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.     

Impact of scale on morphological spatial pattern of forest

Assessing and monitoring landscape pattern structure from multi-scale land-cover maps can utilize morphological spatial pattern analysis (MSPA), only if various influences of scale are known and taken into account. This paper lays part of the foundation for applying MSPA analysis in landscape monitoring by quantifying scale effects on six classes of spatial patterns called: core, edge, perforation, branch, connector and islet. Four forest maps were selected with different forest composition and configuration. The sensitivity of MSPA to scale was studied by comparing frequencies of pattern classes in total forest area for various combinations of pixel size (P) and size parameter (S). It was found that the quantification of forest pattern with MSPA is sensitive to scale. Differences in initial composition and configuration influence the amount but not the general tendencies of the variations of morphological spatial pattern (MSP) class proportions with scale. Increase of P led to data generalization resulting in either a removal of the small size features or their potential transformation into other non-core MSP classes, while an increase of S decreases the MSP core area and this process may transform small core areas into the MSP class islet. We established that the behavior of the MSPA classes with changing scale can be categorized as consistent and robust scaling relations in the forms of linear, power, or logarithmic functions over a range of scales.     

A comparison of quantitative methods for examining landscape pattern and scale

Ecologists have long recognized the importance of spatial and temporal patterns that characterize heterogeneity in landscapes. However, despite the realization that inferences about ecological phenomena are scale dependent, little attention has been paid to determining appropriate scales of measurement (e.g., plot or grain size) in studies of landscape dynamics or ecosystem change. This paper compares the results from three data sets using several quantitative methods available for characterizing landscape heterogeneity and/or for determining scale of measurement. Methods evaluated include tests of non-randomness, estimation of patch size, spectral analysis, fractals, variance ratio analysis, and correlation analysis. The results showed that no one method provides consistently good estimates of scale. Thus, sampling strategies for landscape studies should be derived from estimates of patch size and/or scale of pattern obtained from more than one of these methods.     

Spatial and temporal analysis of landscape patterns

A variety of ecological questions now require the study of large regions and the understanding of spatial heterogeneity. Methods for spatial-temporal analyses are becoming increasingly important for ecological studies. A grid cell based spatial analysis program (SPAN) is described and results of landscape pattern analysis using SPAN are presentedd. Several ecological topics in which geographic information systems (GIS) can play an important role (landscape pattern analysis, neutral models of pattern and process, and extrapolation across spatial scales) are reviewed. To study the relationship between observed landscape patterns and ecological processes, a neutral model approach is recommended. For example, the expected pattern (i.e., neutral model) of the spread of disturbance across a landscape can be generated and then tested using actual landscape data that are stored in a GIS. Observed spatial or temporal patterns in ecological data may also be influenced by scale. Creating a spatial data base frequently requires integrating data at different scales. Spatial is shown to influence landscape pattern analyses, but extrapolation of data across spatial scales may be possible if the grain and extent of the data are specified. The continued development and testing of new methods for spatial-temporal analysis will contribute to a general understanding of landscape dynamics.     

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.     

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.     

Scale detection in real and artificial landscapes using semivariance analysis

Semivariance analysis is potentially useful to landscape ecologists for detecting scales of variability in spatial data. We used semivariance analysis to compare spatial patterns of winter foraging by large ungulates with those of environmental variables that influence forage availability in northern Yellowstone National Park, Wyoming. In addition, we evaluated (1) the ability of semivariograms to detect known scales of variability in artificial maps with one or more distinct scales of pattern, and (2) the influence of the amount and spatial distribution of absent data on semivariogram results and interpretation. Semivariograms of environmental data sets (aspect, elevation, habitat type, and slope) for the entire northern Yellowstone landscape clearly identified the dominant scale of variability in each map layer, while semivariograms of ungulate foraging data from discontinuous study areas were difficult to interpret. Semivariograms of binary maps composed of a single scale of pattern showed clear and interpretable results: the range accurately reflected the size of the blocks of which the maps were constructed. Semivariograms of multiple scale maps and hierarchical maps exhibited pronounced inflections which could be used to distinguish two or three distinct scales of pattern. To assess the sensitivity of semivariance analysis to absent data, often the product of cloud interference or incomplete data collection, we deliberately masked (deleted) portions of continuous northern Yellowstone map layers, using single scale artificial maps as masks. The sensitivity of semivariance analysis to random deletions from the data was related to both the size of the deleted blocks, and the total proportion of the original data set that was removed. Small blocks could be deleted in very high proportions without degrading the semivariogram results. When the size of deleted blocks was large relative to the size of the map, the corresponding variograms became sensitive to the total proportion of data removed: variograms were difficult or impossible to interpret when the proportion of data deleted was high. Despite success with artificial maps, standard semivariance analysis is unlikely to detect multiple scales of pattern in real ecological data. Semivariance analysis is recommended as an effective technique for quantifying some spatial characteristics of ecological data, and may provide insight into the scales of processes that structure landscapes.     

