Final Report: A Hierarchical Patch Dynamics Approach to Regional Modeling and Scaling

EPA Grant Number: R827676
Title: A Hierarchical Patch Dynamics Approach to Regional Modeling and Scaling
Investigators: Wu, Jianguo , Green, Douglas
Institution: Arizona State University - West
EPA Project Officer: Packard, Benjamin H
Project Period: October 15, 1999 through October 14, 2002
Project Amount: $629,540
RFA: Regional Scale Analysis and Assessment (1999) RFA Text |  Recipients Lists
Research Category: Aquatic Ecosystems , Ecological Indicators/Assessment/Restoration

Objective:

The major objectives of this research project were to: (1) develop and test a hierarchical patch dynamics modeling and scaling approach to regional analysis and assessment; and (2) develop an understanding of how the Phoenix landscape has changed over the past several decades as a consequence of urbanization and how land use and land cover change (LUCC) affect ecosystem processes at the regional scale. To achieve these goals, several specific questions were addressed through field work, simulation modeling, and statistical analysis. Efforts were made to develop simulation models to project LUCC and to relate ecosystem processes to LUCC from the local to the regional scale in the Phoenix metropolitan area.

Summary/Accomplishments (Outputs/Outcomes):

The Development of the Hierarchical Patch Dynamics Scaling and Modeling Framework

One of the main goals of this project was to develop a conceptual framework for scaling and modeling across heterogeneous landscapes. We developed the “scaling ladder” approach (see Figure 1) based on the hierarchical patch dynamics (HPD) paradigm that integrates hierarchy theory and patch dynamics. As a result of the integration of the two perspectives, HPD unites structural and functional components of a spatially extended system, like a landscape, into a coherent hierarchical framework; emphasizes the dynamic relationship among pattern, process, and scale in a landscape context; and facilitates information transfer and assessment across scales.

Illustration of the Hierarchical Patch Dynamics Scaling

Figure 1. Illustration of the Hierarchical Patch Dynamics Scaling and Modeling Framework—the Scaling Ladder Approach

The HPD scaling ladder approach is composed of three steps:

(1) Identifying appropriate patch hierarchies. In complex ecological systems, reliable spatial scaling must be based on an adequate account of the spatial heterogeneity of the landscape (e.g., spatially explicit or statistical representations). Thus, it is immensely helpful to be able to identify the spatial patterns—the patch hierarchies—that are relevant to the ecological processes of interest. The identified patch hierarchies can serve as “scaling ladders” that facilitate multiscale modeling and spatial scaling. A number of quantitative methods in spatial pattern analysis exist for identifying patch hierarchies.

(2) Making observations and developing models at focal levels. Once an appropriate patch hierarchy is established, ecological processes can be studied at focal levels (corresponding to characteristic domains of scale) by properly choosing grain size (sampling interval or spatial resolution) and extent (study duration or area). It is crucial to understand the role of scale in making observations. The phenomena of interest are observable only at the appropriate scale of observation.

(3) Extrapolating information across the domains of scale hierarchically. A major role of a patch hierarchy identified in step one is to serve as a scaling ladder that is composed of the domains of scale that are relevant to a particular study. Scaling can be accomplished by changing the grain size and extent of models along the patch hierarchy (see Figure 1). Although a variety of specific scaling techniques can be applied here, a general approach is to link models along the scaling ladder that are built individually around distinctive focal levels. One of the most sensible ways of doing so is to use the output of lower level models as the input to upper level models. Sometimes, the input may take the form of response curves or surfaces that are generated using statistical methods based on the output from a lower level model. Similarly, such hierarchical scaling can be implemented from top down, using the output of higher level models to constrain or drive lower level models. This top-down approach has become increasingly appealing and feasible as remote sensing data, with high temporal and spatial resolutions, are made readily available over large geographic areas.

The HPD scaling scheme provides a conceptual basis for scaling up and down. In particular, the HPD scaling strategy provides a ladder for scaling. Using a “scaling ladder” should enhance greatly the feasibility and minimize the danger of errors in translating information across a wide range of scales in research and decision-making.

