape metrics computed for the patch-mosaic NLCD rasters suggest that forest fragmentation is comparatively more severe in the SEP compared to the AH region (Table 2). For each metric tested, the value from the SEP was more indicative of fragmentation than the value from the AH. Recall, these metric values represent the average from the 125 samples taken from each region. These findings are not unexpected though, since the SEP region includes major cities and large development corridors along the interstate highway system, while the AH region experiences relatively less population pressure. Based solely on comparison of these single-value, patch-mosaic metrics, a logical conclusion would be that the forests in the SEP are considerably more fragmented than those in the AH. However, beyond a basic comparison of values, it is difficult to make any inferences about the nature of that fragmentation from these metrics.
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Frag. Indicator* (-) (+) (-) (+)
74 ha 1.16 28.4 % 65.0
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Table 2 Comparison of landscape metrics for the patch-mosaic model NLCD landscapes in the Southeastern USA Plains (SEP) and Atlantic Highlands (AH) ecoregions. Values represent the average of the 125 samples.
12,532 ha 0.07 80.3 % 15.4
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*Negative signs indicate that lower values are typically indicative of fragmentation, and positive signs indicate higher values are typically more indicative.
Landscape metric results for the gradient surface models
The scalograms generated from the maps produced by thresholding the TCC gradients show the dynamics of landscape spatial structure across density thresholds (Fig. 5). The solid, black lines represent the average metric value from the 125 landscapes, and the gray envelopes represent one standard deviation of values. The red, dashed lines represent the NLCD metric values (Table 2) and allow for comparison of the two data models. The first characteristic to note is that the metrics computed from the TCC data exhibit non-linear behavior across the density thresholds. While the specific scaling functions of each metric are structurally different, there are some notable similarities in scaling relations across the two ecoregions, suggesting that land cover intensity, or density, may be another form of scale, in addition to grain and extent (Wu 2004), in which there is consistency of scaling relationships across landscapes.
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Figure 5. Scalograms created from the thresholded TCC gradient surfaces at 10% threshold increments. Solid black lines represent average values from the 125 samples, and gray envelopes represent ± one standard deviation. Dashed red lines represent the patch-based, NLCD metrics (Table 2). Values have been extended across entire scalogram for comparison but should not be associated with any single threshold.
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Analysis of the gradient data scalograms for mean patch size (MPS: Fig. 5a) show that while the singlevalue, NLCD metrics indicated there were vast differences in MPS between the two ecoregions (Table 2), the landscape structure dynamics are quite similar between the two regions. In both regions, the scaling relationships inflect at approximately the 30% threshold. The first derivative of a smoothed version of these MPS curves would show that the inflection point, or the point with the greatest rate of change in the loss of patch area, occurs when pixels with around 30% canopy cover are removed from analysis, and the steepest slopes are observed between the 20% and 30% thresholds. Stated otherwise, in both ecoregions, as pixels with 20-30% forest cover are removed from consideration, the greatest losses in patch size occur. From a management perspective, since these densities contribute most to gains in patch size, conservation efforts targeted toward these areas would have the greatest impacts on patch area.
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The scalograms for patch density (PD: Fig. 5b) also show structural similarities but with the scaling relationships in the AH more pronounced than in the SEP. In both regions, PD increases as the density threshold increases and fewer, denser pixels comprise the landscape, which is expected. Also in both regions, there are breaks in the scaling relationships at approximately the 20% threshold and the 70% threshold where the rate of PD gains increases. In other words, as low density pixels (<20%) are removed from consideration, the canopy remains relatively well connected, with only small increases in PD (values remain below 2). Between the 20% and 70% thresholds, the rate of PD increases gradually in both ecoregions, but values remain around 2. However, once the 70% threshold is breached and the landscape being analyzed is comprised only of higher density canopy, PD values increase more rapidly in both ecoregions. The differences between the regions become more pronounced in this high density range as PD values reach a maximum of 5.76 in the AH while they peak at only 3.58 in the SEP. While the NLCD single-value metrics suggested that the SEP region had greater PD and was therefore, more fragmented (Table 2), in fact, the TCC data suggests that for the highest densities of forest cover, the AH region is more fragmented.