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.     

Selection of scale for Everglades landscape models

This article addresses the problem of determining the optimal “Model Grain” or spatial resolution (scale) for landscape modeling in the Everglades. Selecting an appropriate scale for landscape modeling is a critical task that is necessary before using spatial data for model development. How the landscape is viewed in a simulation model is dependent on the scale (cell size) in which it is created. Given that different processes usually have different rates of fluctuations (frequencies), the question of selection of an appropriate modeling scale is a difficult one and most relevant to developing spatial ecosystem models. The question of choosing the appropriate scale for modeling is addressed using the landscape indices (e.g., cover fraction, diversity index, fractal dimension, and transition probabilities) recently developed for quantifying overall characteristics of spatial patterns. A vegetation map of an Everglades impoundment area developed from SPOT satellite data was used in the analyses. The data from this original 20 × 20 m data set was spatially aggregated to a 40 × 40 m resolution and incremented by 40 meters on up to 1000 × 1000 m (i.e., 40, 80, 120, 160 … 1000) scale. The primary focus was on the loss of information and the variation of spatial indices as a function of broadening “Model Grain” or scale. Cover fraction and diversity indices with broadening scale indicate important features, such as tree islands and brush mixture communities in the landscape, nearly disappear at or beyond the 700 m scale. The fractal analyses indicate that the area perimeter relationship changes quite rapidly after about 100 m scale. These results and others reported in the paper should be useful for setting appropriate objectives and expectations for Everglades landscape models built to varying spatial scales.     

Detecting hot and cold spots in a seagrass landscape using local indicators of spatial association

Eelgrass (Zostera marina) is an important feature of coastal ecosystems in Atlantic Canada, providing a suite of valuable ecosystem services. These services, and its sensitivity to stressors, have prompted efforts to characterize the spatial and temporal dynamics of eelgrass landscapes in order to facilitate management and monitoring of coastal ecosystem health. Current methods for broad-scale mapping of eelgrass rely on aerial remote sensing and may not be appropriate in certain types of landscapes, particularly in turbid waters and areas lacking distinct boundaries. This study takes a novel approach to the quantification and analysis of seagrass landscape structure at multiple spatial scales using acoustic data and local spatial statistics. Data from a single-beam acoustic survey in Richibucto, New Brunswick, Canada were analyzed with geostatistical techniques and the Getis-Ord G _i ^* local spatial statistic in order to detect statistically significant zones of high and low cover in an estuarine seagrass bed. Results showed distinct and significant patterns in seagrass cover at multiple spatial scales within a region of apparently continuous spatial cover. Boundaries between areas of high and low cover were also detected. This study demonstrates how acoustic data and local spatial statistics can be used to quantify landscape pattern and to further the application of landscape techniques in the marine environment.     

Current velocity and spatial scale as determinants of the distribution and abundance of two rheophilic herbivorous insects

