Landscape GraphsConnectivity Parameters

Habitat Analysis and Conservation Management

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

management’s 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

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 patchHub is a high degree vertexPath is a route from one patch to anotherDistance = 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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MetricsClustering 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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ConnectivityA 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, band 1 neighbor connected – vertex e

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Edge ConnectivityA 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 edgesand 1-edge neighbor connected – blue edge

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Black-footed ferret data

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Ferret data

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