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From: Singleton et al. 2002. Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance

From: Singleton et al. 2002. Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance

From: Singleton et al. 2002. Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance

From: Singleton et al. 2002. Landscape Permeability for Large Carnivores in Washington: A Weighted-Distance

Landscape Linkage Modeling

Prepared by Peter Singleton, USFS PNW Research Station for the State-wide CCLC Meeting, July 28, 2008.

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).

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

Introduction

Darwin’s Finches - 1837:

Images from Robert Rothman http://people.rit.edu/rhrsbi/GalapagosPages/DarwinFinch.html

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?

Analysis Approaches

- Patch Metrics
- Graph Theory
- Cost-distance Analysis
- Combining graph theory and cost-distance
- Circuit Theory
- Individual-based & Population Viability Models
- Patch / HexSim

Analysis Approaches

Simple

Few Assumptions

Needs Less Input Info

Structural focus

- Patch Metrics
- Graph Theory
- Cost-distance Analysis
- Combining graph theory and cost-distance
- Circuit Theory
- Individual-based & Population Viability Models
- Patch / HexSim

Complex

Lots of Assumptions

Needs More Input Info

Process focus

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.

Landscape Metric Example – Effective Mesh Size

11

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

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

Graph Theory

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

Analysis Approaches

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

17

Habitat Suitability:

0 = Barrier

1 = Poor

2 = Moderate

3 = Good

10 = Source

Analysis Steps:

- Identify Patches
- Develop Friction Surface
- Evaluate Landscape

Travel Cost:

0 = 99

1 = 3

2 = 2

3 = 1

10 = Source

Cost-distance

22

16

There are critical assumptions at each one of these steps!

18

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”)

19

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

20

Step 2: Develop friction surface

- Cost Model Parameters:
- Population Density
- 0 - 10 people/mi2 1.0
- 10 - 25 people/mi2 0.8
- 25 - 50 people/mi2 0.5
- 50 - 100 people/mi2 0.3
- >100 people/mi2 0.1
- Road Density
- < 1mi/mi2 1.0
- 1 - 2 mi/mi2 0.8
- 2 - 6 mi/mi2 0.5
- 6 - 10 mi/mi2 0.2
- >10 mi/mi2 0.1
- Land Cover
- All Forest & Wetlands 1.0
- Alpine, shrub, 0.8
- grasslands
- Agriculture, bare 0.3
- Water, urban, ice 0.1
- Slope
- 0 - 20% 1.0
- 20 - 40% 0.8
- >40% 0.6

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

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

Cost-distance Analysis

Step 2: Develop friction surface

and Least-Cost Corridor Assessment. USFS PNW Research Station PNW-RP-549

23

Step 3: Evaluate the landscape

and Least-Cost Corridor Assessment. USFS PNW Research Station PNW-RP-549

24

Step 3: Evaluate the landscape

and Least-Cost Corridor Assessment. USFS PNW Research Station PNW-RP-549

Minimum 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

Cost-distance Analysis

25

Step 3: Evaluate the landscape

Pretty easy to understand with a simple patch – linkage structure, but when things get more complex…

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.

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.

Analysis Approaches

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).

31

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)

- 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

Individual-based model example: Patch / HexSim

33

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

34

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

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

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.

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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