Measuring landscape configuration with normalized metrics

Natural and anthropogenic disturbances on natural landscapes reduce the abundance and alter the spatial arrangement of certain habitat types. Measuring and modeling such alterations, and their biological effects, remains challenging in part because many widely used configuration metrics are correlated with habitat amount. In this paper, we consider the sources of such correlation, and distinguish process or sample-based correlation from functional correlation that may be an artifact of the metrics themselves. Process correlation is not necessarily a serious problem for statistical inference, but functional correlation would be. We propose that functional correlation may be reduced by normalizing metrics by habitat abundance. We illustrate with normalized versions of total core area, mean nearest neighbor distance, and mean shape index, and show informally that the standard versions of these metrics should exhibit functional correlation. We evaluate the normalized metrics on samples of harvested and undisturbed forested landscapes, and on simulated landscapes generated with varying degrees of spatial autocorrelation. Normalization markedly reduced correlations with habitat abundance on natural landscapes, but not on simulated landscapes. The reasons for this appear to be a combination of differing variances in metric values within levels of habitat abundance, and of the precise form of the relationships between habitat abundance and the un-normalized metrics. In all cases, the normalization changes the ordering of landscapes by metric values across levels of habitat abundance. In consequence, normalized and standard metrics cannot both be accurate measures of configuration. We conclude that statistical modeling of ecological response data is needed to finally determine the merits of the normalizations.     

A new data aggregation technique to improve landscape metric downscaling

Scale is a fundamental concept in landscape ecology and considerable attention has been given to the scale-dependent relationships of landscape metrics. Many metrics have been found to exhibit very consistent scaling relationships as map resolution (i.e., pixel or grain size) is increased. However, these scaling relationships tend to break down when attempting to ‘downscale’ them, and the scaling function is often unable to accurately predict metric values for finer resolutions than the original data. The reasons for this breakdown are not well understood. This research examines the downscaling behavior of metrics using various data aggregation techniques in an attempt to better understand the characteristics of metric scaling behavior. First, downscaling performance is examined using the traditional method of aggregation known as ‘majority rules’. Second, a new data aggregation technique is introduced that utilizes fractional land cover abundances obtained from sub-pixel remote sensing classifications in order to capture a greater amount of the spatial heterogeneity present in the landscape. The goal of this new aggregation technique is to produce a more accurate scaling relationship that can be downscaled to predict metric values at fine resolutions. Results indicate that sub-pixel classifications have the potential to transform data aggregation to allow more accurate downscaling for certain landscapes, but accuracy is linked to the spatial heterogeneity of the landscape.     

A factor analysis of landscape pattern and structure metrics

Fifty-five metrics of landscape pattern and structure were calculated for 85 maps of land use and land cover. A multivariate factor analysis was used to identify the common axes (or dimensions) of pattern and structure which were measured by a reduced set of 26 metrics. The first six factors explained about 87% of the variation in the 26 landscape metrics. These factors were interpreted as composite measures of average patch compaction, overall image texture, average patch shape, patch perimeter-area scaling, number of attribute classes, and large-patch density-area scaling. We suggest that these factors can be represented in a simpler way by six univariate metrics - average perimeter-area ratio, contagion, standardized patch shape, patch perimeter-area scaling, number of attribute classes, and large-patch density-area scaling.     

Landscape patterns from mathematical morphology on maps with contagion

The perceived realism of simulated maps with contagion (spatial autocorrelation) has led to their use for comparing landscape pattern metrics and as habitat maps for modeling organism movement across landscapes. The objective of this study was to conduct a neutral model analysis of pattern metrics defined by morphological spatial pattern analysis (MSPA) on maps with contagion, with comparisons to phase transitions (abrupt changes) of patterns on simple random maps. Using MSPA, each focal class pixel on a neutral map was assigned to one of six pattern classes—core, edge, perforated, connector, branch, or islet—depending on MSPA rules for connectivity and edge width. As the density of the focal class (P) was increased on simple random maps, the proportions of pixels in different pattern classes exhibited two types of phase transitions at threshold densities (0.41 ≤ P ≤ 0.99) that were predicted by percolation theory after taking into account the MSPA rules for connectivity and edge width. While there was no evidence of phase transitions on maps with contagion, the general trends of pattern metrics in relation to P were similar to simple random maps. Using an index P for comparisons, the effect of increasing contagion was opposite that of increasing edge width.     

