Dynamic Processes, Model Complexity, and Dynamic Modeling Techniques

1
Dynamic Processes, Model Complexity, and Dynamic
Modeling Techniques

• Dr. Dawn Cassandra Parker
• Dept. of Geography and Env. Science and Policy
• Center for Social Complexity
• George Mason University

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Where we areWhat real-world spatial, temporal,
and behavioral processes do you strive to
represent?andWhat is the minimum level of
complexity for the model?
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Main questions to consider

• What spatial, temporal, and behavioral processes
  do we believe are important in the system we want
  to model?
• How much complexity do we need to build into our
  model to capture those processes?
• How little complexity can we get away with?

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Complexity

• Many uses of this word in modeling
• Here, complex means
• not simple
• having many system elements change within the
  model
• operating at multiple scales
• We will look at sources of spatial, temporal, and
  behavioral complexity
• We will also look at degree of endogeneity and
  cross-scale feedbacks

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Spatial Complexity Spatial autocorrelation

• Example one land use is more likely when it has
  another land use type as a neighbor, due to
• Technology adoption and other imitative behavior
• Scale economies
• Spatial competition
• Negative spatial spillovers/externalities
• Ecological spillovers (edge effects)

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More spatial complexity Spatial dependence

• Example two land uses share a similar spatial
  characteristics, such as
• Soil type
• Accessibility
• Climate
• Topography
• Political zone
• Note this type of spatial dependence may motivate
  combining data at different spatial scales

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More spatial complexity Networks

• Physical
• Transportation infrastructure
• hydrology
• Social
• communication,
• social ties,
• trade and commerce

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Temporal complexity Growth and decay

• Population growth and decline (animal and human)
• Soil degradation
• Carbon sequestration
• Erosion
• Social trends
• Financial investments

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Temporal complexity Temporal lags

• Growth and decay functions lead to temporal
  autocorrelation
• Modeling current state may require information on
  states in previous time periods
• For processes that also diffuse over space, it
  may require both spatial and temporal lags
  (example species colonization)

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Temporal complexity Path dependence

• Different conditions at one time period can lead
  to very different outcomes over space and time
• This is an important source of uncertainty in
  modeling
• Dan Brown will elaborate .

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Temporal complexity forward-looking behavior

• Humans and other animals are forward-looking.
  Examples
• Food and seed storage
• Crop rotation
• Strategic behavior, such as pre-emptive land
  clearing
• Successful models must take this into account
• Therefore, models must build in expectations of
  the future and possible responses

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Behavioral Complexity

• Different types of actors
• Multiple goals
• Heterogeneity within
• Expectations
• Strategies
• Motivations
• Interconnectivity of agents in social, economic,
  and ecological networks

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How many model elements are determined within the
model?

• Issue here is the degree of endogeneity, or
  connectedness, of the components of the dynamic
  system
• The more endogeneity is present, the broader the
  scope of the model, and the larger the number of
  questions that can be asked and answered with the
  model
• The more endogeneity is present in a model, the
  more difficult it is to analyze and understand
  the working of the model

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Cross-scale dynamics

• Higher-level processes often constrain
  lower-level processes
• Lower-level processes may feed back to influence
  higher-level processes

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Example roads, colonization, and deforestation

• National level policies (subsidized timber prices
  and/or roads) encourage road construction and
  deforestation
• National level policies (distribution of land for
  frontier settlement) encourage settlement along
  roads
• Rural ag. producers become more integrated with
  the market (new people, new techniques, new
  opportunities)
• Results may be greater sensitivity to financial
  factors such as ag prices, off-farm wages,
  credit, timber prices) (Angelsen and Kaimowitz)

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Example Residential location and employment

• Spatial structure at one level determined as
  residents locate within commuting distance of
  place of employment
• Spatial structure at another level determined as
  firm locates around other complementary firms
  (result is polycentric node)
• Spatial structure at higher level determined by
  relationship between polycentric nodes
• At a still higher level, spatial structure
  between cities is determined through migration
  (Anas et al.)

