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Landscape Linkage Modeling
Prepared by Peter Singleton, USFS PNW Research Station for the State-wide
CCLC Meeting, July 28, 2008.
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Introduction
Definitions of connectivity:
Merriam 1984: The degree to which absolute isolation is
prevented by landscape elements which allow organisms
to move among patches.
Taylor et al 1993: The degree to which the landscape
impedes or facilitates movement among resource patches.
With et al 1997: The functional relationship among habitat
patches owing to the spatial contagion of habitat and the
movement responses of organisms to landscape structure.
Singleton et al 2002: The quality of a heterogeneous land
area to provide for passage of animals (landscape
permeability).
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Introduction
• Structural Connectivity: The spatial arrangement
of different types of habitat or other elements in
the landscape.
• Functional Connectivity: The behavioral
response of individuals, species, or ecological
processes to the physical structure of the
landscape.
– Potential Connectivity
– Actual Connectivity
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Introduction
Darwin’s Finches - 1837:
Images from Robert Rothman http://people.rit.edu/rhrsbi/GalapagosPages/DarwinFinch.html
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Introduction
Island Biography
• MacArthur & Wilson 1967 The Theory of Island Biogeography
Reserve Design
• Soule 1987 Viable Populations for Conservation
• Meffe & Carroll 1994 Conservation Biology Textbook
Conservation Corridors
• Servheen & Sandstrom 1993 Linkage Zones for Grizzly Bears… End.
Sp. Bul. 18
• Walker & Craighead 1997 Analyzing Wildlife Movement Corridors…
Proc. ESRI Users Conf.
• Around 2000, linkage assessment workshops start happening
• Mid-2000’s, lots of publications addressing corridors / connectivity
Landscape Processes
• Late-2000’s Maturation of landscape genetics
• Future? More empirical data relating landscape process and pattern?
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Introduction
From: Crooks & Sanjayan. 2006. Connectivity Conservation. Cambridge Univ. Press
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Analysis Approaches
1. Patch Metrics
2. Graph Theory
3. Cost-distance Analysis
•
Combining graph theory and cost-distance
4. Circuit Theory
5. Individual-based & Population Viability
Models
•
Patch / HexSim
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Analysis Approaches
1. Patch Metrics
2. Graph Theory
3. Cost-distance Analysis
•
Simple
Few Assumptions
Needs Less Input Info
Structural focus
Combining graph theory and cost-distance
4. Circuit Theory
5. Individual-based & Population Viability
Models
•
Patch / HexSim
Complex
Lots of Assumptions
Needs More Input Info
Process focus
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Analysis Approaches
1) Patch Metrics
• Quantifies Patch Characteristics or Relationships
Between Patches (e.g. patch size, nearest neighbor)
• Emphasizes Structural Connectivity
• Generally must be summarized across a landscape unit
(e.g. watershed or planning unit)
• Very useful for quantifying landscape patterns (e.g.
historic range of variability, monitoring change,
comparing landscapes)
• Structure, not process oriented
• Don’t provide a lot of information about expected
movement patterns
Landscape Metric Example – Effective Mesh Size
From: Girvetz, Thorne, & Jaeger. 2007. Integrating Habitat Fragmentation Analysis into Transportation Planning Using
The Effective Mesh Size Landscape Metric. 2007 ICOET Proceedings.
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Landscape Metric Example – Effective Mesh Size
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From: Girvetz, Thorne, & Jaeger. 2007. Integrating Habitat Fragmentation Analysis into Transportation Planning Using
The Effective Mesh Size Landscape Metric. 2007 ICOET Proceedings.
