Scale problems in reporting landscape pattern at the regional scale

Remotely sensed data for Southeastern United States (Standard Federal Region 4) are used to examine the scale problems involved in reporting landscape pattern for a large, heterogeneous region. Frequency distributions of landscape indices illustrate problems associated with the grain or resolution of the data. Grain should be 2 to 5 times smaller than the spatial features of interest. The analyses also reveal that the indices are sensitive to the calculation scale,i.e., the unit area or extent over which the index is computed. This “sample area” must be 2 to 5 times larger than landscape patches to avoid bias in calculating the indices. Research sponsored by the Office of Research and Development, U.S. Environmental Protection Agency under IAG DW89934440-6 and DW89936104-01 with the U.S. Department of Energy under contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc.     

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.     

Determination of ecological scale

We suggest that ecological processes and physical characteristics possess an inherent scale at which the processes or characteristics occur over the landscape. We propose a conceptual spatial response model that describes the nature of this ecological scale. Based on the proposed spatial model, we suggest methods for estimating the size of study plots or transects and the distance between replicate plots needed to approach statistical independence. Using data on percent cover for Agropyron spicatum, a common arid-land bunchgrass, we demonstrated four relationships that should hold if the spatial response model is appropriate. These relationships are sample variance increases as functions of (1) transect segment length and (2) intersegment length (transect segment dispersal), and correlation decreases as functions of (3) intersegment length and (4) transect segment length. Based on evaluation of these four relationships, cover for A. spicatum is correlated over the landscape on a scale of 400 to 700 m, and a segment length of 64 to 128 m is most appropriate for measuring cover for this species.     

Effects of changing spatial resolution on the results of landscape pattern analysis using spatial autocorrelation indices

Understanding the relationship between pattern and scale is a central issue in landscape ecology. Pattern analysis is necessarily a critical step to achieve this understanding. Pattern and scale are inseparable in theory and in reality. Pattern occurs on different scales, and scale affects pattern to be observed. The objective of our study is to investigate how changing scale might affect the results of landscape pattern analysis using three commonly adopted spatial autocorrelation indices,i.e., Moran Coefficient, Geary Ratio, and Cliff-Ord statistic. The data sets used in this study are spatially referenced digital data sets of topography and biomass in 1972 of Peninsular Malaysia. Our results show that all three autocorrelation indices were scale-dependent. In other words, the degree of spatial autocorrelation measured by these indices vary with the spatial scale on which analysis was performed. While all the data sets show a positive spatial autocorrelation across a range of scales, Moran coefficient and Cliff-Ord statistic decrease and Geary Ratio increases with increasing grain size, indicating an overall decline in the degree of spatial autocorrelation with scale. The effect of changing scale varies in their magnitude and rate of change when different types of landscape data are used. We have also explored why this could happen by examining the formulation of the Moran coefficient. The pattern of change in spatial autocorrelation with scale exhibits threshold behavior,i.e., scale effects fade away after certain spatial scales are reached (for elevation). We recommend that multiple methods be used for pattern analysis whenever feasible, and that scale effects must be taken into account in all spatial analysis.     

Neutral models for the analysis of broad-scale landscape pattern

The relationship between a landscape process and observed patterns can be rigorously tested only if the expected pattern in the absence of the process is known. We used methods derived from percolation theory to construct neutral landscape models,i.e., models lacking effects due to topography, contagion, disturbance history, and related ecological processes. This paper analyzes the patterns generated by these models, and compares the results with observed landscape patterns. The analysis shows that number, size, and shape of patches changes as a function of p, the fraction of the landscape occupied by the habitat type of interest, and m, the linear dimension of the map. The adaptation of percolation theory to finite scales provides a baseline for statistical comparison with landscape data. When USGS land use data (LUDA) maps are compared to random maps produced by percolation models, significant differences in the number, size distribution, and the area/perimeter (fractal dimension) indices of patches were found. These results make it possible to define the appropriate scales at which disturbance and landscape processes interact to affect landscape patterns.     

