Habitat Analysis and Conservation Management Landscape Graphs Connectivity

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. 2

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. 3

Landscape Configurations Necklace Spider Cell Satellite or Pendant 4

More Landscape Configurations Cross Mesh or grid Rigid polygon 5

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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 7

Habitat Networks Habitat patches are vertices in the Habitat Network; Habitat patches are connected by dispersing 8 individuals and these connections are the edges – a set threshold distance apart. Useful graph theory terms: Ø Degree = number of patches (vertices) connected to a patch Ø Hub is a high degree vertex Ø Path is a route from one patch to another Ø Distance = D(x, y) = length of shortest path between x and y. Ø Component - a connected piece that is disconnected from the rest.

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Travels of pronged horn antelope : Blue - December – March 10 White- March – June, Red - July – September

Example of a Habitat Network 11

Metrics Clustering Coefficient – the average fraction of the 12 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 compartmentalizationhighly 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

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 13

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 14

Black-footed ferret data 15

Ferret data 16