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The abrupt change in the rate of increase of PD beyond 70% canopy cover may represent an ecological threshold whereby forest structural changes are occurring more rapidly as these canopy densities are lost. It can be concluded from the scalograms that disproportionately large losses in connectivity occur as the focal class becomes composed entirely of high-density pixels (>70% canopy cover), which explains why PD increases rapidly when pixels below this threshold are removed from analysis. One possible ecological explanation is that core forest stands primarily comprise pixels with greater than 70% canopy cover, and the corridors connecting core areas likely comprise pixels with lower canopy cover proportions. The process of increasing the density threshold “nibbles” away at these connecting corridors but does not actually sever the connection until pixels with greater than 70% canopy cover are removed. At that point, once-connected patches fragment into multiple patches, thus causing the dramatic increases in PD at higher thresholds. The scalograms for largest patch index (LPI: Fig. 5c) show general similarities in the two regions with values declining across thresholds. In the SEP, this decline is more gradual, and there are subtle breaks in slope at the 60% and 70% thresholds. In the AH, the asymptote also breaks abruptly at 60% and more subtly again at the 70% threshold. These results support the findings from the analysis of PD above that there may be an ecological threshold around 70% tree canopy cover beyond which there are rapid increases in fragmentation as denser pixels are removed from analysis. In the SEP, the more gradual declines in LPI suggest that the relationship between tree canopy cover density and the size of the largest patch changes in a more linear fashion. In other words, as low density pixels are removed from analysis, patches are shrinking at approximately the same rate.
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ACCEPTED MANUSCRIPT Lastly, the scalograms for edge density (ED: Fig. 5d) show subtle increases in ED across the density thresholds in the SEP region but an exponential scaling relationship in the AH. The abrupt decline in ED for the 90% threshold in the AH region is likely caused by the relatively small number of pixels with greater than 90% canopy cover (Fig. 4). Here, the number of pixels being analyzed is so small that the edge density value is naturally very small and thus is not necessarily representative of a more connected landscape. Therefore, this result should not be interpreted as an improvement in the fragmentation of the landscape since it is more likely an artifact of the data.
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In sum, the results of the gradient threshold analysis uncover several aspects of landscape structure in the two regions that are not apparent from the single-value metrics computed on the NLCD data. In the SEP, the removal of low density pixels from analysis results in a slower rate of change of the four fragmentation metrics tested compared to the AH. These findings are represented by the more consistent changes in metrics across density thresholds. In the AH, the same process of removing lower density pixels via the threshold approach resulted in more rapid changes in landscape metrics as evidenced by the scalograms. In both regions, there appears to be an ecological threshold around 70% canopy cover, where abrupt changes in fragmentation occur as the landscape being analyzed is composed entirely of the highest density pixels. These changes are especially pronounced in the AH region where the removal of pixels with densities greater than 70% canopy cover results in rapid increases/decreases in fragmentation metrics. Using the method described in this paper for ecological management decisions, it is logical to continue protecting high-density cover areas but also target areas with 30-60% cover as these areas appear to contribute the greatest gains in patch connectivity.
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Our findings using gradient surfaces support several other studies in the field that have utilized patchmosaic data. For instance, Ritters et al. (2004) found that fragmentation caused by development is relatively small for smaller density forests because non-forest land cover types are more common between roads and forests. Our results similarly show that impacts on fragmentation (measured through landscape metrics) were less severe when low density pixels were included in the analysis as evidenced by the gradual changes in metrics at low thresholds. Furthermore, Riitters et al. (2012) found that the relative importance of fragmentation by developed land increased with forest area density, which can also be supported by our gradient threshold analysis, particularly in the AH where fragmentation metrics changed rapidly when the densest pixels were removed from the analysis. Building on Wu (2004), these findings highlight the need for multiscale analyses when utilizing gradient surfaces. Comparison of metric results across models
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An interesting finding from our investigations was that the patch-mosaic metrics computed from the NLCD dataset varied considerably with the TCC scalogram plots by metric and ecoregion. While the two datasets are developed using different classification techniques, both are based on similar input data, and we therefore expected some degree of consistency in the relationship between the metrics computed for the NLCD datasets and those computed for certain TCC thresholds (Fig. 5). For instance, the NLCD forest classes are described as areas dominated by trees generally greater than 5 m tall and comprising more than 20% of the total vegetation cover (Homer et al. 2015). While the TCC product does not specify height requirements, it would be logical to assume that the metrics computed using the NLCD forest pixels would roughly coincide with the values for the 20% threshold from the TCC dataset. In fact, there was very little consistency in the position of the NLCD line in relation to the TCC scalograms. The NLCD metric (red, dashed lines in Fig. 5) intersected the TCC curve near the 20% threshold in only one instance (Fig. 5b: PD in SEP), and in some instances (e.g., Fig. 5a: MPS in AH), the mean NLCD metric value was more than one standard deviation above the mean for the TCC 0% threshold. Recall that the 0% threshold includes every pixel with more than 0% tree cover, suggesting that the NLCD dataset 11
ACCEPTED MANUSCRIPT produced a mean MPS value that exceeded mean MPS when considering all forested pixels in the TCC raster.
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To investigate this issue further, we extracted the TCC values for every NLCD forest pixel in both regions and computed several basic descriptive statistics (Table 3) to gain a better understanding of the canopy composition within the NLCD forest pixels. The forest NLCD pixels in the SEP region contain, on average, about 85% canopy cover while the NLCD pixels in the AH region contain about 79% canopy cover on average. The ranges of canopy cover for each pixel are rather large, with forest pixels in the SEP comprising anywhere from 1% to 100% canopy cover and pixels in the AH containing from 4-87% canopy cover. While these differences do not fully explain the discrepancies between the TCC and NLCD, they do highlight the variations between the two products across geographic regions in terms of the amount of canopy cover captured within NLCD pixels.