Scaling Relations of Landscape Patterns

Although recent studies have shed new light on the problems of scale effects in landscape analyses, most existing studies using landscape metrics consider only a few indices with a narrow range of scales, and few have gone beyond merely reporting the existence of scale effects to explore their generalities across different landscapes. Ecologists are well aware that changing scale often affects landscape metrics, but scaling relations have yet to be developed. Thus, we used data of real and simulated landscapes to address several questions concerning scale effects and scaling:

1. How do changing grain size and changing extent affect different landscape metrics for a given landscape?

2. How does the behavior of various landscape metrics differ among distinctive landscapes?

3. Are there general scaling relations for certain landscape metrics that are consistent across landscapes?

Our results showed that changing grain size and extent had significant effects on both the class- and landscape-level metrics. Although the landscapes under study were quite different in both the composition and configuration of patches, the effects of changing scale fell into two categories (simple scaling functions and unpredictable) for the class-level metrics, and three categories for the landscape-level metrics (simple scaling functions, staircase-like scaling behavior, and unpredictable). Overall, more metrics showed consistent scaling relations with changing grain size than with changing extent at both the class and landscape levels, indicating that effects of changing spatial resolution generally are more predictable than those of changing map sizes. Although the same metrics tended to behave similarly at the class level and the landscape level, the scale responses at the class level were much more variable. These results appear robust not only across different landscapes but also independent of specific map classification schemes.

In addition, our results provide practical guidelines for the scaling of spatial pattern. For example, landscape metrics with simple scaling relations reflect landscape features that can be extrapolated or interpolated across spatial scales readily and accurately, using only a few data points. In contrast, unpredictable metrics represent landscape features for which extrapolation is difficult requiring information on the specifics of the landscape of concern at many different scales. Finally, to quantify spatial heterogeneity using landscape metrics, it is both necessary and desirable to use landscape metric scalograms instead of single-scale values. A comprehensive empirical database containing pattern-metric scalograms and other forms of multiple-scale information of diverse landscapes is crucial for achieving a general understanding of landscape patterns and developing spatial scaling rules.

Urbanization and Its Ecological Effects

In the southwest United States, and the Phoenix metropolitan area in particular, urbanization has changed the desert landscape profoundly. In fact, Phoenix has become the sixth largest city with the highest population growth rate in the United States. To understand the interactions between urbanization and ecological conditions, we have been developing models based on the HPD paradigm to simulate the pattern and process of urban growth and its ecological consequences. Here, we highlight several of our studies that were aimed to understand the spatial and temporal patterns of urbanization and their effects on ecosystem dynamics, using spatial analyses and models based on the HPD scaling and modeling framework.

Gradient Analysis of Urbanization Pattern . Quantifying landscape pattern and its change is essential for the monitoring and assessment of the ecological consequences of urbanization. Combining gradient analysis with landscape metrics, we studied the spatial pattern of urbanization in the Phoenix metropolitan area to understand the landscape structure and ecological consequences of urbanization. Our study has demonstrated that the center and spatial pattern of urbanization can be quantified using a combination of landscape metrics and gradient analysis (see Figure 2). Different land use types exhibited distinctive, but not necessarily unique, spatial signatures that were dependent on specific landscape metrics. For example, for patch type percent coverage, patch density, patch size coefficient of variation, landscape shape index, and area-weighted mean patch shape index, residential and urban land use types displayed similar patterns along the transect from west to the urban center—a largely monotonic gradient with its peak at the urban core. Desert showed a similar pattern for patch density, patch size coefficient of variation, landscape shape index, and area-weighted mean patch shape index but showed a rather different pattern for patch type percent coverage and mean patch size (see Figure 2). For all of the six measures, agriculture displayed a very different, yet unique, multiple-peaked pattern. Therefore, different land use types indeed may show distinctive “spatial signatures” as distance-based “landscape pattern profiles” that may be used to compare urban developmental patterns between cities and dynamics of the same city over time. Such comparisons may help illustrate different underlying processes that are responsible for various forms of urban morphology.

Changes in Landscape Pattern Along an Urban-Rural Transect in the Phoenix Metropolitan Region

Figure 2. Changes in Landscape Pattern Along an Urban-Rural Transect in the Phoenix Metropolitan Region. The values were averages obtained using a 3 x 3 overlapping moving window.

From this study, it was clear, although not surprising, that the degree of human impact on the Phoenix landscape depended on the distance from the urban center. An urbanization center was clearly identifiable with the six landscape metrics when plotted along a transect. Specifically, all the landscape metrics indicated dramatic changes in landscape pattern at 75 km and 155 km, marking the urbanizing front of the Phoenix metropolitan area in the west-east direction. Although the landscape-level metrics were able to characterize the center of urbanization as having the smallest mean patch size and the highest patch richness, patch density, patch size coefficient of variation, landscape shape index, and area-weighted mean shape index, the class-level indices provided more detailed information on the relative contributions of individual land use types. The high degrees of fragmentation and spatial complexity of the urbanization center were able to be quantified in relation to distance and individual land use types. Processes and factors responsible for urbanization, such as socioeconomic activities and land ownership, resulted in the heterogeneous arrangement of land uses in the Phoenix metropolitan area.