Ecosystem services of regulation and support in Amazonian pioneer fronts: searching for landscape drivers

Landscape dynamics result from forestry and farming practices, both of which are expected to have diverse impacts on ecosystem services (ES). In this study, we investigated this general statement for regulating and supporting services via an assessment of ecosystem functions: climate regulation via carbon sequestration in soil and plant biomass, water cycle and soil erosion regulation via water infiltration in soil, and support for primary production via soil chemical quality and water storage. We tested the hypothesis that patterns of land-cover composition and structure significantly alter ES metrics at two different scales. We surveyed 54 farms in two Amazonian regions of Brazil and Colombia and assessed land-cover composition and structure from remote sensing data (farm scale) from 1990 to 2007. Simple and well-established methods were used to characterize soil and vegetation from five points in each farm (plot scale). Most ES metrics were significantly correlated with land-use (plot scale) and land-cover (farm scale) classifications; however, spatial variability in inherent soil properties, alone or in interaction with land-use or land-cover changes, contributed greatly to variability in ES metrics. Carbon stock in above-ground plant biomass and water infiltration rate decreased from forest to pasture land covers, whereas soil chemical quality and plant-available water storage capacity increased. Land-cover classifications based on structure metrics explained significantly less ES metric variation than those based on composition metrics. Land-cover composition dynamics explained 45 % (P < 0.001) of ES metric variance, 15 % by itself and 30 % in interaction with inherent soil properties. This study describes how ES evolve with landscape changes, specifying the contribution of spatial variability in the physical environment and highlighting trade-offs and synergies among ES.     

The behavior of landscape metrics commonly used in the study of habitat fragmentation

A meaningful interpretation of landscape metrics is possible only when the limitations of each measure are fully understood, the range of attainable values is known, and the user is aware of potential shifts in the range of values due to characteristics of landscape patches. To examine the behavior of landscape metrics, we generated artificial landscapes that mimicked fragmentation processes while controlling the size and shape of patches in the landscape and the mode of disturbance growth. We developed nine series of increasingly fragmented landscapes and used these to investigate the behavior of edge density, contagion, mean nearest neighbor distance, mean proximity index, perimeter-area fractal dimension, and mass fractal dimension. We found that most of the measures were highly correlated, especially contagion and edge density, which had a near-perfect inverse correspondence. Many of the measures were linearly-associated with increasing disturbance until the proportion of disturbance on the landscape was approximately 0.40, with non-linear associations at higher proportions. None of the measures was able to differentiate between landscape patterns characterized by dispersed versus aggregated patches. The highest attainable value of each measure was altered by either patch size or shape, and in some cases, by both attributes. We summarize our findings by discussing the utility of each metric.     

A new contagion index to quantify spatial patterns of landscapes

A contagion index was proposed by O'Neill et al. (1988) to quantify spatial patterns of landscapes. However, this index is insensitive to changes in spatial pattern. We present a new contagion index that corrects an error in the mathematical formulation of the original contagion index. The error is identified mathematically. The contagion indices (both original and new) are then evaluated against simulated landscapes.     