Multi-scale predictive habitat suitability modeling based on hierarchically delineated patches: an example for yellow-billed cuckoos nesting in riparian forests,California, USA

The discipline of landscape ecology recognizes the importance of measuring habitat suitability variables at spatial scales relevant to specific organisms. This paper uses a novel multi-scale hierarchical patch delineation method, PatchMorph, to measure landscape patch characteristics at two distinct spatial scales and statistically relate them to the presence of state-listed endangered yellow-billed cuckoos (Coccyzus americanus occidentalis) nesting in forest patches along the Sacramento River, California, USA. The landscape patch characteristics calculated were: patch thickness, area of cottonwood forest, area of riparian scrub, area of other mixed riparian forest, and total patch area. A third, regional spatial variable, delineating the north and south portions of study area was also analyzed for the effect of regional processes. Using field surveys, the landscape characteristics were related to patch occupancy by yellow-billed cuckoos. The area of cottonwood forest measured at the finest spatial scale of patches was found to be the most important factor determining yellow-billed cuckoo presence in the forest patches, while no patch characteristics at the larger scale of habitat patches were important. The regional spatial variable was important in two of the three analysis techniques. Model validation using an independent data set of surveys (conducted 1987–1990) found 76–82% model accuracy for all the statistical techniques used. Our results show that the spatial scale at which habitat characteristics are measured influences the suitability of forest patches. This multi-scale patch and model selection approach to habitat suitability analysis can readily be generalized for use with other organisms and systems.     

How to define a patch: a spatial model for hierarchically delineating organism-specific habitat patches

Landscape analysis and delineation of habitat patches should take into account organism-specific behavioral and perceptual responses to landscape structure because different organisms perceive and respond to landscape features over different ranges of spatial scales. The commonly used methods for delineating habitat based on rules of contiguity do not account for organism-specific responses to landscape patch structure and have undesirable properties, such as being dependent on the scale of base map used for analysis. This paper presents an improved patch delineation algorithm, “PatchMorph,” which can delineate patches across a range of spatial scales based on three organism-specific thresholds: (1) land cover density threshold, (2) habitat gap maximum thickness (gap threshold), and (3) habitat patch minimum thickness (spur threshold). This algorithm was tested on an “idealized” landscape with landscape gaps and spurs of known size, and delineated patches as expected. It was then applied to delineate patches from a neutral random fractal landscape, which showed that as the input gap and spur thickness thresholds were increased, the number of patches decreased from 59 (low thresholds) patches to 1 (high thresholds). The algorithm was then applied to model western yellow-billed cuckoo (Coccyzus americanus occidentalis) nesting habitat patches based on spur and gap thresholds specific to this organism. Both these analyses showed that fewer patches were delineated by PatchMorph than by rules of contiguity, and those patches were larger, had smoother edges, and had fewer gaps within the patches. This algorithm has many applications beyond those presented in this paper, including habitat suitability analysis, spatially explicit population modeling, and habitat connectivity analysis.     

Associations between soil carbon and ecological landscape variables at escalating spatial scales in Florida,USA

The spatial distribution of soil carbon (C) is controlled by ecological processes that evolve and interact over a range of spatial scales across the landscape. The relationships between hydrologic and biotic processes and soil C patterns and spatial behavior are still poorly understood. Our objectives were to (i) identify the appropriate spatial scale to observe soil total C (TC) in a subtropical landscape with pronounced hydrologic and biotic variation, and (ii) investigate the spatial behavior and relationships between TC and ecological landscape variables which aggregate various hydrologic and biotic processes. The study was conducted in Florida, USA, characterized by extreme hydrologic (poorly to excessively drained soils), and vegetation/land use gradients ranging from natural uplands and wetlands to intensively managed forest, agricultural, and urban systems. We used semivariogram and landscape indices to compare the spatial dependence structures of TC and 19 ecological landscape variables, identifying similarities and establishing pattern–process relationships. Soil, hydrologic, and biotic ecological variables mirrored the spatial behavior of TC at fine (few kilometers), and coarse (hundreds of kilometers) spatial scales. Specifically, soil available water capacity resembled the spatial dependence structure of TC at escalating scales, supporting a multi-scale soil hydrology-soil C process–pattern relationship in Florida. Our findings suggest two appropriate scales to observe TC, one at a short range (autocorrelation range of 5.6 km), representing local soil-landscape variation, and another at a longer range (119 km), accounting for regional variation. Moreover, our results provide further guidance to measure ecological variables influencing C dynamics.     