Urban Growth Modeling. We developed computer models to simulate the land use and land cover change in the Phoenix metropolitan region. These models were used to examine a series of model calibration and evaluation methods, and to carry out scenario-based simulation analyses of the future development patterns of the region. The results showed that at finer levels, the noise and uncertainty in input data and the exponentially increased computational requirements would reduce considerably the usefulness and accuracy of such models. At the other extreme, model projections with too coarse a spatial resolution would be of little use at the local and regional scales. A series of scenario analyses suggested that the Metropolitan Phoenix area would soon be densely populated demographically and highly fragmented ecologically unless dramatic actions are taken soon to slow down the population growth significantly. Also, t here would be an urban morphological threshold over which drastic changes in certain aspects of landscape pattern occur. Specifically, the scenarios indicated that as large patches of open lands (including protected lands, parks, and available desert lands) begin to break up, patch diversity would decline partly due to the loss of agricultural lands, and the overall landscape shape complexity also would decrease because of the predominance of urban lands. It seemed that reaching such a threshold could be delayed, but not avoided, if the population in the Phoenix metropolitan region continues to grow.

Effects of Urbanization on Ecosystem Processes . We investigated the effects of three environmental factors associated with urbanization (increased air temperature, elevated CO2, and N deposition) on the ecosystem processes in the Phoenix metropolitan region through ecosystem modeling. Model predictions were validated using field observations. Among other findings, we found that the above-ground net primary productivity (ANPP) of the Sonoran Desert ecosystem showed positive responses to increases in CO2, N deposition, and the combinations of the three environmental factors (see Figure 3). The temperature effect on ANPP was negative when temperature change was larger than 2.0°C and positive when temperature change was small (< 1.0°C). ANPP was more sensitive to changes in maximum air temperature than in minimum air temperature. The combined effects of the three environmental factors were generally larger than single-factor effects, especially when precipitation was favorable. Of the three factors, N deposition and CO2 showed larger effects on ANPP than temperature. With an increase of 24 kg ha-1 y-1 in N deposition rate (the maximum value of N deposition increase in the Phoenix urban area), the average ANPP increased by 30.0 g m-2 y-1 for the 15 simulation years (1988-2002). With an increase of 160 ppm in CO2 concentration (the maximum CO2 increase in the Phoenix urban area), the average increment of ANNP was 40.2 g m-2 y-1 for the 15 simulation years. Changes in temperature showed a relatively smaller influence on ecosystem ANPP, with the largest increase in air temperature (3.0°C for maximum air temperature and 7.5°C for minimum air temperature); the average change of ANPP was -4.6 g m-2 y-1 for the 15 simulation years.

Effects of Urbanization-Induced Environmental Changes on Ecosystem ANPP

Figure 3. Effects of Urbanization-Induced Environmental Changes on Ecosystem ANPP. (a) atmospheric CO2 concentration, (b) dry N deposition, (c) maximum and minimum air temperatures, and (d) maximum versus minimum air temperatures. Graphs a-c share the same legend as is listed in (a).


