T-LoCoH: A Spatiotemporal Method for Analyzing Movement Data EVERYTHING DISPERSES TO MIAMI December 14 - December 16, 2012 Andy Lyons, Wendy Turner & Wayne Getz UC Berkeley, 2012

Outline and Take Home Message Quick review of methods to analyze movement and construct home range and utilization distributions Discuss spatio-temporal issues Present T-LoCoH as an extension of LoCoH methods to include time Worton 1989

These data are more interesting than mere step-size, turning-angle and CRW statistics or home range boundaries and UD plots

Classic Home Range Methods Aggregate Summaries

Classic Home Range Methods Aggregate Summaries Minimum Convex Polygon easy to understand and compute point peeling algorithms can produce UDs sensitive to outliers and point geometry

Classic Home Range Methods Aggregate Summaries Alpha Hull similar to MCP, can model concave geometries

Classic Home Range Methods Local Probability Functions Kernel Density Estimator most common HR estimator widely implemented impose a Gaussian or compact kernels “h” parameter controls width of kernels  smoothing output: raster surface

Classic Home Range Methods Local Probability Functions Kernel Density Estimator most common HR estimator widely implemented impose a Gaussian or compact kernels “h” parameter controls width of kernels  smoothing output: raster surface

Classic Home Range Methods Local Probability Functions Kernel Density Estimator most common HR estimator widely implemented impose a Gaussian or compact kernels “h” parameter controls width of kernels  smoothing output: raster surface

Home Range Hull Methods Local Polygons Characteristic Hull create Delaunay triangles start peeling them off, longest perimeter first pause when N% of points are enclosed, call that the N% utilization distribution output: polygons

Hull Home Range Methods Local Convex Hulls Local Convex Hull (LoCoH) create a little MCP or hull around each point sort those smallest to largest start merging pause when N% of points are enclosed, call that the N% utilization distribution output: polygons

New Home Range Methods Local Probability Functions Brownian Bridge

New Home Range Methods Local Probability Functions Brownian Bridge output: raster probability surface Recent Improvements

Trade-offs among methods hugs the data, defines boundaries smoothed: obscures boundaries omission errors commission errors tailored parameters ‘automatic’

LoCoH =Local Convex Hull LoCoH Algorithm Loop through points For each point, calculate distances to nearby points Pick a set of nearest neighbors k-method r-method a-method Draw local hulls around all points Sort hulls in a meaningful way Start merging hulls When merged hull encompasses x% of points, pause and call that an isopleth Visualize & analyze

LoCoH =Local Convex Hull LoCoH Algorithm Loop through points For each point, calculate distances to nearby points Pick a set of nearest neighbors k-method r-method a-method Draw local hulls around all points Sort hulls in a meaningful way Start merging hulls When merged hull encompasses x% of points, pause and call that an isopleth Visualize & analyze

LoCoH =Local Convex Hull LoCoH Algorithm Loop through points For each point, calculate distances to nearby points Pick a set of nearest neighbors k-method r-method a-method Draw local hulls around all points Sort hulls in a meaningful way Start merging hulls When merged hull encompasses x% of points, pause and call that an isopleth Visualize & analyze 3 4 1 2 5 6 7

LoCoH =Local Convex Hull LoCoH Algorithm Loop through points For each point, calculate distances to nearby points Pick a set of nearest neighbors k-method r-method a-method Draw local hulls around all points Sort hulls in a meaningful way Start merging hulls When merged hull encompasses x% of points, pause and call that an isopleth Visualize & analyze

LoCoH =Local Convex Hull LoCoH Algorithm Loop through points For each point, calculate distances to nearby points Pick a set of nearest neighbors k-method r-method a-method Draw local hulls around all points Sort hulls in a meaningful way Start merging hulls When merged hull encompasses x% of points, pause and call that an isopleth Visualize & analyze Σd ≤ a

LoCoH =Local Convex Hull LoCoH Algorithm Loop through points For each point, calculate distances to nearby points Pick a set of nearest neighbors k-method r-method a-method Draw local hulls around all points Sort hulls in a meaningful way Start merging hulls When merged hull encompasses x% of points, pause and call that an isopleth Visualize & analyze

LoCoH =Local Convex Hull LoCoH Algorithm Loop through points For each point, calculate distances to nearby points Pick a set of nearest neighbors k-method r-method a-method Draw local hulls around all points Sort hulls in a meaningful way Start merging hulls When merged hull encompasses x% of points, pause and call that an isopleth Visualize & analyze 7. 5. 8. 3. 6. 2. 4. 1.

