A Hierarchical Patch Dynamics Approach to Regional Modeling and Scaling

This has been supported by U.S. EPA (Science To Achieve Results, STAR Program, R827676-01-0)
and US NSF (Central Arizona-Phoenix LTER)


The major research goals of this research project were two-fold: (1) To develop and test a hierarchical patch dynamics modeling and scaling approach to regional analysis and assessment, and (2) To 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 affects 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 land use and land cover change (LUCC) and to relate ecosystem processes to LUCC from the local to the regional scale in the Phoenix metropolitan area.


This project has generated a number of products, including 6 books and special journal issues, more than 40 journal papers and book chapters, more than 30 conference presentations and invited talks, and 6 Masters theses and doctoral dissertations.  In the following, we summarize the research achievements of this project in several sections: (1) the development of the hierarchical patch dynamics scaling and modeling framework, (2) field work and database development, (3) scaling relations of landscape patterns, (4) spatiotemporal patterns of urbanization in the Phoenix metropolitan region and ecological effects, and (5) publications and presentations. 
1. 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.  Spatial patchiness is ubiquitous in ecological systems.  The theory of patch dynamics, assuming that ecological systems are dynamic patch mosaics, studies the structure, function and dynamics of patchy systems with an emphasis on their emergent properties that arise from interactions at the patch level.  On the one hand, hierarchy theory provides useful guidelines for “decomposing” complex systems and focuses on a “vertical” perspective.  On the other hand, patch dynamics deals explicitly with the spatial heterogeneity and its change, an apparent "horizontal" or landscape perspective (Wu, 1999, 2000).  The hierarchical patch dynamics (HPD) paradigm integrates hierarchy theory and patch dynamics, and emphasizes the dynamic relationship among pattern, process, and scale in a landscape context (Fig. 1).  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, which facilitates information transfer and assessment across scales.  The hierarchical patch dynamics scaling and modeling framework – known as the “scaling ladder approach” – was developed and reported in a series of publications (Wu 1999, Reynolds and Wu 1999, Wu 2000, Wu and David 2002). 

Fig. 1. Illustration of the hierarchical patch dynamics scaling and modeling framework – the scaling ladder approach.

2. Scaling Relations Of Landscape Patterns

While recent studies have shed new light on the problems of scale effects in landscape analyses, most existing studies using landscape metrics considered 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.  Thus, although ecologists are well aware that changing scale often affects landscape metrics, scaling relations are yet to be developed.  Thus, we used data of real and simulated landscapes to address several questions concerning scale effects and scaling: (i) How do changing grain size and changing extent affect different landscape metrics for a given landscape?  (ii) How does the behavior of various landscape metrics differ among distinctive landscapes?  (iii) 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 are generally more predictable than those of changing map sizes.  While 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 scaling of spatial pattern.  For example, landscape metrics with simple scaling relations reflect those 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 whose extrapolation is difficult, which requires 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, in stead of single-scale values.  Indeed, 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.

3. Urbanization and Its Ecological Effects

In the southwest U.S., the Phoenix metropolitan area in particular, urbanization has profoundly changed the desert landscape.  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 hierarchical patch dynamics 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 hierarchical patch dynamics scaling and modeling framework.

Gradient Analysis of Urbanization Pattern.  Quantifying landscape pattern and its change is essential for the monitoring and assessment of ecological consequences of urbanization.  Combining gradient analysis with landscape metrics, we studied the spatial pattern of urbanization in the Phoenix metropolitan area, Arizona, USA to understand the landscape structure and ecological consequences.  Our study has demonstrated that the center and spatial pattern of urbanization can be quantified using a combination of landscape metrics and gradient analysis.  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 a rather different pattern for patch type percent coverage and mean patch size.  For all the six measures, agriculture displayed a very different, yet unique, multiple-peaked pattern.  Therefore, different land use types may indeed show distinctive “spatial signatures” as distance-based “landscape pattern profiles” which may be used to compare urban developmental patterns between cities and dynamics of the same city over time.  Such comparisons may help understand different underlying processes that are responsible for various forms of urban morphology. 

