Transcript Wayne Getz

EVERYTHING DISPERSES TO MIAMI
December 14 - December 16, 2012
T-LoCoH:
A Spatiotemporal Method for
Analyzing Movement Data
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
omission errors
tailored parameters
smoothed: obscures boundaries
commission errors
‘automatic’
LoCoH Algorithm
1. 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
1. 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
1. 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
6
5
4
3
2
7
1
LoCoH Algorithm
1. 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
1. 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
d  a
LoCoH Algorithm
1. 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
1. 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
7.
5.
8.
3.
6.
2.
1.
4.
LoCoH Algorithm
1. 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
1. 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
20th% isopleth
LoCoH Algorithm
1. 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 Algorithm
1. 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
Euclidean Distance “Time Scaled Distance”
7.
5.
8.
3.
6.
2.
1.
4.
Sort hulls by a time-dependent metric: elongation,
revisitation index, duration / intensity of use
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:
time
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”
y
x
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
duration of use

important
seasonal
resources
infrequently
used resources
year
- long
resources
revisitation index
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
• Single virtual animal moves
between 9 patches
• constant step size and sampling
interval
• unbounded random walk within
1. spatially overlapping
each patch for a predetermined
but temporally separate
# steps
resource edges
• directional movement
to the
next patch
• duration and frequency
of patch use varied
Patch
Visits
Total Pts
p1
2 x 120
240
p2
4 x 60
240
p3
1 x 240
240
p4
6 x 40
240
p5
12 x 20
240
p6
4 x 60
240
p7
6 x 40
240
p8
4 x 60
240
p9
2 x 120
240
2. gradient of
directionality
3. varied frequency
of use
T-LoCoH General Workflow
1. Select a value of s based on the time scale of
interest
2. Create density isopleths that do a “good job”
representing the home range
e.g., no spurious crossovers
3. Compute hull metrics for elongation and/or timeuse
4. Visualize isopleths and/or hull points
5. 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
speed
1
0
0
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
Pre-processing
 remove bursts
 sub-sample
 animations
 Feature Creation
 hulls
 isopleths
 directional routes
 Hull metric creation
 time use
 elongation

Plotting
 hull and isopleth maps
 pair-wise hull metric
scatterplots
 hull-scatter plots
 support for shapefiles &
imagery
 Export formats
 R format
 csv
 shapefiles

http://locoh.cnr.berkeley.edu/tlocoh
Acknowledgements







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