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Example Ag production and price feedbacks

• Spike in demand may cause ag extensification
  (production on previously marginal lands).
  Example organic rice for Japanese consumption
• Increased supply at a local level feeds back to
  depress globally determined price (classic cobweb
  model)
• Note that integration of new markets may have the
  same effects (example coffee production)

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Where we areWhat modeling methodologies are
most appropriate??
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Classifications of Dynamic Models by Technique

• Dynamic Optimization models (mathematical
  programming)
• Cellular Automaton models
• Statistical/Regression models
• Agent based/Multi-agent system models
• Integrated/Hybrid models (not covered today)

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Dynamic Optimization Models

• Optimization models derive an ideal or optimal
  solution for a given system, based on a
  quantitative objective
• Dynamic optimization models incorporate temporal
  lags and/or forward looking behavior
• Models can be positive, under the assumption that
  system agents (generally animals or humans)
  behave as if they optimize
• Models are most often normative and used for
  policy
• Spatial dynamic optimization models are often
  difficult to solve

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Example Carpentier et al. Amazon model

• Purpose of model--Investigate
• Will settlement farmers in the Brazilian Amazon
  adopt more intensive production systems?
• If they do, will this adoption slow
  deforestation?
• What will be the effect will adoption have on
  incomes?

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Modeling framework

• Dynamic linear programming model chooses optimal
  path of land use over time
• Farmers optimize subject to constraints on
  available resources (land, labor, capital)
• In addition, dynamic relationships between
  land-use activities and productivity, as well as
  savings and investments, are accounted for
  through constraints and equations of motion

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Land-use systems
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Spatial complexity

• Only spatial aspect of this model are
  location-specific biophysical conditions and
  socio-economic conditions

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Temporal complexity

• Agents can anticipate future effects of current
  decisions
• Temporal interactions between cropping decisions
  and soil fertility are included
• Like other applications, likely land-use life
  cycles are built in

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Behavioral Complexity

• A wide variety of parameters (prices,
  productivity, resource endowments) affect agent
  decisions
• Agents are forward-looking
• By changing model parameters, a variety of agent
  types could be analyzed, in principle.
• However, no agent-agent interactions are present

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Is this model spatial?

• No
• Object have no explicit location
• Location is not explicitly represented
• Location/distance does not enter into model
  calculations
• The model modifies the landscape only through
  changes in composition
• But
• Travel cost to market could easily be added
• Results could be used to simulate landscape
  change
• See Berger and Deadman et al. for more space

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Some strengths and weaknesses of dynamic
optimization models

• Strengths
• Great for representing temporal dynamics
• Good models of behavior in certain contexts
• Useful for creating benchmarks/goals for policy
• Weaknesses
• Spatial aspects are incorporated with difficulty
• Can easily become difficult or impossible to
  solve
• For normative models sometimes knowing the
  optimal outcomes doesnt help if we dont know
  how to get there

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Cellular Automaton Models

• CA models are dynamic simulation models, where
  cell transitions are based on the state of the
  current cell and the states of neighboring cells.
• Neighbors can be very broadly defined, and may
  include multi-scale influences
• Cellular structures are generally grids, but can
  be any cellular structure, in principle

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Example DUEM model (Batty, Xie, and Sun)

• Purpose of the model
• Demonstrate how urban sprawl can occur without
  population growth

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Model Mechanisms

• Model inputs real-world raster layers to define
  initial land uses
• Possible land-use classes include housing,
  commercial, industrial, vacant, and roads
• Transition rules are influenced by spatial
  influences and temporal constraints

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Spatial Complexity

• The urban system is represented by three nested
  scales Neighborhood, Field, and Region
• Transitions are influenced by
• the other land uses in the local neighborhood
• the density of land uses in the district
• constraints on development in the region
• The radial extent of the neighborhood is
  determined parametrically by the user

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Temporal Complexity

• Land-use generation sequences are restricted (for
  example, streets generate only streets)
• Land uses have life cycles, and can revert to
  vacant land
• Only new land uses generate other new land uses

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Behavioral Complexity

• No explicit behavioral complexity in this model,
  as there are no explicit decision-making agents
• Effects of agent decisions are implicitly
  represented through transition probabilities

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Is the DUEM model spatial?