Neighbourhood landscape effect on population kinetics of the fossorial water vole (<Emphasis Type="Italic">Arvicola terrestris scherman</Emphasis>)

This paper addresses the issue of whether landscape structure affects A. terrestris population kinetics on a neighbourhood spatial scale, and if so, at what spatial scale is that effect at its maximum. We investigated how the growth of A. terrestris populations is influenced by the landscape context of parcels used for hay production in the French Jura Mountains. Five landscape metrics (relative area of grassland, mean patch area of grassland, patch density of grassland, woodland patch density in grassland, grassland–woodland edge density) were computed over an increasing radius around each parcel (max. 3 km). Redundancy analysis showed that the extent, rate and early onset of A. terrestris population growth were favoured in open grassland areas. Landscape effects on A. terrestris populations as determined by the five metrics are scale-dependent: mean patch area of grassland, patch density of grassland and woodland patch density in grassland had an impact on a grassland parcel within a neighbourhood radius of about 800 m, while relative area of grassland and grassland–woodland edge density had an impact within a neighbourhood radius of about 400 m. Those findings corroborate earlier hypotheses about a multifactorial regulation of A. terrestris populations and a spatial hierarchy of regulating factors. They have potential implications in terms of landscape management and small mammal pest control.     

Comparative influence of isolation,landscape, and wetland characteristics on egg-mass abundance of two pool-breeding amphibian species

The distribution and abundance of species are shaped by local and landscape processes, but the dominant processes may differ with scale and increasing human disturbance. We investigated population responses of two pool-breeding amphibian species to differences in local and landscape characteristics in suburbanizing, southeastern New Hampshire, USA. In 2003 and 2004, we sampled 49 vernal pools for spotted salamander (Ambystoma maculatum) and wood frog (Lithobates sylvaticus) egg masses. Using egg masses as a proxy for breeding-female population size, we examined the relative influence of five land-use and three isolation variables at two scales (300 and 1000 m) and five wetland variables on egg-mass abundance. For both species, road density at the landscape scale (1000 m) and hydroperiod most strongly predicted egg-mass abundance, with abundance decreasing as roads became denser and hydroperiods shortened. Wetland isolation was also an important predictor, with abundance greatest at more isolated pools, suggesting that both species concentrate at isolated pools when alternative breeding sites are scarce. Surprisingly, no 300-m parameters were strongly associated with salamander egg-mass abundance, whereas several landscape parameters were. In suburbanizing areas, it is at least as important to consider landscape-scale road density as to consider hydroperiod when designing conservation plans for these species. Furthermore, both isolated and clustered pools provide these species important habitat and may require protection. Finally, the conceptual framework for spotted-salamander management must be expanded so that spatial configuration at the landscape scale becomes a regular, integrated component of conservation planning for this species.     

Analysis and simulation of land-use change in the central Arizona – Phoenix region,USA

To understand how urbanization has transformed the desert landscape in the central Arizona – Phoenix region of the United States, we conducted a series of spatial analyses of the land-use pattern from 1912–1995. The results of the spatial analysis show that the extent of urban area has increased exponentially for the past 83 years, and this urban expansion is correlated with the increase in population size for the same period of time. The accelerating urbanization process has increased the degree of fragmentation and structural complexity of the desert landscape. To simulate land-use change we developed a Markov-cellular automata model. Model parameters and neighborhood rules were obtained both empirically and with a modified genetic algorithm. Land-use maps for 1975 and 1995 were used to implement the model at two distinct spatial scales with a time step of one year. Model performance was evaluated using Monte-Carlo confidence interval estimation for selected landscape pattern indices. The coarse-scale model simulated the statistical patterns of the landscape at a higher accuracy than the fine-scale model. The empirically derived parameter set poorly simulated land-use change as compared to the optimized parameter set. In summary, our results showed that landscape pattern metrics (patch density, edge density, fractal dimension, contagion) together were able to effectively capture the trend in land-use associated with urbanization for this region. The Markov-cellular automata parameterized by a modified genetic algorithm reasonably replicated the change in land-use pattern.     