Evaluation of landscape connectivity at community level using satellite-derived NDVI

Landscape connectivity, defined as the degree to which the landscape facilitates or impedes movement among resource patches, has been considered to be a key issue for biodiversity conservation. However, the use of landscape connectivity measurements has been strongly criticised due to uncertainties in the methods used and the lack of validation. Moreover, measurements are typically restricted to the population level, whereas management is generally carried out at the community level. Here, we used satellite imagery and network metrics to predict the landscape connectivity at community level for semi-natural herbaceous patches in an urban area near Paris (France). We tested different measurement methods, both taking into account and ignoring the spatial heterogeneity of matrix resistance estimated by the normalised difference vegetation index (NDVI), and quantifying the link strength between patches with the shortest path and flow metrics. We assessed the fit of these connectivity predictions with empirical data on plant communities embedded in an urban matrix. Our results indicate that the best fit with the empirical data is obtained when the connectivity is estimated with the flow metric and takes into account the matrix heterogeneity. Overall, our study helps to estimate the landscape connectivity of urban areas and makes recommendations for ways in which we might optimise landscape planning with respect to conservation of urban biodiversity.     

The influence of thematic resolution on metric selection for biodiversity monitoring in agricultural landscapes

The objective of this paper is to investigate the relationship between landscape pattern metrics and agricultural biodiversity at the Temperate European scale, exploring the role of thematic resolution and a suite of biological and functional groups. Factor analyses to select landscape-level metrics were undertaken on 25 landscapes classified at four levels of thematic resolution. The landscapes were located within seven countries. The different resolutions were considered appropriate to taxonomic and functional group diversity. As class-level metrics are often better correlated to ecological response, the landscape-level metric subsets gained through exploratory analysis were additionally used to guide the selection of class-level metric subsets. Linear mixed models were then used to detect correlations between landscape- and class-level metrics and species richness values. Taxonomic groups with differing requirements (plants, birds, different arthropod groups) and also functional arthropod groups were examined. At the coarse scale of thematic resolution grain metrics (patch density, largest patch index) emerged as rough indicators for the different biological groups whilst at the fine scale a diversity metric (e.g. Simpson’s diversity index) was appropriate. The intermediate thematic resolution offered most promise for biodiversity monitoring. Metrics included largest patch index, edge density, nearest neighbour, the proximity index, circle and Simpson’s diversity index. We suggest two possible applications of these metrics in the context of biodiversity monitoring and the identification of biodiversity hot spots in European agricultural landscapes.     

Determining an appropriate minimum mapping unit in vegetation mapping for ecosystem restoration: a case study from the Everglades,USA

This paper documents the analyses that were conducted with regards to investigating an appropriate Minimum Mapping Unit (MMU) to be used to capture the potential changes in vegetation patterns for a 10,924 square km restoration project being conducted in south Florida, USA. Spatial landscape and class metrics that were shown to change predictably with increasing grain size were adopted from previous studies and applied to a multi-scale analysis. Specifically, this study examines the effects of changing grain size on landscape metrics, utilizing empirical data from a real landscape encompassing 234,913 ha of south Florida’s Everglades. The objective was to identify critical thresholds within landscape metrics, which can be used to provide insight in determining an appropriate MMU for vegetation mapping. Results from this study demonstrate that vegetation heterogeneity will exhibit dissimilar patterns when investigating the loss of information within landscape and class metrics, as grain size is increased. These results also support previous findings that suggest that landscape metric “scalograms” (the response curves of landscape metrics to changing grain size), are more likely to be successful for linking landscape pattern to ecological processes as both pattern and process in ecological systems often operate on multiple scales. This study also incorporates an economic cost for various grain dependant vegetation mapping scales. A final selection of the 50 × 50 m grain size for mapping vegetation was based on this study’s investigation of the “scalograms”, the costs, and a composite best professional judgment of seasoned scientists having extensive experience within these ecosystems.     