LoCoH =Local Convex Hull LoCoH Algorithm Loop through points For each point, calculate distances to nearby points Pick a set of nearest neighbors k-method r-method a-method Draw local hulls around all points Sort hulls in a meaningful way Start merging hulls When merged hull encompasses x% of points, pause and call that an isopleth Visualize & analyze

LoCoH =Local Convex Hull LoCoH Algorithm Loop through points For each point, calculate distances to nearby points Pick a set of nearest neighbors k-method r-method a-method Draw local hulls around all points Sort hulls in a meaningful way Start merging hulls When merged hull encompasses x% of points, pause and call that an isopleth Visualize & analyze 20th% isopleth

LoCoH Algorithm Loop through points For each point, calculate distances to nearby points Pick a set of nearest neighbors k-method r-method a-method Draw local hulls around all points Sort hulls in a meaningful way Start merging hulls When merged hull encompasses x% of points, pause and call that an isopleth Visualize & analyze

T-LoCoH Approach T-LoCoH Algorithm Loop through points For each point, calculate distances to nearby points Pick a set of nearest neighbors k-method r-method a-method Draw local hulls around all points Sort hulls in a meaningful way Start merging hulls When merged hull encompasses x% of points, pause and call that an isopleth Visualize & analyze Euclidean Distance “Time Scaled Distance” 7. 5. 8. 3. 6. 2. Sort hulls by a time-dependent metric: elongation, revisitation index, duration / intensity of use 4. 1. New visualization tools

Time Scaled Distance Want the “distance” to reflect both how far apart two points are in space as well as time We transform the time difference between two points to spatial units by asking: how far would the animal have traveled had it been moving at maximum speed in same direction? This time-distance becomes a third axis in “space time” x y time

Time-Scaled Distance (TSD) space-selection s=0 time-selection s ≈ 1

points from other visits to this area

Sorting Hulls in a Meaningful Way: Time-Use revisitation rate duration or intensity of use revisitation index duration of use important seasonal resources year - long infrequently used resources

Sorting Hulls in a Meaningful Way: Identify Canonical Activity Modes

Sorting Hulls in a Meaningful Way: Elongation eccentricity of bounding ellipsoid perimeter : area ratio

Sorting Hulls in a Meaningful Way: Hull Metrics Density area number of nearest neighbors number of enclosed points Time Use revisitation rates mean visit duration Time (parent point) hour of day month date Elongation / Movement Phase eccentricity of ellipsoid bounding the hull perimeter / area ratio average speed of nearest neighbors standard deviation of nearest neighbor speeds Ancillary Variables ancillary variables associated with hulls proportion of enclosed points that have property X

Simulated Data 1. spatially overlapping but temporally separate Single virtual animal moves between 9 patches constant step size and sampling interval unbounded random walk within each patch for a predetermined # steps directional movement to the next patch duration and frequency of patch use varied 1. spatially overlapping but temporally separate resource edges 2. gradient of directionality 3. varied frequency of use Patch Visits Total Pts p1 2 x 120 240 p2 4 x 60 p3 1 x 240 p4 6 x 40 p5 12 x 20 p6 p7 p8 p9

T-LoCoH General Workflow Select a value of s based on the time scale of interest Create density isopleths that do a “good job” representing the home range e.g., no spurious crossovers Compute hull metrics for elongation and/or time- use Visualize isopleths and/or hull points Interpret and/or plot against environmental variables

With Time k = 3 Without Time s = 0.1 s = 0 Isopleth level indicates the proportion of total points enclosed along a gradient of point density (red highest density, light blue lowest).

With Time k = 7 Without Time s = 0.1 s = 0 Isopleth level indicates the proportion of total points enclosed along a gradient of point density (red highest density, light blue lowest).

With Time k = 15 Without Time s = 0.1 s = 0 Isopleth level indicates the proportion of total points enclosed along a gradient of point density (red highest density, light blue lowest).

Simulated Data: Density Isopleths Hulls sorted from most number of points per unit area (red) to least (blue)

Simulated Data: Elongation Isopleths Hulls sorted by eccentricity of bounding ellipse (left) or perimeter/area ratio (right) from most (red) to least (blue) elongated.

Simulated Data: Revisitation Isopleths Hulls sorted by number of separate visits (inter-visit gap = 24 time steps)

Simulated Data: Duration Isopleths Hulls sorted by mean number of locations per visit (inter-visit gap = 24 time steps).

Etosha National Park, Namibia

Female springbok

Female springbok: density isopleths Text

Female Springbok: Hull revisitation rate and duration over time

Female Springbok: Directional Routes Map of directional routes formed by identifying hulls with a perimeter area ratio value in the top 15%. Blue dots are known water points.

Hour of day Hour of day vs Avg. Speed 1 speed hour 24 Hour of day vs Avg. Speed

Territorial male

a = 3700

Male Springbok: Hulls in Time-Use Space

Male Springbok: Hulls in Time-Use Space

Next step to include Environmental Variables

Association Hull Metrics count of spatially overlapping hulls for two individuals number of separate visits in overlapping hulls time lag of overlapping hulls

T-LoCoH for R http://locoh.cnr.berkeley.edu/tlocoh Plotting hull and isopleth maps pair-wise hull metric scatterplots hull-scatter plots support for shapefiles & imagery Export formats R format csv shapefiles Pre-processing remove bursts sub-sample animations Feature Creation hulls isopleths directional routes Hull metric creation time use elongation http://locoh.cnr.berkeley.edu/tlocoh

Acknowledgements http://locoh.cnr.berkeley.edu/tlocoh Andy Lyons Scott Fortmann-Roe Wendy Turner Chris Wilmers George Wittemyer Sadie Ryan Werner Kilian Namibian Ministry of Environment and Tourism staff of the Etosha Ecological Institute Berkeley Initiative in Global Change Biology NIH Grant GM83863 http://locoh.cnr.berkeley.edu/tlocoh