• Yes
• Spatial outcomes will change as we change
  starting landscapes
• Representations of land uses and road networks
  are a part of the model
• Distance from other land uses influences cell
  transitions and growth of new roads
• The model grows a new urban landscape

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Some strengths and weaknesses of cellular
automaton models

• Strengths
• Models are very strong at representing local
  spatial processes
• Models tend to do well at replicating real-world
  spatial patterns, especially fractal structures
• Weaknesses
• Models may place too much emphasis on local
  interactions
• Models are not strong at representing behavior
• Often, models require projections of rates and
  quantities of change to run

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Statistical/Regression Models

• These models find a set of best-fit model
  coefficients that express a statistical
  relationship between a dependent variable (often
  land use or cover) and a series of independent
  variables (representing drivers of LUCC)
• Models produce a transition probability,
  conditional on states of independent variables
• Models are only dynamic when some set of rules is
  used to generate transitioned landscapes using
  those estimated probabilities

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Example CLUE-S model (Verburg et al.)

• Purpose of the model
• Projections of land-use change under status quo
• Scenario analysis
• Hypothetical impacts of new protected area
• Identify possible hot-spots of land-use change

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Model structure

• Non-spatial model determines aggregate demand for
  land
• Spatial statistical model determines transition
  probabilities for particular land uses
• User-determined conversion rules limit possible
  transitions, in order to correctly reflect
  temporal dynamics
• Dynamic allocation protocol allocates change
  based on estimated transition probabilities and
  conversion elasticities

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Model structure
Structure
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Spatial Complexity
Characteristics
Characteristics complexity

• Interaction through accessibility
• The suitability of a location is (partly)
  determined by its access to facilities and/or
  other land uses
• Direct interaction
• Influence of neighboring land uses
• Centripetal forces economies of scale, labor
  markets etc.
• Centrifugal forces congestion, environmental
  pollution etc.

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Temporal Complexity

• Not all land use conversions are reversible
• Urban area and residential area
• Deforestation of primary rain forest
• Other conversions are very costly
• Fruit tree plantations
• Some locations are converted after a short time
  period
• Abandonment after shifting cultivation (nutrient
  depletion)

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Characteristics
Characteristics complexity
Example of the translation of a land use change
sequence into a land use conversion matrix
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Behavioral Complexity

• Location and community specific information such
  as population density, literacy and income enter
  the statistical model
• There is no explicit decision-making function
• There are no explicit agent-agent-interactions

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Sibuyan island, Philippines
Applications
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Applications
forest
grassland
oil palm
rice
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Is the CLUE-S model spatial?

• Yes
• Because of neighborhood effects and
  transportation cost, estimated transition
  probabilities would change if land uses were
  rearranged in space
• CLUE-S inputs and output spatial data
• Neighborhood effects and transport cost enter
  into the model
• When used for dynamic simulation, CLUE-S produces
  a map of projected land uses over time

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Some strengths and weaknesses of spatial
statistical/regression models

• Strengths
• Models provide information on key drivers of
  change
• Spatial and temporal lags can be incorporated
• Data can be entered at multiple scales
• Weaknesses
• Models themselves dont produce projections of
  spatial change
• Arbitrary transition rules may lead to different
  change projections for the same data
• Simulations of change require projections of
  rates and quantities of change
• Models may have little out-of-sample power

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Multi-agent/Agent-Based Models

• Spatial agent-based models are simulation models
  consisting of
• A collection of autonomous decision-making agents
  
• An interaction environment (landscape model)
• Interdependencies among agents, their
  environment, or both
• Rules governing sequencing of actions and
  information flows
• More from Dan Brown and Kevin Johnston

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Example SLUDGE (Simulated land use dependent on
edge-effect externalities) (Parker et al.)