Using patch isolation metrics to predict animal movement in binary landscapes

Habitat isolation can affect the distribution and abundance of wildlife, but it is an ambiguous attribute to measure. Presumably, isolation is a characteristic of a habitat patch that reflects how spatially inaccessible it is to dispersing organisms. We identified four isolation metrics (nearest-neighbor distance, Voronoi polygons, proximity index, and habitat buffers) that were representative of the different families of metrics that are commonly used in the literature to measure patch isolation. Using simulated data, we evaluated the ability of each isolation metric to predict animal dispersal. We examined the simulated movement of organisms in two types of landscapes: an artificially-generated point-pattern landscapes where patch size and shape were consistent and only the arrangement of patches varied, and realistic landscapes derived from a geographic information system (GIS) of forest-vegetation maps where patch size, shape, and isolation were variable. We tested the performance of the four isolation metrics by examining the strength of the correlation between observed immigration rate in the simulations and each patch isolation metric. We also evaluated whether each isolation metric would perform consistently under varying conditions of patch size/shape, total amount of habitat in the landscape, and proximity of the patch to the landscape edge. The results indicate that a commonly-used distance-based metric, nearest-neighbor distance, did not adequately predict immigration rate when patch size and shape were variable. Area-informed isolation metrics, such as the amount of available habitat within a given radius of a patch, were most successful at predicting immigration. Overall, the use of area-informed metrics is advocated despite the limitation that these metrics require parameterization to reflect the movement capacity of the organism studied.This revised version was published online in May 2005 with corrections to the Cover Date.     

The response of elephants to the spatial heterogeneity of vegetation in a Southern African agricultural landscape

Based on the agricultural landscape of the Sebungwe in Zimbabwe, we investigated whether and how the spatial distribution of the African elephant (Loxodonta africana) responded to spatial heterogeneity of vegetation cover based on data of the early 1980s and early 1990s. We also investigated whether and how elephant distribution responded to changes in spatial heterogeneity between the early 1980s and early 1990s. Vegetation cover was estimated from a normalised difference vegetation index (NDVI). Spatial heterogeneity was estimated from a new approach based on the intensity (i.e., the maximum variance exhibited when a spatially distributed landscape property such as vegetation cover is measured with a successively increasing window size or scale) and dominant scale (i.e., the scale or window size at which the intensity is displayed). We used a variogram to quantify the dominant scale (i.e., range) and intensity (i.e., sill) of NDVI based congruent windows (i.e., 3.84 km × 3.84 km in a 61 km × 61 km landscape). The results indicated that elephants consistently responded to the dominant scale of spatial heterogeneity in a unimodal fashion with the peak elephant presence occurring in environments with dominant scales of spatial heterogeneity of around 457–734 m. Both the intensity and dominant scale of spatial heterogeneity predicted 65 and 68% of the variance in elephant presence in the early 1980s and in the early 1990s respectively. Also, changes in the intensity and dominant scale of spatial heterogeneity predicted 61% of the variance in the change in elephant distribution. The results imply that management decisions must take into consideration the influence of the levels of spatial heterogeneity on elephants in order to ensure elephant persistence in agricultural landscapes.     

Landscape characteristics affecting streams in urbanizing regions of the Delaware River Basin (New Jersey,New York,and Pennsylvania,U.S.)

Widespread and increasing urbanization has resulted in the need to assess, monitor, and understand its effects on stream water quality. Identifying relations between stream ecological condition and urban intensity indicators such as impervious surface provides important, but insufficient information to effectively address planning and management needs in such areas. In this study we investigate those specific landscape metrics which are functionally linked to indicators of stream ecological condition, and in particular, identify those characteristics that exacerbate or mitigate changes in ecological condition over and above impervious surface. The approach used addresses challenges associated with redundancy of landscape metrics, and links landscape pattern and composition to an indicator of stream ecological condition across a broad area of the eastern United States. Macroinvertebrate samples were collected during 2000–2001 from forty-two sites in the Delaware River Basin, and landscape data of high spatial and thematic resolution were obtained from photointerpretation of 1999 imagery. An ordination-derived ‘biotic score’ was positively correlated with assemblage tolerance, and with urban-related chemical characteristics such as chloride concentration and an index of potential pesticide toxicity. Impervious surface explained 56% of the variation in biotic score, but the variation explained increased to as high as 83% with the incorporation of a second land use, cover, or configuration metric at catchment or riparian scales. These include land use class-specific cover metrics such as percent of urban land with tree cover, forest fragmentation metrics such as aggregation index, riparian metrics such as percent tree cover, and metrics related to urban aggregation. Study results indicate that these metrics will be important to monitor in urbanizing areas in addition to impervious surface.     

