Spatial Graphs for Assessing Woodland Caribou Habitat Connectivity CIT EGSA-Timber Status Report July 23 2003 Dan O’Brien, MSc, RPBio (Cortex Consultants Inc.) Micheline Manseau, PhD (Parks Canada) Andrew Fall, PhD (Gowlland Technologies Ltd.) Marie-Josée Fortin, PhD (Dept. Zoology, University of Toronto) Chase Habitat Supply Modelling Workshop November 23 – 25, 2004 Connectivity of woodland caribou

Presentation Outline Using spatial graphs to measure structural connectivity of a landscape Application An assessment of Woodland caribou (Rangifer tarandus caribou) habitat connectivity in Manitoba Methods for detecting an association between distribution of caribou and the structural connectivity of their range

Habitat Connectivity Connectivity is the degree to which landscape facilitates or impedes dispersal among resource patches (Taylor et al. 1993) Structural connectivity linkage of resource patches by physical adjacency Functional connectivity linkage of resource patches by processes that depend on dispersal and movement behaviour of the species

Habitat Connectivity Approaches to analyzing connectivity fall on a continuum STRUCTURAL FUNCTIONAL INTRA-PATCH METRICS e.g., patch cohesion INTERPATCH METRICS e.g., nearest neighbour distance SPATIAL GRAPHS INDIVIDUAL BASED DISPERSAL MODELS

Spatial Graphs for measuring landscape connectivity CIT EGSA-Timber Status Report July 23 2003 Nearest Neighbor links Shortest links connecting patches, such that each patch forms at least one link Nearest Neighbor for a patch, is simply its closest patch Nearest Neighbor Graph: All patches linked to nearest neighbor – each patch has at least one link Minimum Spanning Tree: Triangulation, whererby all patches are linked into a single component (Delaunay Triangulation) – Simply add links of increasing weight/ length, until a single connected component. - Includes all nearest neighbor links, and some additional ones to create a single component - Shows the underlying “Backbone of connectivity” Minimum Planar Graph: All patches are linked together Properties of MPG - at least one link between each pair of patches – links are direct (cannot cross other other links or other patches - Graph is minimum weight Graph is spatial because links connect between closest perimeter cell (I.e., perimeter links), rather than patch centroids (or points).

Spatial Graphs for measuring landscape connectivity CIT EGSA-Timber Status Report July 23 2003 Minimum Spanning Tree The minimum set of links such that each patch is connected into a single component There can be no other link with greater length linked to a patch “Backbone” of connectivity Nearest Neighbor for a patch, is simply its closest patch Nearest Neighbor Graph: All patches linked to nearest neighbor – each patch has at least one link Minimum Spanning Tree: Triangulation, whererby all patches are linked into a single component (Delaunay Triangulation) – Simply add links of increasing weight/ length, until a single connected component. - Includes all nearest neighbor links, and some additional ones to create a single component - Shows the underlying “Backbone of connectivity” Minimum Planar Graph: All patches are linked together Properties of MPG - at least one link between each pair of patches – links are direct (cannot cross other other links or other patches - Graph is minimum weight Graph is spatial because links connect between closest perimeter cell (I.e., perimeter links), rather than patch centroids (or points).

Spatial Graphs for measuring landscape connectivity CIT EGSA-Timber Status Report July 23 2003 Minimum Planar Graph (MPG) At least one link between each pair of patches, No link can cross any another link All links are shortest path between pairs of patches Nearest Neighbor for a patch, is simply its closest patch Nearest Neighbor Graph: All patches linked to nearest neighbor – each patch has at least one link Minimum Spanning Tree: Triangulation, whererby all patches are linked into a single component (Delaunay Triangulation) – Simply add links of increasing weight/ length, until a single connected component. - Includes all nearest neighbor links, and some additional ones to create a single component - Shows the underlying “Backbone of connectivity” Minimum Planar Graph: All patches are linked together Properties of MPG - at least one link between each pair of patches – links are direct (cannot cross other other links or other patches - Graph is minimum weight Graph is spatial because links connect between closest perimeter cell (I.e., perimeter links), rather than patch centroids (or points).

Spatial Graphs for measuring landscape connectivity CIT EGSA-Timber Status Report July 23 2003 The MPG is a Triangulation of Patches Linked patches form a Delauney Triangulation The dual is the Voronoi surface Voronoi boundaries are equidistant from all patches Each point in Voronoi polygon is closest to the interior patch than any other Nearest Neighbor for a patch, is simply its closest patch Nearest Neighbor Graph: All patches linked to nearest neighbor – each patch has at least one link Minimum Spanning Tree: Triangulation, whererby all patches are linked into a single component (Delaunay Triangulation) – Simply add links of increasing weight/ length, until a single connected component. - Includes all nearest neighbor links, and some additional ones to create a single component - Shows the underlying “Backbone of connectivity” Minimum Planar Graph: All patches are linked together Properties of MPG - at least one link between each pair of patches – links are direct (cannot cross other other links or other patches - Graph is minimum weight Graph is spatial because links connect between closest perimeter cell (I.e., perimeter links), rather than patch centroids (or points).

