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Incorporating Systems Dynamics and Spatial
Heterogeneity in Integrated Assessment of
Agricultural Production Systems
John M. Antle Jetse J. Stoorvogel
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• Question How can ag systems be quantified used
  to understand rural poverty and resource
  degradation?
• Hypothesis Spatial heterogeneity and dynamic
  properties of these systems are key to
  understanding their behavior (and linkages to
  poverty degradation)
• e.g., in understanding non-adoption of
  conservation techs
• A key question is how much detail is needed to
  answer important policy questions!!!

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• Characterizing Agricultural Systems
• agro-ecosystems are complex, dynamic systems
  with spatially varying inputs and outputs that
  are the result of physical, biological, and human
  decision-making processes
• complexity ? qualitative analysis of little
  value
• spatial and temporal variability, feedbacks are
  key features
• goal is to simulate systems, not optimize them
• to support policy decision making, need to
  address
• participatory approach (Tradeoff Analysis)
• data availability (minimum data sets,
  reliability)
• response time
• replicability, adaptability

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• Modeling Approach
• reduced form
• modular
• integrated
• modular has advantage of plug and play
• Model Coupling
• loose coupling
• close coupling shorter time steps

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Figure 1. Examples of loose coupling (heavy
dashed lines) and close coupling (light dashed
lines) of economic decision models and crop
ecosystem models.
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• Temporal Scale and System Dynamics
• temporal variability operates on time steps
  determined by bio-phys processes and econ
  decision making
• crop models (daily time steps, seasonal outputs)
• ecosystem models (monthly time steps, seasonal
  and multi-year outputs)
• economic models
• static n.c. models
• intra-seasonal models (multiple day time steps)
• inter-seasonal models (crop rotations,
  investment)

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• Spatial Heterogeneity
• ag systems depend on site-specific soil, climate
• farm decision making units are heterogeneous
• interacts with system dynamics
• Thresholds
• bio-physical
• temperature, soils, etc.
• economic
• investment costs, uncertainty, discounting
• interact with spatial heterogeneity

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Figure 2. The effect of differences in the
thickness of the fertile A-horizon on the dry
matter production of potatoes as simulated with
DSSAT.
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Implementing the Modular Modeling
Approach Econometric-Process Simulation
Models (Antle Capalbo, 2001)
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General Version of E-P Model (1) max ?a
v(past , wast , zast , est)
?ast (2) ?ast ?a(pst , wst , zst ,
est) (3) qast ?ast ?qa(past , wast , zast ,
est)/?past (4) xiast -?ast ?xia(past , wast ,
zast , est)/?wiast.

• Implementation
• Estimate system (3) (4) for each activity
• Using site-specific data
• Simulate (2) by choosing activity with highest
  expected value
• Simulate (3) (4) for the chosen activity
• Characterizes population (no corner solutions).

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• Using Crop Models to Simulate Spatial Variability
  in Productivity
• conventional approach ad hoc use of dummy
  variables, soils climate variables in
  production functions
• alternative approach use crop models to
  estimate expected, or inherent, productivity
• qs f(xs, zs, es) production function
• qs g(x, es) crop model with average
  management x
• qs h(xs, zs, qs) h(xs, zs, g(x, es))
• note separability of e from x, z
• this is example of loose coupling

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• Loose Coupling Tradeoff Analysis of Ecuadors
  Potato-Pasture System
• max vst ?st v(ppst , wpst , zpst , ?st-1 ,
  qp(es0))
• ?st
  (1-?st) v(pgst ,
  wgst , zgst , ?st-1 , qg(es0))

(6) qp qp(es0), qg qg(es0) (7) ?st
?(ppst , wpst , zpst , qp, pgst , wgst , zgst ,
qg, ?st-1) (8) xpst - ?st ?v(ppst , wpst ,
zpst , ?st-1, qp)/?wpst (9) Lst ?st
xpst (10) ?st ?(est(?st-1 ?st-2 ), ?st-1).
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• Loose Coupling and Feedback
• Feedback without foresight replace (6)-(10)
  with
• (6) qp qp(est-1), qg qg(est-1).
• (7) ?st ?(ppst, wpst, zpst, qp, pgst, wgst,
  zgst, qg, ?st-1)
• (8) xpst - ?st ?v(ppst, wpst, zpst, ?st-1, qp
  )/?wpst
• (9) Lst ?(est) xpst
• ?st ?(est(?st-1 ?st-2 ), ?st-1).

• Feedback with foresight max n.p.v. of returns
• (10) with expected management gives expected
  future soils
• (6), (7), (8) and (9) using loose coupling with
  feedback give solution for expected soils
• Advance one step and repeat, using previous
  periods soils to initialize (10)

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• Close Coupling
• Interactions on shorter time step, e.g., inherent
  productivity depends on current period
  management
• (6) qp qp(xast, est-1), qg qg(xast,
  est-1).
• (7) ?st ?(ppst, wpst, zpst, qp, pgst, wgst,
  zgst, qg, ?st-1)
• (8) xpst - ?st ?v(ppst, wpst, zpst, ?st-1, qp
  )/?wpst
• (9) Lst ?(est) xpst
• ?st ?(est(?st-1 ?st-2 ), ?st-1).
• Solution Decompose each model into sub-processes
  in loosely coupled form?

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Loose Coupling without Feedback
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• Application The Ecuador Potato-Pasture System
• See www.tradeoffs.montana.edu and
  www.tradeoffs.nl for loosely-coupled model
  details
• Potato crop model
• Econometric-process simulation model
• Leaching model
• Tillage erosion model

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Tillage Erosion and Leaching
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(No Transcript)
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Loose Coupling without Foresight Ecuador Model,
average population results
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Thresholds and Interactions Tillage Erosion and
Leaching in the Ecuador Model Four illustrative
cases show spatial heterogeneity interacting with
soil threshold and system dynamics
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• Conclusions
• Modular approach appears promising.
• Example shows
• loosely coupled model without feedbacks is a
  reasonably good approximation
• feedbacks may be important in cases where there
  are strong feedbacks and thresholds.

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• Conclusions (cont.)
• Needed extensions
• Include ag system model in household model
• Link farm-level models to market models
• Modular, loosely-coupled model paradigm should
  be useful for both
• key issues are standardization of spatial and
  temporal units, formats for input and output
  data.

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Prodn System
Defining the Boundaries of Agricultural
Production Systems
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This presentation and related publications
available at www.tradeoffs.montana.edu