Habitat Analysis and
Conservation Management
Landscape Graphs
Connectivity Parameters
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
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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 management’s optimal
responses to these changes.
Landscape Configurations
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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
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White- March – June,
Red - July – September
Example of a Habitat Network
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Metrics
 Clustering Coefficient – the average fraction of the vertex’s
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
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