Analysis Approaches
2) Graph Theory
• Focused on quantifying relationships between patches
• More focused on process
• Solidly based in mathematical theory with many
applications in other fields (e.g. geography, computer
science, logistics)
• Provides a language for describing relationships
between patches
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Graph Theory
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Vocabulary:
•
•
•
•
•
•
•
Patch (Node) – the points of interest
Link (Edge) – connections between the nodes
Path – a sequence of connected nodes
Tree – a set of paths that do not return to the same node
Spanning Tree – a tree that includes every node in the graph
Connected Graph – a graph with a path between every pair of nodes
Component (Subgraph) – part of the graph where every node is
adjacent to another node in that part of the graph
• Node-connectivity – the minimum number of nodes that must be
removed from a connected graph before it becomes disconnected
• Line-connectivity – the minimum number of links that must be removed
before a graph becomes disconnected
From: Urban & Keitt. 2001. Landscape Connectivity: A graph-theoretic approach. Ecology 82:1205-1218
Graph Theory
From: Urban & Keitt. 2001. Landscape Connectivity: A graph-theoretic approach. Ecology 82:1205-1218
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Graph Theory
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From: Urban & Keitt. 2001. Landscape Connectivity: A graph-theoretic approach. Ecology 82:1205-1218
Analysis Approaches
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3) Cost-distance Analysis
• More focus on matrix
• Can quantify isolation between patches
• Spatially explicit – can identify routes and bottlenecks
• Based on the concept of “movement cost” that has some
foundation in ecological theory, but lacks extensive empirical
documentation
• Several important assumptions about parameters and scale
must be considered
Cost-distance Analysis
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Analysis Steps:
1) Identify Patches
2) Develop Friction
Surface
3) Evaluate
Landscape
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1
2
10
1
0
2
1
1
1
3
3
10
3
1
2
1
3
2
10
3
0
2
3
3
3
1
1
10
1
3
2
6
5
2
10
6
103
4
3
3
4
5
4
10
1
4
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Habitat Suitability:
0 = Barrier
1 = Poor
2 = Moderate
3 = Good
10 = Source
Travel Cost:
0 = 99
1=3
2=2
3=1
10 = Source
Cost-distance
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There are critical assumptions at each one of these steps!
Cost-distance Analysis
Results from cost-distance analysis:
• Minimum cost-distance
• Cost / Euclidean ratios
• nth best corridor area delineations
• Spatially explicit maps
Many cost-distance applications have failed to take advantage of this
information by focusing on least-cost paths or corridors
(“Failing to see the landscape for the corridor”)
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Cost-distance Analysis
Step 1: Identifying source patches:
Large roadless areas and units highlighted in focal species management plans.
From: Singleton et al. 2002. Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance
and Least-Cost Corridor Assessment. USFS PNW Research Station PNW-RP-549
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Cost-distance Analysis
Step 2: Develop friction surface
Road Density
Land Cover
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Cost Model Parameters:
Population Density
0 - 10 people/mi2
10 - 25 people/mi2
25 - 50 people/mi2
50 - 100 people/mi2
>100 people/mi2
1.0
0.8
0.5
0.3
0.1
Road Density
< 1mi/mi2
1 - 2 mi/mi2
2 - 6 mi/mi2
6 - 10 mi/mi2
>10 mi/mi2
1.0
0.8
0.5
0.2
0.1
Land Cover
All Forest & Wetlands
Alpine, shrub,
grasslands
Agriculture, bare
Water, urban, ice
Slope
0 - 20%
20 - 40%
>40%
1.0
0.8
0.3
0.1
1.0
0.8
0.6
From: Singleton et al. 2002. Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance
and Least-Cost Corridor Assessment. USFS PNW Research Station PNW-RP-549
Cost-distance Analysis
Step 2: Develop friction surface
From: Singleton et al. 2002. Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance
and Least-Cost Corridor Assessment. USFS PNW Research Station PNW-RP-549
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Step 2: Develop friction surface
Cell Weighted Distance (m)
Cost-distance Analysis
9000
8100
7200
6300
5400
4500
3600
2700
1800
900
900
0.01 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
Dispersal Habitat Suitability
From: Singleton et al. 2002. Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance
and Least-Cost Corridor Assessment. USFS PNW Research Station PNW-RP-549
Cost-distance Analysis
Step 3: Evaluate the landscape
From: Singleton et al. 2002. Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance
and Least-Cost Corridor Assessment. USFS PNW Research Station PNW-RP-549
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Cost-distance Analysis
Step 3: Evaluate the landscape
From: Singleton et al. 2002. Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance
and Least-Cost Corridor Assessment. USFS PNW Research Station PNW-RP-549
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Cost-distance Analysis
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Step 3: Evaluate the landscape
Minimum Cost
Distance (km)
Actual Linear
Distance (km)
Cost Distance /
Linear Distance
Ratio
Fraser River
Canyon
Upper Columbia
River
I-90 Snoqualmie
Pass
Okanogan Valley
288.1
27.9
10.3
423.5
46.3
9.1
630.4
33.5
18.8
633.5
80.8
7.8
Southwestern
Washington
6943.8
116.2
82.6
Fracture Zone
Pretty easy to understand with a simple patch – linkage structure,
but when things get more complex…
From: Singleton et al. 2002. Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance
and Least-Cost Corridor Assessment. USFS PNW Research Station PNW-RP-549
A Digression: Integrating Cost-Distance Analysis
and Graph Theory
From: O’Brien et al 2006. Testing the importance of spatial configuration of winter habitat for
woodland Caribou: an application of graph theory. Biological Conservation 130:70-83.
