landscape linkage modeling peter singleton & brad mcrae cclc meeting, june 18, 2010. 1

Landscape Linkage ModelingLandscape Linkage ModelingLandscape Linkage ModelingLandscape Linkage Modeling

Peter Singleton & Brad McRaeCCLC Meeting, June 18, 2010.

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Introduction• Landscape Configuration is Important!

– Animals need to be able to move at a variety of scales

– Intra-territorial movements• Habitat resources need to configured in a way that

they are accessible

– Inter-territorial movements• Metapopulation function• Dispersal• Range Shifts

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

Standard Definitions from Merriam-Webster.com

Connectivity: Connect – 1. to join or fasten together usually by something intervening (Latin com- + nectere to bind)

Linkage: Link – 1. a connecting structure (Old Norse hlekkr chain)

Corridor: 1. a passageway into which compartments or rooms open, 2. an area or narrow stretch of land identified by a specific common characteristic or purpose, 3. a land path used by migrating animals (Italian correre to run)

Permeability: Permeate – 1. to diffuse through or penetrate something 2. to pass through the pores of interstices of (Latin permeatus, from per- through + meare to go, pass)

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 BiogeographyReserve Design• Soule 1987 Viable Populations for Conservation• Meffe & Carroll 1994 Conservation Biology TextbookConservation 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-’00’s, lots of publications addressing corridors / connectivityLandscape Processes• Late-’00’s Maturation of landscape genetics & modeling techniques• Future?

– More empirical data relating landscape process and pattern?– More sophisticated simulation modeling– Address climate change adaptation concerns

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Introduction

• Types of ecological models– Conceptual models

• Consistent syntheses of existing information that allow a systematic exploration of the way we think a process works

– Statistical models• Based on empirical information

– Simulation models• Similar to conceptual models, but provide a more

detailed exploration of a specific process

Analysis Approaches7

1. Patch Metrics

2. Graph Theory

3. Cost-distance Analysis• Combining graph theory and cost-distance

4. Circuit Theory

5. Individual-based Models

Analysis Approaches

1. Patch Metrics

2. Graph Theory

3. Cost-distance Analysis• Combining graph theory and cost-distance

4. Circuit Theory

5. Individual-based

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


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 foraging 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. 2008. Using Circuit Theory to Model Connectivity in Ecology, Evolution, and Conservation. Ecology.

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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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Integrating Cost-Distance & Circuit Resistance Analysis

Sage Grouse Cores& Resistance Surface

Circuit Resistance Least-Cost Corridors

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

(covered in another chapter)

• Spatially explicit population models (SEPMs)– Integrates PVA with a heterogeneous landscape where vital rates vary

(e.g. Ramas GIS)


Individual-based model example: HexSim

HexSim:• IBM & SEPM• Flexible cell and group resolution• Survival / reproduction / dispersal probabilities

are related to the habitat characteristics of the cell

• Models individual dispersal movements through the landscape

• Flexible assumptions about behavior (originally developed for spotted owl PVA, but is being applied to a variety of species)

• Developed by Nathan Schumacher, EPA, Corvallis OR (http://www.epa.gov/hexsim/)

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Individual-based model example: 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• Challenges common to all of these

approaches:– Identifying areas to link up (cores)– Parameterizing resistance layers– Interpreting cumulative resistance indices

• How much resistance is too much?

– Communicating uncertainty while providing useful information to decision makers

• Lots of cartographic challenges

– Conceptual models can be very difficult to interpret• Models provide information, not answers

– Too much focus on corridor delineation and not enough on assessing relative permeability values

DiscussionThe 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

• Simulation Modeling– HexSim, CDPOP

• Climate Change– How do we integrate climate change concerns into

connnectivity analysis?

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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• Models provide information, not answers• Validate, validate, validate …

Closing 38

landscape linkage modeling peter singleton & brad mcrae cclc meeting, june 18, 2010. 1

Documents

landscape structure

landscape unit

landscape elements

specific process slide

quantifying landscape

circuit theory

patches analysis approaches

habitat patches