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84.8 93 20.5 1 - 100
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Table 3. Basic descriptive statistics for percent tree cover canopy (TCC) within the NLCD forest pixels
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Another possible reason for the discrepancies between the metrics computed from the NLCD forest pixels and the TCC is the dissimilar methods used to generate each product. The NLCD is updated based on a change detection algorithm (Xian et al. 2009; Jin et al. 2013) while the TCC (2011 edition) utilized random forest modeling that incorporated finer spatial scale data such as orthoimagery and forest inventory analysis (FIA) plots (Coulston et al. 2012). While both studies report sufficient accuracies for mapping, the TCC pilot study notes pseudo R2 values as low as 0.53. This pilot study also did not include a sampling area the AH region (Coulston et al. 2012), which may also contribute to mapping accuracy in that region. Specifically, the AH is heavily forested in parts, yet the TCC product has surprisingly few pixels with greater than 90% canopy cover (Fig. 4). While we do not know the precise cause of the metric discrepancies seen in this study, researchers should use caution when using these two products in tandem as they are not cross validated. Considerations when using the threshold method
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There are several factors to consider when using the threshold method described in this paper for analysis of gradient surfaces. First, the discretization process invariably collapses some of the heterogeneity captured by gradient datasets. By setting finer threshold increments, users can minimize the loss of heterogeneity. However, there is a tradeoff between increased heterogeneity and additional processing time. In a previous study, Frazier and Wang (2013) found that threshold increments less than 10% did not provide considerable detail to warrant the additional processing time. However, researchers should evaluate their specific objectives and select a threshold increment that best suits their study. Second, the gradient rasters used in this study were produced by the MRLC, providing a straightforward dataset to compare to the NLCD patch-mosaic. In situations where a gradient dataset is not available, spectral unmixing methods (Keshava and Mustard 2002) can be applied directly to remotely sensed images to create gradient datasets of land cover. However, while several studies have investigated the propagation impacts of pixel-based classification errors on landscape metrics (Fang et al. 2006; Huang et al. 2006; Iverson 2007; Burnicki 2012), to our knowledge, no studies have examined the impact of sub12
ACCEPTED MANUSCRIPT pixel gradient classification error on landscape metrics. This is an area in need of future attention. Without a thorough understanding of the impact of gradient classification accuracy on landscape metrics, it is difficult to discern whether apparent ecological thresholds, such as those observed for PD (Fig. 4b), are an artifact of the classification scheme used to create the data. 5.
Conclusions
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In this study, we introduced an approach for extracting increased landscape pattern information from gradient surfaces using a common toolset (i.e., FRAGSTATS) to bridge the gaps between the patchmosaic model and the gradient surface model. Framing our investigation around a comparison of forest fragmentation in two ecoregions in the eastern U.S., we demonstrated how a thresholding approach can be used to discretize gradient surfaces into multiple discrete maps that can then be analyzed as patch-mosaic models. We created scalograms showing metric change across a continuum of forest density scales and compared them to single-value metrics computed for patch-mosaic landscape to illustrate how the additional information can be analyzed in an ecological context. Our results highlight several key findings. First, scalograms are able to depict the dynamics of landscape spatial structure across density threshold in a manner not possible with single-value metrics. The scalograms fostered the identification of ecological thresholds where there were abrupt changes in landscape dynamics at certain land cover proportions, and these thresholds have the potential to be used to target landscape management and conservation decisions.
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In this study, all metrics tested generated non-linear scaling relationships across the density thresholds, suggesting that spatial pattern analyses using gradient datasets might also require multi-scale analyses. In particular, the notable similarities in scaling relationships across the two ecoregions suggest that land cover density, or pixel value intensity, may be another form of scale in which consistent and robust scaling laws apply. Two components of scale, grain and extent, have received much attention in the landscape ecology literature for the consistent and robust scaling relationships they produce with respect to landscape metrics. In this study, we show that pixel density may be another scale component with similar relationships. Lastly, when analyzing landscape metrics based on gradient data, research is needed to investigate the impacts of classification accuracy on the derived metrics, as this area has not received much attention to date.
Acknowledgements
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This work was funded, in part, by a grant to A. Frazier and P. Kedron from the National Science Foundation (#SBE-1561021).
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Highlights
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Single-value metrics from patch-based data do not capture landscape dynamics Thresholding gradients produces binary maps to analyze with landscape metrics Scalograms of density thresholds indicate nonlinear landscape structure dynamics Scalograms generated from gradients permit identification of ecological thresholds Density scalograms show consistent and/or robust scaling relationships are possible
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