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Landscape Linkage ModelingLandscape Linkage ModelingLandscape Linkage ModelingLandscape Linkage Modeling
Prepared by Peter Singleton, USFS PNW Research Station for the State-wide CCLC Meeting, July 28, 2008.
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IntroductionDefinitions 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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IntroductionIsland 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• Combining graph theory and cost-distance
4. Circuit Theory
5. Individual-based & Population Viability Models
• Patch / HexSim
SimpleFew AssumptionsNeeds Less Input InfoStructural focus
ComplexLots of AssumptionsNeeds More Input InfoProcess focus
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Analysis Approaches1) 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
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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
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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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
Analysis Approaches12
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Graph Theory
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
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From: Urban & Keitt. 2001. Landscape Connectivity: A graph-theoretic approach. Ecology 82:1205-1218
Graph Theory 14
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Graph Theory
From: Urban & Keitt. 2001. Landscape Connectivity: A graph-theoretic approach. Ecology 82:1205-1218
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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
Analysis Approaches16
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Analysis Steps:
1) Identify Patches
2) Develop Friction Surface
3) Evaluate Landscape
3 1 2 10
1 0 2 1
1 1 3 3
10 3 1 2
Cost-distance Analysis
1 3 2 10
3 0 2 3
3 3 1 1
10 1 3 2
Habitat Suitability:0 = Barrier1 = Poor2 = Moderate3 = Good10 = Source
Travel Cost:0 = 991 = 32 = 23 = 110 = Source
6 5 2 10
6 103 4 3
3 4 5 4
10 1 4 6
Cost-distance2216
There are critical assumptions at each one of these steps!
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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”)
Cost-distance Analysis 18
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Cost-distance AnalysisStep 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 AnalysisStep 2: Develop friction surface
Cost Model Parameters:Cost Model Parameters:
Population DensityPopulation Density0 - 10 people/mi0 - 10 people/mi2 2 1.0 1.0 10 - 25 people/mi10 - 25 people/mi22 0.80.825 - 50 people/mi25 - 50 people/mi2 2 0.50.550 - 100 people/mi50 - 100 people/mi2 2 0.30.3>100 people/mi>100 people/mi2 2 0.10.1
Road DensityRoad Density< 1mi/mi< 1mi/mi22 1.01.01 - 2 mi/mi1 - 2 mi/mi22 0.80.82 - 6 mi/mi2 - 6 mi/mi22 0.50.56 - 10 mi/mi6 - 10 mi/mi22 0.20.2>10 mi/mi>10 mi/mi22 0.10.1
Land CoverLand CoverAll Forest & Wetlands All Forest & Wetlands 1.01.0Alpine, shrub,Alpine, shrub, 0.80.8
grasslands grasslands Agriculture, bareAgriculture, bare 0.30.3Water, urban, iceWater, urban, ice 0.10.1
SlopeSlope 0 - 20%0 - 20% 1.01.0
20 - 40% 20 - 40% 0.80.8 >40%>40% 0.60.6
Cost Model Parameters:Cost Model Parameters:
Population DensityPopulation Density0 - 10 people/mi0 - 10 people/mi2 2 1.0 1.0 10 - 25 people/mi10 - 25 people/mi22 0.80.825 - 50 people/mi25 - 50 people/mi2 2 0.50.550 - 100 people/mi50 - 100 people/mi2 2 0.30.3>100 people/mi>100 people/mi2 2 0.10.1
Road DensityRoad Density< 1mi/mi< 1mi/mi22 1.01.01 - 2 mi/mi1 - 2 mi/mi22 0.80.82 - 6 mi/mi2 - 6 mi/mi22 0.50.56 - 10 mi/mi6 - 10 mi/mi22 0.20.2>10 mi/mi>10 mi/mi22 0.10.1
Land CoverLand CoverAll Forest & Wetlands All Forest & Wetlands 1.01.0Alpine, shrub,Alpine, shrub, 0.80.8
grasslands grasslands Agriculture, bareAgriculture, bare 0.30.3Water, urban, iceWater, urban, ice 0.10.1
SlopeSlope 0 - 20%0 - 20% 1.01.0
20 - 40% 20 - 40% 0.80.8 >40%>40% 0.60.6
Road Density
Land Cover
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 AnalysisStep 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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Cost-distance AnalysisStep 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
0
900
1800
2700
3600
4500
5400
6300
7200
8100
9000
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
Cell
Wei
ghte
d Di
stan
ce (m
)
90
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Step 3: Evaluate the landscape
Cost-distance Analysis
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 3: Evaluate the landscape
Cost-distance Analysis
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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Fracture ZoneMinimum Cost Distance (km)
Actual Linear Distance (km)
Cost Distance / Linear Distance
Ratio
Fraser River Canyon
288.1 27.9 10.3
Upper Columbia River
423.5 46.3 9.1
I-90 Snoqualmie Pass
630.4 33.5 18.8
Okanogan Valley 633.5 80.8 7.8
Southwestern Washington
6943.8 116.2 82.6
Step 3: Evaluate the landscape
Cost-distance Analysis
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
Pretty easy to understand with a simple patch – linkage structure, but when things get more complex…
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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.
A Digression: Integrating Cost-Distance Analysis and Graph Theory
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A Digression: Integrating Cost-Distance Analysis and Graph Theory
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.
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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
Analysis Approaches
From: McRae et al. in press. Using Circuit Theory to Model Connectivity in Ecology, Evolution, and Conservation. Ecology (expected publication fall 2008).
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A B
C D
E F
Simple landscapes
Lea
st-c
ost
pat
h d
ista
nce
R
esis
tan
ce d
ista
nce
Slide by Brad McRae
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A more realistic landscape
Circuit theory: Least-cost path:
High
Low
Slide by Brad McRae
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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)
Analysis Approaches31
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Individual-based model example: Patch / HexSim
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/)
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Individual-based model example: Patch / HexSim
From: USFWS 2008. Final Recovery Plan for the Northern Spotted Owl. May 2008. USFWS Region 1, Portland OR.Analysis by Marcot & RaphaelImages by Bruce Marcot
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Individual-based model example: Patch / HexSim
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
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Discussion
Different approaches provide different information and require different inputs and assumptions
Information Data Model
Provided Inputs Assumptions Focus
Landscape Metrics Less Less Fewer (implicit) Structure
Graphs
Cost-distance
Circuit Theory
IBM / SEPM More More More (explicit)Function
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DiscussionAll 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
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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 …
Closing 38