Organisms frequently show marked preferences for specific environmental conditions, but these preferences may change with landscape scale. Patterns of distribution or abundance measured at different scales may reveal something about an organism's perception of the environment. To test this hypothesis, we measured densities of two herbivorous aquatic insects that differed in body morphology and mobility in relation to current velocity measured at different scales in the upper Colorado River (Colorado, USA). Streambed densities of the caddisfly larva Agapetus boulderensis (high hydrodynamic profile, low mobility) and mayfly nymph Epeorus sp. (low hydrodynamic profile, high mobility) were assessed at 3 spatial scales: whole riffles, individual cobbles within riffles, and point locations on cobbles. Riffles were several meters in extent, cobbles measured 10–30 cm in size, and the local scale was within a few centimeters of individual larvae (themselves ca. 0.5–1.0 cm in size). We also quantified the abundance of periphytic food for these herbivores at the cobble and riffle scales. Agapetus favored slow current (<30 cm s^–1) across all scales. Epeorus, by contrast, favored fast current (60–80 cm s^–1) at the local and riffle scale, but not at the cobble scale. Only Agapetus showed a significant relationship to current at the cobble scale, with greatest larval densities occurring at velocities near 30 cm s^–1. We had predicted an inverse correlation between grazer density and periphytic abundance; however, this occurred only for Agapetus, and then only at the cobble scale. These data suggest that organisms respond to environmental gradients at different spatial scales and that the processes driving these responses may change with scale, e.g., shifting from individual habitat selection at local and cobble scales to population responses at the riffle scale. This study also highlights the importance of using the appropriate scale of measurement to accurately assess the relationship between organisms and environmental gradients across scale.     

An aggregation index (AI) to quantify spatial patterns of landscapes

There is often need to measure aggregation levels of spatial patterns within a single map class in landscape ecological studies. The contagion index (CI), shape index (SI), and probability of adjacency of the same class (Qi), all have certain limits when measuring aggregation of spatial patterns. We have developed an aggregation index (AI) that is class specific and independent of landscape composition. AI assumes that a class with the highest level of aggregation (AI =1) is comprised of pixels sharing the most possible edges. A class whose pixels share no edges (completely disaggregated) has the lowest level of aggregation (AI =0). AI is similar to SI and Qi, but it calculates aggregation more precisely than the latter two. We have evaluated the performance of AI under varied levels of (1) aggregation, (2) number of patches, (3) spatial resolutions, and (4) real species distribution maps at various spatial scales. AI was able to produce reasonable results under all these circumstances. Since it is class specific, it is more precise than CI, which measures overall landscape aggregation. Thus, AI provides a quantitative basis to correlate the spatial pattern of a class with a specific process. Since AI is a ratio variable, map units do not affect the calculation. It can be compared between classes from the same or different landscapes, or even the same classes from the same landscape under different resolutions.     

Relationships between landcover proportion and indices of landscape spatial pattern

Recent studies have related percolation theory and critical phenomena to the spatial pattern of landscapes. We generated simulated landscapes of forest and non-forest landcover to investigate the relationship between the proportion of forest (P_i) and indices of patch spatial pattern. One set of landscapes was generated by randomly assigning each pixel independently of other pixels, and a second set was generated by randomly assigning rectilinear clumps of pixels. Indices of spatial pattern were calculated and plotted against P_i. The random-clump landscapes were also compared with real agricultural landscapes. The results support the use of percolation models as neutral models in landscape ecology, and the performance of the indices studied with these neutral models can be used to help interpret those indices calculated for real landscapes.     

Estimating the spatial scales of landscape effects on abundance

Context

Spatial variation in abundance is influenced by local- and landscape-level environmental variables, but modeling landscape effects is challenging because the spatial scales of the relationships are unknown. Current approaches involve buffering survey locations with polygons of various sizes and using model selection to identify the best scale. The buffering approach does not acknowledge that the influence of surrounding landscape features should diminish with distance, and it does not yield an estimate of the unknown scale parameters.

Objectives

The purpose of this paper is to present an approach that allows for statistical inference about the scales at which landscape variables affect abundance.

Methods

Our method uses smoothing kernels to average landscape variables around focal sites and uses maximum likelihood to estimate the scale parameters of the kernels and the effects of the smoothed variables on abundance. We assessed model performance using a simulation study and an avian point count dataset.

Results

The simulation study demonstrated that estimators are unbiased and produce correct confidence interval coverage except in the rare case in which there is little spatial autocorrelation in the landscape variable. Canada warbler abundance was more highly correlated with site-level measures of NDVI than landscape-level NDVI, but the reverse was true for elevation. Canada warbler abundance was highest when elevation in the surrounding landscape, defined by an estimated Gaussian kernel, was between 1300 and 1400 m.

Conclusions

Our method provides a rigorous way of formally estimating the scales at which landscape variables affect abundance, and it can be embedded within most classes of statistical models.

