Getting to a Better Definition of Ecosystem Services Structure of the SPAN Model The Flow Algorithm Flow Results Acknowledgements Math for the Curious Service Path Attribution Networks (SPANs) Spatially Quantifying the Flow of Ecosystem Services from Landscapes to People Gary W. Johnson Kenneth J. Bagstad Robert R. Snapp Ferdinando Villa Ecoinformatics Collaboratory Gund Institute for Ecological Economics Department of Computer Science University of Vermont ACES 2010 Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Transcript
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Service Path Attribution Networks (SPANs)Spatially Quantifying the Flow of Ecosystem
Services from Landscapes to People
Gary W. Johnson Kenneth J. Bagstad Robert R. SnappFerdinando Villa
Ecoinformatics CollaboratoryGund Institute for Ecological Economics
Department of Computer ScienceUniversity of Vermont
ACES 2010Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
State of the Art
Today’s state of practice:Calculating “ES Provision” values
– often from land-use/land-cover (LULC).
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
Makes no distinctionbetween “Potential”and “Realized”services
Does not capture thebeneficiaries of theseservices
Assumes that allforests are the same
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Land Use is a Bad Proxy
Because an LULC class is NOT the whole picture.
Forest 6= Forest 6= Forest
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Ecosystem Services are Flows
Ecosystem services are the effects on human well-being of theflow of benefits from ecosystems to people over given extentsof space and time.
Villa et al. 2009
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Some Example Flow Types
Fisher et al. 2009Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
What is Flowing?
Service Medium: Matter, energy, or information that transmitsthe service between locations.
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
What is Flowing?
Service Medium: Water (hydrologic cycle)
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
What is Flowing?
Service Medium: Carbon Dioxide (atmospheric mixing)
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
What is Flowing?
Service Medium: Pollen (transported by pollinators)
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
What is Flowing?
Service Medium: Wildfire (combustion and propagation)
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
What is Flowing?
Service Medium: Scenic Beauty (line of sight)
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Relationships with the Service Medium
Beneficial DetrimentalDrinking Water Flood Water
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
SPAN Flow Abstraction
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Model Terminology
Service Medium: Matter, energy, or information thattransmits the service (benefit or detriment) betweenlocations.Service Carriers: Agents with Weight and Routeproperties that are governed by a service-specificmovement function.Location Properties:
Service Source: Total productionService Sink: Absorption capacityService Use: Use capacity
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Model Terminology
Service Medium: Matter, energy, or information thattransmits the service (benefit or detriment) betweenlocations.Service Carriers: Agents with Weight and Routeproperties that are governed by a service-specificmovement function.Location Properties:
Service Source: Total productionService Sink: Absorption capacityService Use: Use capacity
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Model Terminology
Service Medium: Matter, energy, or information thattransmits the service (benefit or detriment) betweenlocations.Service Carriers: Agents with Weight and Routeproperties that are governed by a service-specificmovement function.Location Properties:
Service Source: Total productionService Sink: Absorption capacityService Use: Use capacity
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Mapping from Geospace to Vertices
Source, Sink, and Use values are computed by region.Each region is mapped to a vertex in the SPAN graph.Flow paths designated by directed edges (these need notbe adjacency relationships).
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Mapping from Geospace to Vertices
Service flows will accrue at use locations on the landscape.
Note: Beneficiary regions may be of different scale thanprovisioning regions.
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Network Traversal Example
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Network Traversal Example
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Network Traversal Example
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Network Traversal Example
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Network Traversal Example
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Network Traversal Example
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Network Traversal Example
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Network Traversal Example
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Network Traversal Example
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Flow Connectivity Information
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Results of a Flow Analysis
Benefitsheds: To where (and whom) the benefits fromeach region flow.Provisionsheds: The sources of ecosystem servicebenefits.Flow Interruptions: Which Sink and Rival Use locationsblock downstream access to the service medium (for goodor for ill).Critical Flow Corridors: What parts of the landscapeexhibit the greatest flow density.
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Results of a Flow Analysis
Benefitsheds: To where (and whom) the benefits fromeach region flow.Provisionsheds: The sources of ecosystem servicebenefits.Flow Interruptions: Which Sink and Rival Use locationsblock downstream access to the service medium (for goodor for ill).Critical Flow Corridors: What parts of the landscapeexhibit the greatest flow density.
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Results of a Flow Analysis
Benefitsheds: To where (and whom) the benefits fromeach region flow.Provisionsheds: The sources of ecosystem servicebenefits.Flow Interruptions: Which Sink and Rival Use locationsblock downstream access to the service medium (for goodor for ill).Critical Flow Corridors: What parts of the landscapeexhibit the greatest flow density.
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Results of a Flow Analysis
Benefitsheds: To where (and whom) the benefits fromeach region flow.Provisionsheds: The sources of ecosystem servicebenefits.Flow Interruptions: Which Sink and Rival Use locationsblock downstream access to the service medium (for goodor for ill).Critical Flow Corridors: What parts of the landscapeexhibit the greatest flow density.
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Informing Policy
Improve human efficiency in using what they receive.Manage landscapes to create greater Source values.Decrease Sink effects (landscape management).Decrease Rival Use effects (institutional).Rechannel or add Flow paths.
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Informing Policy
Improve human efficiency in using what they receive.Manage landscapes to create greater Source values.Decrease Sink effects (landscape management).Decrease Rival Use effects (institutional).Rechannel or add Flow paths.
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Informing Policy
Improve human efficiency in using what they receive.Manage landscapes to create greater Source values.Decrease Sink effects (landscape management).Decrease Rival Use effects (institutional).Rechannel or add Flow paths.