• Purpose of the model--Investigate
• Can spatial externalities lead to economically
  inefficient levels of landscape fragmentation?
• How do initial land-use patterns influence future
  land-use fragmentation?
• Are spatial externalities sufficient to produce
  urban sprawl?
• How to interactions between spatial externalities
  and transportation costs influence sprawl?

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What is a spatial externality?

• Costs or benefit to a neighbor of a surrounding
  land use, which are not taken into account when
  the generating neighbor makes a decision about
  land use

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Model Mechanisms

• Model operates as a hybrid CA/ABM model, with a
  single agent in each cell
• Agents form expectations regarding land-use
  profitability, based on neighboring land uses and
  current land use pattern and composition
• Agents choose the highest-valued land use in each
  time period
• A landscape evolves where no agent can do better
  by changing land uses
• The model reports land rents, economic welfare
  measures, and measures of landscape fragmentation

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Spatial Complexity

• Neighborhood effects payoffs to a given land
  use depend on the actions of four neighbors
• Induced landscape heterogeneity payoffs now vary
  spatially
• Spatial pattern effects Landscape productivity
  depends on the spatial arrangement of land uses,
  as well as amount of land in each use
• Transportation costs affect payoffs to each land
  use

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Temporal Complexity

• Agents form expectations about the future
  productivity of the urban land use
• Little other temporal complexity
• No constraints on land-use transitions
• No land-use life cycles

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Behavioral Complexity

• Prices, landscape pattern, and actions of
  neighbors influence agent decisions
• Agents have fairly mathematically sophisticated
  decision rules
• However
• Agents are homogeneous
• Agents are not forward-looking
• Agents interact with other agents indirectly

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NIMBY plus Ag/Urban setback
Demand Function pu 140.8/q Transportation
Costs 0.01 Externality Damage on A by U
0.125 Us Aversion Distance to U
0.125 Urban/Ag Setback 0
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Outcome Summary
Economic Outcomes
Market-Clearing Rent for U 1.05 Proportion
Urban Parcels 0.189 Average Urban
Production 0.788 Average Urban Transport
Cost 0.056 Proportion Agricultural
Parcels 0.811 Average Agricultural
Production 0.932 Change in Total Surplus -0.0267
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Is the SLUDGE model spatial?

• Yes
• Because of neighborhood effects and
  transportation cost, land-use transitions, land
  rents, and welfare measures would change if land
  uses were rearranged in space
• SLUDGE operates on a spatial landscape model
• Neighborhood effects and transport cost enter
  into the model
• The SLUDGE landscape changes as the model runs

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Some strengths and weaknesses of agent-based
models

• Strengths
• Models can incorporate important sources of
  spatial, temporal, and behavioral complexity
• Very strong format for integrated models
  (human-environment interactions
• Potentially strong for cross-scale feedbacks
• Weaknesses
• Can be difficult to map and communicate model
  mechanisms and outcomes
• Error propagation is potentially very high
• Can be very data hungry

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Summing Up
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Acknowledgements

• Project and overview article authors authors
  (references follow)
• Students from Land-use modeling class for
  discussions and article summaries (esp. Maction
  Komwa and Rich DeBell)
• Thanks to you for your interest and ESRI for
  sponsorship

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Additional Resources

• MODLUC international graduate workshop
  http//www.geo.ucl.ac.be/LUCC/MODLUC_Course/MODLUC
  .html
• CSISS sponsored MaSpace resources
  http//www.csiss.org/resources/maslucc/
• Class resources, Land-use Modeling Techniques
  and Applications http//mason.gmu.edu/dparker3/
  lumta_04/lumta.html
• Class resources, Spatial Agent-based Models of
  Human-Environment Interactions
  http//mason.gmu.edu/dparker3/spat_abm/spat_abm.h
  tml
• This talk available at http//mason.gmu.edu/dpar
  ker3/talks/dcp_esri2005.ppt

