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Landscape Linkage Modeling Prepared by Peter Singleton, USFS PNW Research Station for the State-wide CCLC Meeting, July 28,

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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). 2

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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 3

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Introduction Darwins Finches : Images from Robert Rothman 4

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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-2000s, lots of publications addressing corridors / connectivity Landscape Processes Late-2000s Maturation of landscape genetics Future? More empirical data relating landscape process and pattern? 5

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Introduction From: Crooks & Sanjayan Connectivity Conservation. Cambridge Univ. Press 6

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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 7

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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 Simple Few Assumptions Needs Less Input Info Structural focus Complex Lots of Assumptions Needs More Input Info Process focus 8

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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 Dont provide a lot of information about expected movement patterns 9

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Landscape Metric Example – Effective Mesh Size From: Girvetz, Thorne, & Jaeger Integrating Habitat Fragmentation Analysis into Transportation Planning Using The Effective Mesh Size Landscape Metric ICOET Proceedings. 10

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Landscape Metric Example – Effective Mesh Size From: Girvetz, Thorne, & Jaeger Integrating Habitat Fragmentation Analysis into Transportation Planning Using The Effective Mesh Size Landscape Metric ICOET Proceedings. 11

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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 Approaches 12

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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 Landscape Connectivity: A graph-theoretic approach. Ecology 82:

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From: Urban & Keitt Landscape Connectivity: A graph-theoretic approach. Ecology 82: Graph Theory 14

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Graph Theory From: Urban & Keitt Landscape Connectivity: A graph-theoretic approach. Ecology 82:

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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 Approaches 16

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Analysis Steps: 1)Identify Patches 2)Develop Friction Surface 3)Evaluate Landscape Cost-distance Analysis 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 There are critical assumptions at each one of these steps! 17

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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 Analysis Step 1: Identifying source patches: Large roadless areas and units highlighted in focal species management plans. From: Singleton et al Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance and Least-Cost Corridor Assessment. USFS PNW Research Station PNW-RP

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Cost-distance Analysis Step 2: Develop friction surface Cost Model Parameters: Population Density people/mi people/mi people/mi people/mi >100 people/mi Road Density < 1mi/mi mi/mi mi/mi mi/mi >10 mi/mi Land Cover All Forest & Wetlands 1.0 Alpine, shrub, 0.8 grasslands grasslands Agriculture, bare0.3 Water, urban, ice0.1 Slope % % % % 0.8 >40% 0.6 >40% 0.6 Cost Model Parameters: Population Density people/mi people/mi people/mi people/mi >100 people/mi Road Density < 1mi/mi mi/mi mi/mi mi/mi >10 mi/mi Land Cover All Forest & Wetlands 1.0 Alpine, shrub, 0.8 grasslands grasslands Agriculture, bare0.3 Water, urban, ice0.1 Slope % % % % 0.8 >40% 0.6 >40% 0.6 Road Density Land Cover From: Singleton et al Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance and Least-Cost Corridor Assessment. USFS PNW Research Station PNW-RP

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Cost-distance Analysis Step 2: Develop friction surface From: Singleton et al Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance and Least-Cost Corridor Assessment. USFS PNW Research Station PNW-RP

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Cost-distance Analysis Step 2: Develop friction surface From: Singleton et al Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance and Least-Cost Corridor Assessment. USFS PNW Research Station PNW-RP

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Step 3: Evaluate the landscape Cost-distance Analysis From: Singleton et al Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance and Least-Cost Corridor Assessment. USFS PNW Research Station PNW-RP

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Step 3: Evaluate the landscape Cost-distance Analysis From: Singleton et al Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance and Least-Cost Corridor Assessment. USFS PNW Research Station PNW-RP

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Fracture Zone 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 Southwestern Washington Step 3: Evaluate the landscape Cost-distance Analysis From: Singleton et al 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… 25

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From: OBrien et al Testing the importance of spatial configuration of winter habitat for woodland Caribou: an application of graph theory. Biological Conservation 130: A Digression: Integrating Cost-Distance Analysis and Graph Theory 26

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A Digression: Integrating Cost-Distance Analysis and Graph Theory FunConn ArcGIS Toolbox: From: Theobald et al FunConn v1 Users Manual: ArcGIS tools for Functional Connectivity Modeling. Colorado State University. 27

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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). 28

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A B C D E F Simple landscapes Least-cost path distance Resistance distance Slide by Brad McRae 29

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A more realistic landscape Circuit theory: Least-cost path: High Low Slide by Brad McRae 30

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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 Approaches 31

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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/) 32

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Individual-based model example: Patch / HexSim From: USFWS Final Recovery Plan for the Northern Spotted Owl. May USFWS Region 1, Portland OR. Analysis by Marcot & Raphael Images by Bruce Marcot 33

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Individual-based model example: Patch / HexSim From: Carroll 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 34

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Discussion Different approaches provide different information and require different inputs and assumptions InformationDataModel ProvidedInputsAssumptionsFocus Landscape MetricsLessLessFewer (implicit)Structure Graphs Cost-distance Circuit Theory IBM / SEPMMoreMoreMore (explicit)Function 35

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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. 36

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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 37

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Petes 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

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