1. 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

2. 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

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

4. Classic Home Range Methods Aggregate Summaries

5. 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

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

7. 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

8. 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

9. 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

10. 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

11. 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

12. New Home Range Methods Local Probability Functions
Brownian Bridge

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

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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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.

22. 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

23. 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

24. 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

25. 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

26. 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

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

30. points from
other visits to this area

31. 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

32. Sorting Hulls in a Meaningful Way: Identify Canonical Activity Modes

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

34. 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

35. 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

36. 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

37. 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).

38. 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).

39. 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).

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

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

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

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

44. Etosha National Park, Namibia

45. Female springbok

46. Female springbok: density isopleths
Text

47. Female Springbok: Hull revisitation rate and duration over time

48. 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.

49. Hour of day Hour of day vs Avg. Speed1
speed
hour 24
Hour of day vs
Avg. Speed

50. Territorial male

51. a = 3700

52. Male Springbok: Hulls in Time-Use Space

53. Male Springbok: Hulls in Time-Use Space

55. Next step to include Environmental Variables

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

57. 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

58. 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