Landscape Linkage Modeling Prepared by Peter Singleton, USFS PNW Research Station for the State-wide...

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

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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Graph Theory 14

Graph Theory


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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 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

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


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21



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



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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




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)


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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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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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

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Landscape Linkage Modeling Prepared by Peter Singleton, USFS PNW Research Station for the State-wide...

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