Journal Articles on this Report : 32 Displayed | Download in RIS Format

Other project views: All 73 publications 44 publications in selected types All 33 journal articles
Type Citation Project Document Sources
Journal Article Berling-Wolff S, Wu J. Modeling urban landscape dynamics: a review. Ecological Research 2004;19(1):119-129.
abstract available   full text available
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  • Abstract: SpringerLink
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  • Journal Article Collins JP, Kinzig A, Grimm NB, Fagan WF, Hope D, Wu JG, Borer ET. A new urban ecology: modeling human communities as integral parts of ecosystems poses special problems for the development and testing of ecological theory. American Scientist 2000;88(5):416-425.
    abstract available   full text available
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  • Abstract: JSTOR - Abstract
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  • Journal Article Fagan WF, Meir E, Carroll SS, Wu J. The ecology of urban landscapes: modeling housing starts as a density-dependent colonization process. Landscape Ecology 2001;16(1):33-39.
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  • Journal Article Gao Q, Yu M, Yang X, Wu J. Scaling simulation models for spatially heterogeneous ecosystems with diffusive transportation. Landscape Ecology 2001;16(4):289-300.
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  • Journal Article Green DM, Oleksyszyn M. Enzyme activities and carbon dioxide flux in a Sonoran desert urban ecosystem. Soil Science Society of America Journal 2002;66(6):2002-2008.
    abstract available   full text available
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  • Full-text: Soil Science Society of America Journal-Full Text HTML
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  • Abstract: Soil Science Society of America Journal-Abstract
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  • Other: Soil Science Society of America Journal-Full Text PDF
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  • Journal Article He FL, Gaston KJ, Wu JG. On species occupancy-abundance models. Ecoscience 2002;9(1):119-126.
    abstract available   full text available
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  • Full-text: University of Alberta-Full Text PDF
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  • Abstract: Ecoscience-Abstract
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  • Journal Article Jenerette GD, Wu J. Analysis and simulation of land-use change in the central Arizona-Phoenix region, USA. Landscape Ecology 2001;16(7):611-626.
    abstract available   full text available
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  • Full-text: Arizona State University PDF
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  • Abstract: SpringerLink
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  • Journal Article Jenerette GD, Wu J. Interaction of ecosystem processes with spatial heterogeneity: the puzzle of nitrogen limitation. Oikos 2004;107(2):273-282.
    abstract available   full text available
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  • Full-text: Arizona State University-Full Text PDF
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  • Abstract: Wiley InterScience-Abstract
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  • Journal Article Li H, Wu J. Use and misuse of landscape indices. Landscape Ecology 2004;19(4):389-399.
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  • Journal Article Luck MA, Jenerette GD, Wu J, Grimm NB. The urban funnel model and the spatially heterogeneous ecological footprint. Ecosystems 2001;4(8):782-796.
    abstract available   full text available
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  • Full-text: Arizona State University PDF
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  • Abstract: SpringerLink
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  • Journal Article Luck M, Wu J. A gradient analysis of urban landscape pattern: a case study from the Phoenix metropolitan region, Arizona, USA. Landscape Ecology 2002;17(4):327-339.
    abstract available   full text available
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  • Full-text: Arizona State University-Full Text PDF
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  • Abstract: SpringerLink-Abstract
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  • Journal Article Musacchio LR, Wu J. Collaborative landscape-scale ecological research: emerging trends in urban and regional ecology. Urban Ecosystems 2004;7(3):175-178.
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  • Full-text: Arizona State University-Full Text PDF
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  • Abstract: Springer-Citation
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  • Journal Article Qi Y, Xu M, Wu J. Temperature sensitivity of soil respiration and its effects on ecosystem carbon budget: nonlinearity begets surprises. Ecological Modelling 2002;153(1-2):131-142.
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  • Full-text: Science Direct-Full Text HTML
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  • Abstract: Science Direct-Abstract
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  • Journal Article Ren H, Wu J, Peng S. Concept of ecosystem management and its essential elements (Article in Chinese). Ying Yong Sheng Tai Xue Bao 2000;11(3):455-458.
    abstract available  
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  • Journal Article Ren H, Wu J, Peng SL. Evaluation and monitoring of ecosystem health. Tropical Geography 2000;20(4):310-316. R827676 (Final)
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    Journal Article Shao GF, We WC, Wu G, Zhou XH, Wu JG. An explicit index for assessing the accuracy of cover-class areas. Photogrammetric Engineering and Remote Sensing 2003;69(8):907-913.
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  • Full-text: American Society of Photogrammetry and Remote Sensing
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  • Journal Article Shen W, Wu J, Lin Y, Ren H, Li M. Effects of changing grain size on landscape pattern analysis. Acta Ecologica Sinica 2003;23(12):2506-2519. R827676 (Final)
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    Journal Article Shen W, Wu J , Ren H , Lin Y, Li M. Effects of changing spatial extent on landscape pattern analysis. Acta Ecologica Sinica 2003;23(11):2219-2231. R827676 (Final)