     

Disturbance increases negative spatial autocorrelation in species diversity

Context

Ecological processes that shape diversity and spatial pattern of ecological communities are often altered by disturbance. Spatial patterns (spatial autocorrelation) in species diversity are thus expected to change with disturbance.

Objective

When examining spatial patterns, ecologists traditionally lump positive and negative spatial autocorrelation into the overall spatial autocorrelation. By contrast, here we aim to understand disturbance effects on both positive and negative spatial autocorrelation of species richness and evenness, which may be related to environmental filtering and restricted dispersal, and to competition, respectively.

Methods

For 8 years, we monitored the spatial autocorrelation in species richness and evenness of riparian plant communities in both uncut control and experimentally clearcut sites in the boreal forest of Alberta, Canada. The overall spatial autocorrelation for each of these two indices of diversity was separately decomposed into the components of positive and negative spatial autocorrelations through eigendecomposition of the spatial weighting matrix.

Results

Negative spatial autocorrelation in richness and evenness were more pronounced in the clearcut than uncut sites, although positive spatial autocorrelations in all indices of diversity remained unchanged. Effect of disturbance was not detected on the overall spatial autocorrelation.

Conclusions

Disturbance increases negative spatial autocorrelation in species richness and evenness, with a stronger increase in evenness than richness, which underscores the importance of competition in structuring post-disturbance riparian communities. Our results also highlight the need for assessing positive and negative spatial autocorrelation and different aspects of diversity separately in understanding disturbance effects on the spatial pattern, or identifying processes from patterns.

     

Effects of spatial habitat heterogeneity on habitat selection and annual fecundity for a migratory forest songbird

Understanding how spatial habitat patterns influence abundance and dynamics of animal populations is a primary goal in landscape ecology. We used an information-theoretic approach to investigate the association between habitat patterns at multiple spatial scales and demographic patterns for black-throated blue warblers (Dendroica caerulescens) at 20 study sites in west-central Vermont, USA from 2002 to 2005. Sites were characterized by: (1) territory-scale shrub density, (2) patch-scale shrub density occurring within 25 ha of territories, and (3) landscape-scale habitat patterns occurring within 5 km radius extents of territories. We considered multiple population parameters including abundance, age ratios, and annual fecundity. Territory-scale shrub density was most important for determining abundance and age ratios, but landscape-scale habitat structure strongly influenced reproductive output. Sites with higher territory-scale shrub density had higher abundance, and were more likely to be occupied by older, more experienced individuals compared to sites with lower shrub density. However, annual fecundity was higher on sites located in contiguously forested landscapes where shrub density was lower than the fragmented sites. Further, effects of habitat pattern at one spatial scale depended on habitat conditions at different scales. For example, abundance increased with increasing territory-scale shrub density, but this effect was much stronger in fragmented landscapes than in contiguously forested landscapes. These results suggest that habitat pattern at different spatial scales affect demographic parameters in different ways, and that effects of habitat patterns at one spatial scale depends on habitat conditions at other scales.     

The influence of scale and the spatial characteristics of landscapes on land-cover mapping using remote sensing

Statistical analyses provide a means for assessing relationships between landscape spatial pattern and errors in the estimates of cover-type proportions as land-cover data are aggregated to coarser scales. Results from a multiple-linear regression model suggest that as patch sizes, variance/mean ratio, and initial proportions of cover types increase, the proportion error moves in a positive direction and is governed by the interaction of the spatial characteristics and the scale of aggregation. However, the standard linear model does not account for the different directions of scale-dependent proportion error since some classes become larger and others become smaller as the scene is aggregated. Addition of indicator variables representing class-type significantly improves the performance by allowing the model to respond differently to different classes. A regression tree model provides a much simpler fit to the complex scaling behavior through an interaction between patch size and aggregation scale. An understanding of the relationships between landscape pattern, scale, and proportion error may advance methods for correcting land-cover area estimates. Such methods could also facilitate high-resolution calibration and validation of coarse-scale remote-sensing-based land-cover mapping algorithms. Ongoing initiatives to produce global land-cover datasets from remote sensing, such as efforts within the IGBP and the EOS MODIS Land-Team, include significant emphasis on high level calibration and validation activities of this nature.