It was clear, though not surprising, from this study 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.  While 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, while not new findings of the sort, 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 considerably reduce 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 to be taken soon to significantly slow down the population growth.  Also, there 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) would begin to break up, patch diversity would decline due partly to the loss of agricultural lands, and the overall landscape shape complexity would also decreases 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 urbanization on the ecosystem processes in the Phoenix metropolitan region through ecosystem modeling.  Based on the ecosystem model, PALS (Patch AridLand Simulator) originally developed for the Chihuahuan Desert in the Jornada basin by James F. Reynolds and his associates (Reynolds et al. 1993, 1997, Reynolds and Wu 1999), we developed PALS-PHX which is suited for the Sonoran Desert in the Phoenix region (Shen, Wu, et al. to be submitted).  Model parameterization and simulation experiments were based on data from the Central Arizona –Phoenix Long-Term Ecological Research (CAP-LTER) project and our own field work supported by the EPA STAR program. 

Model predictions were validated using field observations.  The results showed that PALS-FT was able to simulate ANPP of this typical Sonoran Desert ecosystem reasonably well, with a relative error of –2.4% at the ecosystem level and generally <25% at the functional-type level.  We then used the model to simulate ANPP and its seasonal and inter-annual dynamics for a similar ecosystem within the CAP LTER study area.  The model predicted an average annual ANPP of 72.3 g m-2 y-1, ranging from 11.3 g m-2 y-1 to 229.6 g m-2 y-1 in a 15-year simulation.  The simulated average ANPP of the Sonoran Desert ecosystem was close to field observations, and the range of variation also was close to that reported by other researchers for arid and semiarid ecosystems.  The dynamics of ecosystem ANPP in response to fluctuations in annual precipitation simulated by the model agreed well with the known relationship between ANPP and precipitation in arid and semiarid systems.  A closer examination of this relationship at the level of plant functional types further revealed that seasonal distribution of rainfall significantly affected ANPP.  In addition, we are continuing our efforts to investigate how urbanizatioin-induced environmental changes (increases in CO2, temperature, and N deposition) affect ecosystem processes.