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References

• Agarwal, C., G. M. Green, J. M. Grove, T. Evans,
  and C. Schweik. 2002. A review and assessment of
  land-use change models Dynamics of space, time,
  and human choice. Burlington, VT USDA Forest
  Service Northeastern Forest Research Station
  Publication NE-297. http//www.fs.fed.us/ne/newtow
  n_square/publications/technical_reports/pdfs/2002/
  gtrne297.pdf.
• Anas, A., R. Arnott, and K. A. Small. 1998. Urban
  Spatial Structure. Journal of Economic Literature
  36 (3) 1426-1464
• Angelsen, A., and D. Kaimowitz. 1999. Rethinking
  the causes of tropical deforestation Lessons
  from economics models. The World Bank Research
  Observer 14 (1) 73-98. http//www.worldbank.org/r
  esearch/journals/wbro/obsfeb99/pdf/article4.pdf.

65
References, Cont.

• Batty, M. Forthcoming. Urban Growth Models in D.
  J. Maguire, M. F. Goodchild, and M. Batty, eds.
  GIS, Spatial Analysis and Modeling. ESRI Press,
  Redlands, CA
• Berger, T. 2001. Agent-based spatial models
  applied to agriculture A simulation tool for
  technology diffusion, resource use changes, and
  policy analysis. Agricultural Economics 25 (2-3)
  245-260
• Briassoulis, H. 1999. Analysis of Land Use
  Change Theoretical and Modeling Approaches.
  Regional Research Institute, West Virginia
  University. http//www.rri.wvu.edu/WebBook/Briasso
  ulis/contents.htm.

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References, Cont.

• Carpentier, C. L., S. A. Vosti, and J. Witcover.
  2000. Intensified production systems on western
  Brazilian Amazon settlement farms could they
  save the forest? Agriculture, Ecosystems and
  Environment 82 (1-3) 73-88.
• Deadman, P., D. Robinson, E. Moran, and E.
  Brondizio. In Press. Effects of Colonist
  Household Structure on Land-Use Change in the
  Amazon Rainforest An Agent-Based Simulation
  Approach. Environment and Planning B

67
References, cont.

• Geist, H., and E. F. Lambin. 2002. Proximate
  causes and underlying driving forces of tropical
  deforestation. Bioscience 52 (2) 143-150.
  http//www.geo.ucl.ac.be/LUCC/pdf/02_February_Arti
  cle_Geist_.pdf.
• Lambin, E. F., H. Geist, and E. Lepers. 2003.
  Dynamics of land-use and land-cover change in
  tropical regions. Annual Review of Environmental
  Resources 28 205-241
• Parker, D. C. Forthcoming. Integration of
  Geographic Information Systems and Agent-Based
  Models of Land Use Prospects and Challenges in
  D. J. Maguire, M. F. Goodchild, and M. Batty,
  eds. GIS, Spatial Analysis and Modeling. ESRI
  Press, Redlands

68
References, cont.

• Parker, D. C., S. M. Manson, M. A. Janssen, M.
  Hoffmann, and P. Deadman. 2003. Multi-Agent
  Systems for the Simulation of Land-Use and
  Land-Cover Change A Review. Annals of the
  Association of American Geographers 93 (2).
  http//www.csiss.org/events/other/agent-based/pape
  rs/maslucc_overview.pdf.
• Parker, D. C., and V. Meretsky. 2004. Measuring
  pattern outcomes in an agent-based model of
  edge-effect externalities using spatial metrics.
  Agriculture, Ecosystems and Environment 101
  (2-3) 233-250

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References, cont.

• Verburg, P. H., P. Schot, M. Dijst, and A.
  Velkamp. Forthcoming. Land-Use Change Modeling
  Current Practice and Research Priorities.
  GeoJournal. http//www.geo.ucl.ac.be/LUCC/MODLUC_C
  ourse/PDF/T.20Veldkamp20(intro).pdf.
• Verburg, P. H., W. Soepboer, A. Veldkamp, R.
  Limpiada, V. Espaldon, and S. S. A. Mastura.
  2002. Modelling the spatial dynamics of regional
  land use The Clue-S model. Environmental
  Management 30 (3) 391-405. http//www.geo.ucl.ac.
  be/LUCC/MODLUC_Course/PDF/P.20Verbrug20b.pdf.