Connections That Matter: A Graph Theoretic Analysis of Grizzly Bear Movement in the Yellowhead Ecosy

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Connections That Matter A Graph Theoretic
Analysis of Grizzly Bear Movement in the
Yellowhead Ecosystem, Alberta, Canada
Barbara L. Schwab, Clarence Woudsma, Gordon B.
Stenhouse, Steven E. Franklin and Scott E. Nielsen
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Presentation Outline

• The FMF Grizzly Bear Research Project
• What is Graph Theory?
• Regional Setting
• Methodology
• Least-cost path modeling
• Graph theory generation
• Results

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FMF Grizzly Bear Research Project

• 5 year research program to support management
  goals and aid in decisions
• Developed in full consultation with
• Government , industry and public stakeholders

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Suitable Landscape Conditions

• Combination of field research, RS, GPS and GIS
  are used to derive current landscape conditions
  and forecast future scenarios for management
  purposes.
• Goal is to develop connectivity measures,
  similar to those applied in the analysis of
  habitat fragmentation

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What is Graph Theory?

• Branch of mathematics used to quantify the level
  of landscape / habitat connectivity
• Graph defined
• Simply, a graph consists of two primary
  components
• Nodes (habitat patches)
• Edges (connections between patches)

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Regional Setting

• Approximately 10000 km2
• Home to 30 of Albertas grizzly bear population

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Natural vs. Disturbed Landscapes
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Specific Objectives

• To apply a graph theoretic model in the analysis
  of movement and connectivity patterns associated
  with grizzly bear populations
• Develop and explore alternative methods of graph
  creation
• Validation using grizzly bear telemetry data

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Methodology

• Defining and validating cost surfaces
• Basis of Least-cost Path procedure / edge
  creation
• Graph generation
• Determining habitat patches / node creation
• Creating connections / LCP edges
• Graph analysis
• Evaluating connectivity

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Cost Surface Developmentand Least-cost Path
Modeling

• Linkage Zone Model (LZM)
• cumulative scored map identifying levels of
  danger to grizzly bears from human influence
• following Servheen and Sandstrom (1993) and
  Purves and Doering (1998)

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Cost Surface Developmentand Least-cost Path
Modeling
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Edge Validation

• 211 LCP paths (844) modeled using each cost
  surface
• 372 withheld mid-path GPS data points for
  comparison
• Distance (m) of points to paths modeled
  calculated
• Results (mean distance)
• LZM 387.51
• SCS 359.89
• RSF 306.31 (P 0.031)
• Homogeneous 378.67

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Graph Generation1. Nodes / Habitat Patches

• Nodes represent type of habitat important to
  bears
• Forms the basis for graph construction

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Graph Generation2. Edges / Connections

• LCP edges are created that join each node to
  every other node
• Output graph forms the basis for continued
  connectivity analysis

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Graph Analysis

• Graphs were generated for 3 females for 1999 and
  2000 using 95 kernel home ranges
• Edge distances were defined by mean daily
  movement rates (km/day) for each female
• Connectivity measures include

Gamma ? e / (n (n 1) / 2) Beta ß e /
n Values range from 0 - 1
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ResultsMountain versus Foothills

• Limited levels of disturbance
• Increased levels of connectivity (? 0.346, ß
  5.886)

• Increased levels of disturbance
• Decreased levels of connectivity (? 0.023, ß
  2.694)

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Results

• Overall, graph theory is an effective method
  for modeling habitat connectivity

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Results

• RSF based cost surfaces best modeled grizzly bear
  movement at the path scale
• LCP modeling best represents functional distances
  and connections
• As levels of disturbance increase, levels of
  habitat connectivity decrease
• Largely dependant on defined daily movement rates
• Efforts needed to apply graph theory at the
  landscape level

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Acknowledgements

• Foothills Model Forest Grizzly Bear Research
  Project
• Gordon Stenhouse
• Robin Munro
• Julie Dugas
• And all other project members
• University of Calgary Department of Geography
• Clarence Woudsma
• Steve Franklin
• Medina Hansen

• Duke University Landscape Ecology Lab
• Dean Urban
• Andy Bunn
• University of Calgary Computing Sciences
• Doug Phillips
• University of Alberta Department of Biological
  Sciences
• Scott Nielsen
• Mark Boyce

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Questions?