A note on contagion indices for landscape analysis

The landscape contagion index measures the degree of clumping of attributes on raster maps. The index is computed from the frequencies by which different pairs of attributes occur as adjacent pixels on a map. Because there are subtle differences in the way the attribute adjacencies may be tabulated, the standard index formula may not always apply, and published index values may not be comparable. This paper derives formulas for the contagion index that apply for different ways of tabulating attribute adjacencies — with and without preserving the order of pixels in pairs, and by using two different ways of determining pixel adjacency. When the order of pixels in pairs is preserved, the standard formula is obtained. When the order is not preserved, a new formula is obtained because the number of possible attribute adjacency states is smaller. Estimated contagion is also smaller when each pixel pair is counted twice (instead of once) because double-counting pixel adjacencies makes the attribute adjacency matrix symmetric across the main diagonal.     

Predicting nutrient and sediment loadings to streams from landscape metrics: A multiple watershed study from the United States Mid-Atlantic Region

There has been an increasing interest in evaluating the relative condition or health of water resources at regional and national scales. Of particular interest is an ability to identify those areas where surface and ground waters have the greatest potential for high levels of nutrient and sediment loadings. High levels of nutrient and sediment loadings can have adverse effects on both humans and aquatic ecosystems. We analyzed the ability of landscape metrics generated from readily available, spatial data to predict nutrient and sediment yield to streams in the Mid-Atlantic Region in the United States. We used landscape metric coverages generated from a previous assessment of the entire Mid-Atlantic Region, and a set of stream sample data from the U.S. Geological Survey. Landscape metrics consistently explained high amounts of variation in nitrogen yields to streams (65 to 86% of the total variation). They also explained 73 and 79% of the variability in dissolved phosphorus and suspended sediment. Although there were differences in the nitrogen, phosphorus, and sediment models, the amount of agriculture, riparian forests, and atmospheric nitrate deposition (nitrogen only) consistently explained a high proportion of the variation in these models. Differences in the models also suggest potential differences in landscape-stream relationships between ecoregions or biophysical settings. The results of the study suggest that readily available, spatial data can be used to assess potential nutrient and sediment loadings to streams, but that it will be important to develop and test landscape models in different biophysical settings.     

Spatial preference heterogeneity in policies for improving urban green spaces

Urban green spaces (UGSs) enhance the quality of urban dwellers’ lives. Thus, efficient policies for improving UGSs—which should reflect urban residents’ needs—are necessary. Additionally, it is crucial to manage the spatial distribution of residents’ preferences to find regions that can produce greater utility within limited budgets. Using online surveys conducted in 2015, which obtained 414 valid responses, this study analyzed urban residents’ preferences for UGS improvement policies and investigated spatial preference heterogeneity for such policies in the planned city of Seongnam, South Korea. A mixed logit model was applied to analyze policy preferences, and the preference heterogeneity level was assessed by coefficient of variation. Additionally, hot spot analysis was performed to examine spatial heterogeneity. The Getis-ord Gi* was computed to identify the spatial clusters of the estimated coefficients and the marginal willingness to pay (WTP). The results indicated a high preference for enhancing quality and connectivity. While the results showed that preference heterogeneity existed in each UGS improvement policy, heterogeneity levels differed per attribute. Statistically significant local spatial clusters of estimated coefficients and marginal WTP were observed for each UGS improvement policy despite global autocorrelation being insignificant. It was observed that estimate coefficients with low coefficient of variation can make extensive spatial clusters; otherwise, the opposite trend might occur. Additionally, marginal WTP hot spots did not change according to attribute but appeared in similar locations. Therefore, spatial heterogeneity analysis is necessary to manage UGSs with higher net utilities given limited budgets. These findings will ensure the satisfaction of all urban residents by identifying their preferences for UGS policies. They will also help prioritize cost-effective implementation of policy considering spatial preference heterogeneity.