Effects of changing spatial scale on the analysis of landscape pattern

The purpose of this study was to observe the effects of changing the grain (the first level of spatial resolution possible with a given data set) and extent (the total area of the study) of landscape data on observed spatial patterns and to identify some general rules for comparing measures obtained at different scales. Simple random maps, maps with contagion (i.e., clusters of the same land cover type), and actual landscape data from USGS land use (LUDA) data maps were used in the analyses. Landscape patterns were compared using indices measuring diversity (H), dominance (D) and contagion (C). Rare land cover types were lost as grain became coarser. This loss could be predicted analytically for random maps with two land cover types, and it was observed in actual landscapes as grain was increased experimentally. However, the rate of loss was influenced by the spatial pattern. Land cover types that were clumped disappeared slowly or were retained with increasing grain, whereas cover types that were dispersed were lost rapidly. The diversity index decreased linearly with increasing grain size, but dominance and contagion did not show a linear relationship. The indices D and C increased with increasing extent, but H exhibited a variable response. The indices were sensitive to the number (m) of cover types observed in the data set and the fraction of the landscape occupied by each cover type (P _k); both m and P _kvaried with grain and extent. Qualitative and quantitative changes in measurements across spatial scales will differ depending on how scale is defined. Characterizing the relationships between ecological measurements and the grain or extent of the data may make it possible to predict or correct for the loss of information with changes in spatial scale.     

Boundary-fitted grid in landscape modeling

Landscape modeling requires the delineation of system boundaries and interior features. Quite often, these components are complex and difficult to accurately represent. A rectangular grid is used to represent the study and adjacent non-study areas in most cases. When the non-study area occupies a large portion of the grid, computer memory is wasted, and computational time increases. An elliptical grid generator for non-orthogonal curvilinear coordinates is used to generate a boundary-fitted grid for a landscape model. In a boundary-fitted grid coordinate system, one coordinate axis follows the landscape domain boundary and is non-orthogonal to the second axis. The boundary-fitted grid uses elliptic partial differential equations to distribute grid points inside the landscape domain. Although the boundary-fitted grid follows the domain boundary, the grid pattern and point allocation remain structured. Thus, a landscape model can use a boundary-fitted grid without changing the model’s data structure or the computational scheme. In this study, a boundary-fitted grid and a raster-based grid were applied to the Everglades Landscape Fire Model. Use of the boundary-fitted grid decreased model simulation time by about one fifth and computer storage by 58% relative to the raster-based grid. Also, the linear characteristics of interior geographical features such as rivers and airboat trails were preserved by the boundary-fitted grid, but not by the raster-based grid. This preservation provided a more reasonable base map for simulating ecological processes, such as fire across heterogenous landscapes.     

Presettlement landscape heterogeneity: Evaluating grain of resolution using General Land Office Survey data

General Land Office Survey (GLOS) records from the A.D. 1840s provide data for quantitative characterization of presettlement vegetation across western Mackinac County, Michigan, located within the mixed conifer-northern hardwoods forest region. We analyzed data from land survey plat maps and 1958 bearing, witness, and line trees from 162 surveyed section and quarter-section corners in order to map vegatation cover types at a level of spatial resolution appropriate for characterizing landscape heterogeneity using standard landscape ecological metrics. As also demonstrated by a number of both classic and contemporary plant-ecological studies, the distribution of landforms, soils properties, hydrology, and location of fire breaks all contribute to the heterogeneity in vegetation observed at a landscape scale in the region. Through a series of spatial landscape analyses with differing grain of resolution, in this study we determine that a grid cell size of 65 ha (0.5 mi×0.5 mi or 0.25 mi²) to 259 ha (1 mi²) gives a conservative characterization of landscape heterogeneity using standard metrics and is therefore appropriate for use of GLOS data to study historical landscape changes.     