Forming links along a cost surface CIT EGSA-Timber Status Report July 23 2003 Patches are linked along the least-cost (accumulated cost) paths Links represents biological characteristics such as dispersal ability within and between patches within the matrix Nearest Neighbor for a patch, is simply its closest patch Nearest Neighbor Graph: All patches linked to nearest neighbor – each patch has at least one link Minimum Spanning Tree: Triangulation, whererby all patches are linked into a single component (Delaunay Triangulation) – Simply add links of increasing weight/ length, until a single connected component. - Includes all nearest neighbor links, and some additional ones to create a single component - Shows the underlying “Backbone of connectivity” Minimum Planar Graph: All patches are linked together Properties of MPG - at least one link between each pair of patches – links are direct (cannot cross other other links or other patches - Graph is minimum weight Graph is spatial because links connect between closest perimeter cell (I.e., perimeter links), rather than patch centroids (or points).

Application: Woodland Caribou Boreal ecotype is threatened in Canada (COSEWIC 2002) In southern Manitoba woodland caribou are generally sedentary Habitat selection is strongest during winter months Late seral Jack Pine stands and sparsely treed rock outcrops High abundance of terrestrial lichens and low snow cover Photo: Jared Hobbs (www.hobbsphotos.com)

The Owl Lake Woodland Caribou WINTER HOME RANGE GPS telemetry location data from Owl Lake herd (southeast MB) Popn Size: 65 – 75 11 collared adults (9 male, 2 female) Focused on winter points (Nov 1 – March 15)

Habitat Map and Cost Surface Habitat Class Cost (OR-1) JPD/STR 1 TMG/MCU 1.0077 MCL/IMU 1.7339 YNG/WL 3.5396 BURN 3.3029 WATER 3.5952

Graph Extraction HIGH QUALITY PATCHES LEAST COST LINKS

Graph Thresholding

Graph Thresholding

Graph Thresholding

Graph Thresholding At each threshold compute a landscape level metric, Expected Cluster Size (ECS) Expected Cluster Size: mean size of a cluster for randomly selected habitat cells (area weighted mean cluster size at threshold distance, d)

Graph Thresholding

Are caribou responding to structural connectivity? Point Expected Cluster Size Telemetry points associated with the closest patch At each threshold scale points are assigned the area of the cluster containing the associated patch ECS is then computed from cluster sizes measured for each location point This represents the expected size of a cluster of habitat associated for a randomly selected location point.

Are caribou responding to structural connectivity? Randomization Test Point ECS computed for 100 sets of random points distributed randomly in each habitat type in proportion to selection by caribou Observed Point ECS compared to mean of random point sets Distance thresholds where caribou points were greater than 95% CI, indicate scales at which caribou are more closely associated with highly connected clusters of high quality habitat than if randomly distributed within the home range

Are caribou responding to structural connectivity? Above 1000 cost units, PECS for late winter points is 7,500ha and similar to maximum cluster size Differences greatest at scales between 500 – 1900 cost units

Independent Validation Kississing Herd PATCHES FILTERED TO 25 ha NE of The Pas, MB Historical home range Current winter home range

Are caribou responding to structural connectivity? Between 500 and 4500, PECS for late winter points is ~7,500 ha, but less than Max Cluster Size Greatest differences at scales between 500 – 4500 cost units

Summary Strong association between distribution of caribou and connected clusters of habitat Affinity for clusters ~7500ha, and link thresholds 500 – 2000 cost units. In the Owl Lake herd, caribou associated with clusters near the maximum cluster sizes at these thresholds. Kississing also show strong affinity to larger clusters, but associated with clusters below the max available. In the Kississing range availability of clusters is greater in both sizes and numbers; hence, greater potential for range expansion.

Conclusions Spatial graphs are a useful method for assessing the connectivity of woodland caribou habitat For identifying and mapping core areas of well connected habitat and can quantify how these areas contribute to overall landscape connectivity For identifying scales where associations between caribou and connected habitat are strongest Allows the patch definition to be scaled-up from inventory polygons to connected clusters which incorporate differential matrix quality

Conclusions Increasing matrix quality may improve utilization of existing high quality habitat Facilitate movement between patches (optimal foraging) Maintaining low densities (spacing out as an anti-predator strategy) Supports the idea that definition of critical habitat should include not only abundance but also spatial arrangement of high quality habitat, in addition to the relative quality of the intervening matrix habitat

Acknowledgements Funding from Parks Canada Species at Risk Recovery Action and Education Fund Field support was provided by Manitoba Conservation and Manitoba Hydro Owl Lake GPS telemetry data collected as part of MB Hydro's Research and Development of Animal Borne Technology on Woodland Caribou Project Participating partners: Manitoba Hydro Manitoba Model Forest Ltd. Manitoba Natural Resources Natural Resources Institute of the University of Manitoba TAEM Consultants.