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A Digression: Integrating Cost-Distance Analysis
and Graph Theory
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FunConn ArcGIS Toolbox: http://www.nrel.colostate.edu/projects/starmap/
From: Theobald et al. 2006. FunConn v1 User’s Manual: ArcGIS tools for Functional Connectivity Modeling. Colorado State University.
Analysis Approaches
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4) Circuit Theory
• Based on electrical
engineering theory
• Generates a measure of
“flow” through each cell in a
landscape
• Integrates all possible
pathways into calculations
• Corresponds well with
random-walk models
• Resistance measures can be
used in graph-theory
applications
From: McRae et al. in press. Using Circuit Theory to Model Connectivity in Ecology,
Evolution, and Conservation. Ecology (expected publication fall 2008).
Simple landscapes
C
D
E
F
Resistance distance
B
Least-cost path distance
A
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Slide by Brad McRae
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A more realistic landscape
High
Low
Circuit theory:
Least-cost path:
Slide by
Brad
McRae
Analysis Approaches
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5) Individual Based Models & Other Approaches
• Individual-based movement models (IBM)
– Simulates movement of an individual through the landscape (e.g.
PATH)
– Many scales, from dispersal (coarse) to foraging (fine)
• Population viability models (PVA)
– Uses demographic information to project population persistence (e.g.
Vortex)
• Spatially explicit population models (SEPMs)
– Integrates PVA with a heterogeneous landscape where vital rates vary
(e.g. Ramas GIS)
Individual-based model example: Patch / HexSim
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HexSim (updated version of Patch):
• IBM & SEPM
• Each cell represents a female home range
• Survival / reproduction / dispersal probabilities
are related to the habitat characteristics of the
cell
• Models individual dispersal movements through
the landscape
• Assumes territorial, non-social behavior
(originally developed for spotted owl PVA)
• Developed by Nathan Schumacher, EPA,
Corvallis OR (http://www.epa.gov/hexsim/)
Individual-based model example: Patch / HexSim
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From: USFWS 2008. Final
Recovery Plan for the Northern
Spotted Owl. May 2008. USFWS
Region 1, Portland OR.
Analysis by Marcot & Raphael
Images by Bruce Marcot
Individual-based model example: Patch / HexSim
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From: Carroll 2005. Carnivore Restoration in the Northeastern U.S. and Southeastern Canada: A Regional-Scale Analysis of
Habitat and Population Viability for Wolf, Lynx, and Marten. Wildlands Project – Special Paper No. 2. Richmond VA
Discussion
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Different approaches provide different information
and require different inputs and assumptions
Landscape Metrics
Graphs
Cost-distance
Circuit Theory
IBM / SEPM
Information
Provided
Less
Data Model
Inputs Assumptions Focus
Less Fewer (implicit) Structure
More
More
More (explicit) Function
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Discussion
All of these modeling approaches involve major
assumptions about:
• Habitat associations
– Parameterizing source areas or habitat patch
characteristics
• Dispersal behavior
– Resistance to movement
Some projects have addressed some of these
issues by using parameters based on empirical
RSFs, but assumptions about dispersal habitat
selection remain difficult.
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Discussion
The future of linkage modeling
• Better empirical techniques:
– Integration of detection probability and
movement probabilty into resource selection
analysis
• Model validation:
– Landscape genetics
– GPS telemetry studies
Closing
Pete’s cornball philosophy of landscape modeling:
• Know your question
• Know your data
• Keep it simple
• Own your assumptions
• Be open to surprises, but always check twice
• All models are wrong, but some models are useful
• Validate, validate, validate …
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