Many of the publications can be downloaded at http://leml.asu.edu/, click PUBLICATIONS.)
  1. Buyantuyev, A. and J. Wu. 2007. Effects of thematic resolution on landscape pattern analysis. Landscape Ecology 22:7-13.
  2. Buyantuyev, A. and J. Wu. 2007. Estimating vegetation cover in an urban environment based on Landsat ETM+ imagery: A case study in Phoenix, USA. International Journal of Remote Sensing 28: 269-291.
  3. Neil, K. and J. Wu. 2006. Effects of urbanization on plant flowering phenology. Urban Ecosystems 9:243-257.
  4. Jenerette, G. D., J. Wu, N. Grimm, and D. Hope. 2006. Points, patches and regions: Scaling soil biogeochemical patterns in an urbanized arid ecosystem. Global Change Biology 12:1532-1544.
  5. Wu, J. 2006. Cross-disciplinarity, landscape ecology, and sustainability science. Landscape Ecology 21:1-4.
  6. Wu, J. and H. Li. 2006. Concepts of scale and scaling. In: J. Wu, B. Jones, H. Li and O.L. Loucks (eds). Scaling and Uncertainty Analysis in Ecology. Springer, Dordrecht, The Netherlands. pp. 3-15.
  7. Wu, J. and H. Li. 2006. Perspectives and methods in scaling: A review. In: J. Wu, B. Jones, H. Li and O.L. Loucks (eds). Scaling and Uncertainty Analysis in Ecology. Springer, Dordrecht, The Netherlands. pp. 17-44.
  8. Li, H. and J. Wu. 2006. Uncertainty analysis in ecological studies: An overview. In: J. Wu, B. Jones, H. Li and O.L. Loucks (eds). Scaling and Uncertainty Analysis in Ecology. Springer, Dordrecht, The Netherlands. pp. 45-66.
  9. Wu, J., H. Li, B. Jones, and O. L. Loucks. 2006. Scaling with known uncertainty: A synthesis. In: J. Wu, B. Jones, H. Li and O.L. Loucks (eds). Scaling and Uncertainty Analysis in Ecology. Springer, Dordrecht, The Netherlands. pp. 329-346.
  10. Shen, W., J. Wu, P. R. Kemp, J. F. Reynolds, and N. B. Grimm. 2005. Simulating the dynamics of primary productivity of a Sonoran ecosystem: Model parameterization and validation. Ecological Modelling 189:1-24.
  11. Berling-Wolff, S. and J. Wu. 2004. Modeling urban landscape dynamics: A case study in Phoenix, USA. Urban Ecosystems 7:215-240.
  12. Musacchio, L. and J. Wu. 2004. Collaborative landscape-scale ecological research: emerging trends in urban and regional ecology. Urban Ecosystems 7:175-178.
  13. Li, H. and J. Wu. 2004. Use and misuse of landscape indices. Landscape Ecology 19: 389-399.
  14. Jenerette, G. D. and J. Wu. 2004. Interactions of ecosystem processes with spatial heterogeneity in the puzzle of nitrogen limitation. Oikos 107:273-282.
  15. Shen, W., G. D. Jenerette, J. Wu and R. H. Gardner. 2004. Evaluating empirical scaling relations of pattern metrics with simulated landscapes. Ecography 27: 459-469.
  16. Wu, J. 2004. Effects of changing scale on landscape pattern analysis: Scaling relations. Landscape Ecology 19:125-138.
  17. Berling-Wolff, S. and J. Wu. 2004. Urban growth models: A historical review. Ecological Research 19:119-129.
  18. Wu, J., G. D. Jenerette, and J. L. David. 2003. Linking land use change with ecosystem processes: A hierarchical patch dynamics model. In: Subhro Guhathakurta (ed.), Integrated Land Use and Environmental Models. Springer, Berlin. pp.99-119.
  19. Shen, W., J. Wu, Y. Lin, H. Ren, and M. Li. 2003. Effects of changing grain size on landscape pattern analysis. Acta Ecologica Sinica 23(11):2506-2231.
  20. Shen, W., J. Wu, H. Ren, Y. Lin and M. Li. 2003. Effects of changing spatial extent on landscape pattern analysis. Acta Ecologica Sinica 23(12):2219-2519.
  21. Wu, J., W. Shen, W. Sun, and P. T. Tueller. 2002. Empirical patterns of the effects of changing scale on landscape metrics. Landscape Ecology 17:761-782.
  22. Wu, J. and R. Hobbs. 2002. Key issues and research priorities in landscape ecology: An idiosyncratic synthesis. Landscape Ecology 17:355-365.
  23. Luck, M. and J. Wu. 2002. A gradient analysis of the landscape pattern of urbanization in the Phoenix metropolitan area of USA. Landscape Ecology 17:327-339.
  24. Wu, J. and D. Marceau. 2002. Modeling complex ecological systems: An introduction.  Ecological Modelling 153:1-6.
  25. Wu, J. and J. L. David. 2002. A spatially explicit hierarchical approach to modeling complex ecological systems: Theory and applications.  Ecological Modelling 153:7-26.
  26. Wu, J. and W. Shen. 2002. The science of complexity and its applications in ecology. Pages 6-15 In: J. Wu, X. Han and J. Huang (eds), Lectures in Modern Ecology: From Basic Ecology to Environmental Issues. Science and Technology Press, Beijing.
  27. Zhu, W., J. Wu and L. Zhang. 2002. Urban Ecology: An ecological field facing new challenges. Pages 220-229 In: J. Wu, X. Han and J. Huang (eds), Lectures in Modern Ecology: From Basic Ecology to Environmental Issues. Science and Technology Press, Beijing.
  28. Luck, M., G. D. Jenerette, J. Wu and N. Grimm. 2001. The urban funnel model and spatially heterogeneous ecological footprint. Ecosystems 4:782-796.
  29. Jenerette, G. D. and J. Wu. 2001. Analysis and simulation of land use change in the central Arizona - Phoenix region. Landscape Ecology 16:611-626.
  30. Wu, J. and Y. Qi. 2000. Dealing with scale in landscape analysis: An overview. Geographic Information Sciences 6(1):1-5.
  31. Wu, J., D. E. Jelinski, M. Luck and P. T. Tueller. 2000. Multiscale analysis of landscape heterogeneity: Scale variance and pattern metrics. Geographic Information Sciences 6(1):6-19.
  32. Zipperer, W. C., J. Wu, R. V. Pouyat, and S. T. A. Pickett. 2000.  The application of ecological principles to urban and urbanizing landscapes. Ecological Applications 10(3): 685-688.   
  33. Collins, J.P., A.P. Kinzig, N.B. Grimm, W.F. Fagan, D. Hope, J. Wu, and E.T. Borer. 2000. A new urban ecology. American Scientist 88:416-425.
  34. Jenerette, G. D. and J. Wu. 2000. On the definitions of scale. Bulletin of Ecological Society of America 81(1): 104-105.
  35. Wu, J.  1999.  Hierarchy and scaling: Extrapolating information along a scaling ladder. Canadian Journal of Remote Sensing 25(4): 367-380.  

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