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    Journal Article Shen W, Jenerette GD, Wu J, Gardner RH. Evaluating empirical scaling relations of pattern metrics with simulated landscapes. Ecography 2004;27(4):459-469.
    abstract available   full text available
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  • Full-text: Arizona State University-Full Text PDF
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  • Abstract: Wiley InterScience-Abstract
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  • Journal Article Tong C, Wu J, Yong S, Yang J, Yong W. A landscape-scale assessment of steppe degradation in the Xilin River Basin, Inner Mongolia, China. Journal of Arid Environments 2004;59(1):133-149.
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  • Abstract: Science Direct-Abstract
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  • Journal Article Wu J, Hobbs R. Key issues and research priorities in landscape ecology: an idiosyncratic synthesis. Landscape Ecology 2002;17(4):355-365.
    abstract available   full text available
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  • Full-text: Arizona State University-Full Text PDF
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  • Abstract: SpringerLink-Abstract
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  • Journal Article Wu J. Hierarchy and scaling: extrapolating information along a scaling ladder. Canadian Journal of Remote Sensing 1999;25(4):367-380.
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  • Full-text: Arizona State University-Full Text PDF
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  • Abstract: CiteSeer-Abstract
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  • Journal Article Wu J, Liu Y, Jelinski DE. Effects of leaf area profiles and canopy stratification on simulated energy fluxes: the problem of vertical spatial scale. Ecological Modelling 2000;134(2-3):283-297.
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  • Other: Arizona State University-Full Text PDF
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  • Journal Article Wu J, Qi Y. Dealing with scale in landscape analysis: an overview. Geographic Information Sciences 2000;6(1):1-5.
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  • Full-text: Arizona State University PDF
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  • Abstract: Taylor Francis Online-Abstract
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  • Journal Article Wu J. Landscape ecology: concepts and theory. Chinese Journal of Ecology 2000;19(1):42-52.
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  • Journal Article Wu J, Jelinski DE, Luck M, Tueller PT. Multiscale analysis of landscape heterogeneity: scale variance and pattern metrics. Geographic Information Sciences 2000;6(1):6-19.
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  • Full-text: Taylor Francis Online-Full Text HTML
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  • Abstract: Taylor Francis Online-Abstract
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  • Other: Arizona State University-Full Text PDF
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  • Journal Article Wu J, David JL. A spatially explicit hierarchical approach to modeling complex ecological systems: theory and applications. Ecological Modeling 2002;153(1-2):7-26.
    abstract available   full text available
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  • Full-text: Science Direct-Full Text PDF
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  • Abstract: Science Direct-Abstract and Full Text HTML
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  • Other: Arizona State University-Full Text PDF
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  • Journal Article Wu J, Marceau D. Modeling complex ecological systems: an introduction. Ecological Modelling 2002;153(1-2):1-6.
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  • Full-text: Science Direct-Full Text PDF
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  • Journal Article Wu J, Shen W, Sun W, Tueller PT. Empirical patterns of the effects of changing scale on landscape metrics. Landscape Ecology 2002;17(8):761-782.
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  • Full-text: Arizona State University-Full Text PDF
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  • Abstract: SpringerLink-Abstract
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  • Journal Article Wu J. Effects of changing scale on landscape pattern analysis: scaling relations. Landscape Ecology 2004;19(2):125-138.
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  • Full-text: Arizona State University-Full Text PDF
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  • Abstract: SpringerLink-Abstract
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  • Journal Article Zhang H, Wu J. A statistical thermodynamic model of the organizational order of vegetation. Ecological Modelling 2002;153(1-2):69-80.
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  • Full-text: Science Direct-Full Text PDF
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  • Abstract: Science Direct-Abstract & Full Text HTML
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  • Other: Arizona State University-Full Text PDF
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  • Journal Article Zipperer WC, Wu J, Pouyat RV, Pickett STA. The application of ecological principles to urban and urbanizing landscapes. Ecological Applications 2000;10(3):685-688.
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  • Other: JSTOR - HTML
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  • Supplemental Keywords:

    land, soil, urban, urbanization, stressors, ecosystem, landscapes, land use and land cover change, regionalization, scaling, terrestrial, habitat, integrated assessment, sustainable development, ecology, landscape ecology, modeling, LANDSAT, remote sensing, field measurements, Southwest, agriculture,, RFA, Scientific Discipline, Air, Geographic Area, Ecosystem Protection/Environmental Exposure & Risk, Ecology, Ecosystem Protection, Environmental Chemistry, climate change, State, Ecological Effects - Environmental Exposure & Risk, Environmental Monitoring, Regional/Scaling, ecological exposure, scaling, urbanization, hierarchical patch dynamics, spatial scale, functional complexity, modeling, anthropogenic, Arizona (AZ), ecosystem, agriculture, regional survey data, remote sensing imagery, field measurements, land use

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    Progress and Final Reports:

    Original Abstract
  • 2000 Progress Report
  • 2001 Progress Report