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Informing Policy
Improve human efficiency in using what they receive.Manage landscapes to create greater Source values.Decrease Sink effects (landscape management).Decrease Rival Use effects (institutional).Rechannel or add Flow paths.
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Informing Policy
Improve human efficiency in using what they receive.Manage landscapes to create greater Source values.Decrease Sink effects (landscape management).Decrease Rival Use effects (institutional).Rechannel or add Flow paths.
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Viewshed Analysis For Kent, WA - Part 1
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Viewshed Analysis For Kent, WA - Part 1
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Viewshed Analysis For Kent, WA - Part 1
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Viewshed Analysis For Kent, WA - Part 1
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Viewshed Analysis For Kent, WA - Part 1
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Viewshed Analysis For Kent, WA - Part 1
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Viewshed Analysis For Kent, WA - Part 1
Theoretical Source Theoretical Sink Theoretical Use
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Viewshed Analysis For Kent, WA - Part 2
Possible Flow Blocked Flow Actual Flow
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Viewshed Analysis For Kent, WA - Part 3
Possible Source Actual Sink Possible Use
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Viewshed Analysis For Kent, WA - Part 3
Theoretical Source Theoretical Sink Theoretical Use
Possible Source Actual Sink Possible Use
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Open Problems and Next Steps
Determining upper limits on downsampling spatial datasetswithout encountering aliasing artifacts in service flowpaths.Enabling flow path analysis along human transportationnetworks.Investigating flow path substitutability in identifying criticalflow corridors.Finding optimal landscape modifications to maximize ESflow given cost (or other) constraints on spatialdevelopment activities.
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Open Problems and Next Steps
Determining upper limits on downsampling spatial datasetswithout encountering aliasing artifacts in service flowpaths.Enabling flow path analysis along human transportationnetworks.Investigating flow path substitutability in identifying criticalflow corridors.Finding optimal landscape modifications to maximize ESflow given cost (or other) constraints on spatialdevelopment activities.
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Open Problems and Next Steps
Determining upper limits on downsampling spatial datasetswithout encountering aliasing artifacts in service flowpaths.Enabling flow path analysis along human transportationnetworks.Investigating flow path substitutability in identifying criticalflow corridors.Finding optimal landscape modifications to maximize ESflow given cost (or other) constraints on spatialdevelopment activities.
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Open Problems and Next Steps
Determining upper limits on downsampling spatial datasetswithout encountering aliasing artifacts in service flowpaths.Enabling flow path analysis along human transportationnetworks.Investigating flow path substitutability in identifying criticalflow corridors.Finding optimal landscape modifications to maximize ESflow given cost (or other) constraints on spatialdevelopment activities.
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Acknowledgements
Funding: National Science Foundation grant 9982938Advisors: Ferdinando Villa, Robert SnappARIES Team Members: Kenneth Bagstad, Brian Voigt,Marta Ceroni, Sergey Krivov, Joshua FarleyConservation International: Miroslav Honzak, RosimeiryPortela, Nalini RaoEarth Economics: David Batker, Maya Kocian, JenHarrison-Cox
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Thank You
Any Questions?
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Service Carriers
Service carrier: (A, P, R, Q, X ),Actual Weight A: Medium carried including sink and rival use effects.
Possible Weight P: Like actual weight but disregarding sink effects.
Route R: Vertex list (v1, v2, . . . , vN) along travel path.
Sink Effects Q : V → ∆A: Absorption by landscapes in vertex v ∈ V .
Use Effects X : V → ∆A: Destructive use by people in vertex v ∈ V .
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Theoretical Source, Sink, Use
Sourcetheoretical(v) =
8>><>>:Sourcerel(v)× |U| , if service medium is relative
Sourceabs(v), otherwise
Sinktheoretical(v) =
8>><>>:Sinkrel(v)× |S| × |U| , if service medium is relative
Sinkabs(v), otherwise
Usetheoretical(v) =
8>><>>:Userel(v)×
Ps∈S Sourcerel(s)
|U| , if service medium is relative
Useabs(v), otherwise
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Possible Source, Use, Flow
Sourcepossible(v) =Xu∈U
X(A,P,R,Q,X)∈Cache(u)|First(R)=v
P
Usepossible(v) =X
(A,P,R,Q,X)∈Cache(v)
P
Losspossible(R, X , v) =X
v′∈Subroute(R,v)
X(v′)
Flowcontribpossible(P, R, X , v) =
8>>><>>>:Undecay
`P + Losspossible(R, X , v),
Subroute(R, v)) , if |Subroute(R, v)| > 0
0, otherwise
Flowpossible(v) =Xu∈U
X(A,P,R,Q,X)∈Cache(u)
Flowcontribpossible(P, R, X , v)
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
The Flow AlgorithmFlow Results
AcknowledgementsMath for the Curious
Actual Source, Sink, Use, Flow
Sourceactual(v) =Xu∈U
X(A,P,R,Q,X)∈Cache(u)|First(R)=v
A
Sinkactual(v) =Xu∈U
X(A,P,R,Q,X)∈Cache(u)
Q(v)
Useactual(v) =X
(A,P,R,Q,X)∈Cache(v)
A
Lossactual(R, Q, X , v) =X
v′∈Subroute(R,v)
Q(v′) + X(v′)
Flowcontribactual (A, R, Q, X , v) =
8>>><>>>:Undecay (A + Lossactual(R, Q, X , v),
Subroute(R, v)) , if |Subroute(R, v)| > 0
0, otherwise
Flowactual(v) =Xu∈U
X(A,P,R,Q,X)∈Cache(u)
Flowcontribactual (A, R, Q, X , v)
Johnson, G.W., et al. Spatially Quantifying Ecosystem Service Flows
Getting to a Better Definition of Ecosystem ServicesStructure of the SPAN Model