The effect of spatial scale on Konza landscape classification using textural analysis

Spatial scale is inherent in the definition of landscape heterogeneity and diversity. For example, a landscape may appear heterogeneous at one scale but quite homogeneous at another scale. In assessing the impact of burning and grazing on the Konza Prairie Research Natural Area (a tallgrass prairie), spatial scale is extremely important. Textural contrast algorithms were applied to various scales of remote sensing data and related to landscape units for assessment of heterogeneity under a variety of burning treatments. Acquired data sets included Landsat multispectral scanner (MSS), with 80 m resolution, Landsat thematic mapper (TM), with 30 m resolution, and high resolution density sliced aerial photography (with a 5 m resolution). Results suggest that heterogeneous areas of dense patchiness (e.g., unburned areas) must be analyzed at a finer scale than more homogeneous areas which are burned at least every four years.     

Indices of landscape pattern

Landscape ecology deals with the patterning of ecosystems in space. Methods are needed to quantify aspects of spatial pattern that can be correlated with ecological processes. The present paper develops three indices of pattern derived from information theory and fractal geometry. Using digitized maps, the indices are calculated for 94 quadrangles covering most of the eastern United States. The indices are shown to be reasonably independent of each other and to capture major features of landscape pattern. One of the indices, the fractal dimension, is shown to be correlated with the degree of human manipulation of the landscape.     

The modifiable areal unit problem and implications for landscape ecology

Landscape ecologists often deal with aggregated data and multiscaled spatial phenomena. Recognizing the sensitivity of the results of spatial analyses to the definition of units for which data are collected is critical to characterizing landscapes with minimal bias and avoidance of spurious relationships. We introduce and examine the effect of data aggregation on analysis of landscape structure as exemplified through what has become known, in the statistical and geographical literature, as theModifiable Areal Unit Problem (MAUP). The MAUP applies to two separate, but interrelated, problems with spatial data analysis. The first is the “scale problem”, where the same set of areal data is aggregated into several sets of larger areal units, with each combination leading to different data values and inferences. The second aspect of the MAUP is the “zoning problem”, where a given set of areal units is recombined into zones that are of the same size but located differently, again resulting in variation in data values and, consequently, different conclusions. We conduct a series of spatial autocorrelation analyses based on NDVI (Normalized Difference Vegetation Index) to demonstrate how the MAUP may affect the results of landscape analysis. We conclude with a discussion of the broader-scale implications for the MAUP in landscape ecology and suggest approaches for dealing with this issue.     

Scaling properties in landscape patterns: New Zealand experience

In this paper we present a case study of spatial structure in landscape patterns for the North and South Islands of New Zealand. The aim was to characterise quantitatively landscape heterogeneity and investigate its possible scaling properties. The study examines spatial heterogeneity, in particular patchiness, at a range of spatial scales, to help build understanding on the effects of landscape heterogeneity on water movement in particular, and landscape ecology in general.We used spatial information on various landscape properties (soils, hydrogeology, vegetation, topography) generated from the New Zealand Land Resource Inventory. To analyse this data set we applied various methods of fractal analyses following the hypothesis that patchiness in selected landscape properties demonstrates fractal scaling behaviour at two structural levels: (1) individual patches; and (2) mosaics (sets) of patches.Individual patches revealed scaling behaviour for both patch shape and boundary. We found self-affinity in patch shape with Hurst exponent H from 0.75 to 0.95. We also showed that patch boundaries in most cases were self-similar and in a few cases of large patches were self-affine. The degree of self-affinity was lower for finer patches. Similarly, when patch scale decreases the orientation of patches tends to be uniformly distributed, though patch orientation on average is clearly correlated with broad scale geological structures. These results reflect a tendency to isotropic behaviour of individual patches from broad to finer scales. Mosaics of patches also revealed fractal scaling in the total patch boundaries, patch centers of mass, and in patch area distribution. All these reflect a special organisation in patchiness represented in fractal patch clustering. General relationships which interconnect fractal scaling exponents were derived and tested. These relationships show how scaling properties of individual patches affect those for mosaics of patches and vice-versa. To explain similarity in scaling behaviour in patchiness of different types we suggest that the Self-Organised Criticality concept should be used. Also, potential applications of our results in landscape ecology are discussed, especially in relation to improved neutral landscape models.