Landscape Graphs

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Habitat Analysis and Conservation Management

• Landscape Graphs
• Connectivity Parameters

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Landscape Ecology

• Graphs are used to model complex landscapes,
  uncovering patterns of interaction or flow, to
  better analyze fluxes. This analysis provides
  guidance in land acquisition, reserve design, and
  management.
• Landscape graphs are defined by
• Vertices consist of the landscape elements (e.g.
  local ecosystems, land uses, ecotopes, and
  biotopes - grasslands, bean fields, woods,
  highways, roads, rivers, streams, etc.)
• Edges represent common boundaries between
  elements or points where adjoining elements meet.

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The Model

• Landscape Graphs are used to
• Identify common configurations within landscapes
• Understand the ecological and management
  implications of the configurations
• Examine the connectivity of elements in
  landscapes
• Understand relationships between dispersion,
  connectivity and stability
• Understand landscape changes and managements
  optimal responses to these changes.

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Landscape Configurations

• Necklace
• Spider
• Cell
• Satellite
• or Pendant

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More Landscape Configurations

• Cross
• Mesh or grid
• Rigid polygon

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Landscape Graph of a suburban rural area in
Northwest Montana W woods, F field, L
house, R road, B bog, P powerline
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Habitat Networks

• Habitat patches are vertices in the Habitat
  Network
• Habitat patches are connected by dispersing
  individuals and these connections are the edges
  a set threshold distance apart.
• Useful graph theory terms
• Degree number of patches (vertices) connected
  to a patch
• Hub is a high degree vertex
• Path is a route from one patch to another
• Distance D(x,y) length of shortest path
  between x and y.
• Component - a connected piece that is
  disconnected from the rest.

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Travels of pronged horn antelope

• Blue - December March White- March
  June, Red - July September

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Example of a Habitat Network
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Metrics

• Clustering Coefficient the average fraction of
  the vertexs neighbors that are also neighbors of
  each other.
• high dispersal (disease, disturbance)
  resilient to patch removal
• Connectivity correlation vertex degree/average
  vertex degree of its neighbors measures
  compartmentalization- highly connected hubs
• high slows movement and isolates
  resilient to diisturbances
• Diameter length of the longest shortest path
  Distance - D(x,y) - shortest path between x and
  y.
• Characteristic path length (CPL) is the average
  shortest path lengths over all pairs of vertices
• Short patchy population

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Connectivity

• A graph G is k - connected if k is the minimum
  number of vertices that need to be removed to
  disconnect the graph.
• A graph G is n- neighbor connected if n is the
  minimum number of vertices along with their
  neighbors that need to be removed to disconnect
  the graph, leave the empty set, or a complete
  graph.
• a b
• e
• c d
• This graph is 3-connected vertices c, e, b
• and 1 neighbor connected vertex e

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Edge Connectivity

• A graph G is K-edge connected if K is the minimum
  number of edges that need to be removed to
  disconnect the graph.
• A graph G is N-edge neighbor connected if N is
  the minimum number of edges along with their edge
  neighbors that need to be removed to disconnect
  the graph, leaves the empty set or a single
  vertex..
• a
• d
  b
• c
• This graph is 2-edge connected red edges
• and 1-edge neighbor connected blue edge

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Black-footed ferret data
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Ferret data