T-LoCoH: A Spatiotemporal Method for Analyzing Movement Data Andy Lyons, Wendy Turner & Wayne Getz...
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Transcript of T-LoCoH: A Spatiotemporal Method for Analyzing Movement Data Andy Lyons, Wendy Turner & Wayne Getz...
T-LoCoH: T-LoCoH: A Spatiotemporal Method A Spatiotemporal Method for Analyzing Movement for Analyzing Movement
DataDataAndy Lyons, Wendy Turner & Wayne GetzAndy Lyons, Wendy Turner & Wayne Getz
UC Berkeley, 2012UC Berkeley, 2012
EVERYTHING DISPERSES TO MIAMIDecember 14 - December 16, 2012
Outline and Take Home Outline and Take Home MessageMessage
Quick review of Quick review of methods to analyze methods to analyze movement and movement and construct home range construct home range and utilization and utilization distributionsdistributions
Discuss spatio-Discuss spatio-temporal issuestemporal issues
Present T-LoCoH as an Present T-LoCoH as an extension of LoCoH extension of LoCoH methods to include methods to include time time
Worton 1989
These These data are data are more more interestiinteresting than ng than mere mere step-step-size, size, turning-turning-angle and angle and CRW CRW statisticstatistics or home s or home range range boundarieboundaries and UD s and UD plotsplots
Classic Home Range MethodsClassic Home Range MethodsAggregate SummariesAggregate Summaries
Minimum Minimum Convex Convex PolygonPolygon easy to easy to understand and understand and computecompute
point peeling point peeling algorithms can algorithms can produce UDs produce UDs
sensitive to sensitive to outliers and outliers and point geometrypoint geometry
Classic Home Range MethodsClassic Home Range MethodsAggregate SummariesAggregate Summaries
Alpha HullAlpha Hull similar to similar to MCP, can model MCP, can model concave concave geometriesgeometries
Classic Home Range MethodsClassic Home Range MethodsAggregate SummariesAggregate Summaries
Kernel Density Kernel Density EstimatorEstimator
most common HR most common HR estimatorestimator
widely implementedwidely implemented impose a Gaussian impose a Gaussian or compact kernelsor compact kernels
““hh ”” parameter parameter controls width of controls width of kernels kernels smoothingsmoothing
output: raster output: raster surfacesurface
Classic Home Range MethodsClassic Home Range MethodsLocal Probability FunctionsLocal Probability Functions
Kernel Density Kernel Density EstimatorEstimator
most common HR most common HR estimatorestimator
widely implementedwidely implemented impose a Gaussian impose a Gaussian or compact kernelsor compact kernels
““hh ”” parameter parameter controls width of controls width of kernels kernels smoothingsmoothing
output: raster output: raster surfacesurface
Classic Home Range MethodsClassic Home Range MethodsLocal Probability FunctionsLocal Probability Functions
Kernel Density Kernel Density EstimatorEstimator
most common HR most common HR estimatorestimator
widely implementedwidely implemented impose a Gaussian impose a Gaussian or compact kernelsor compact kernels
““hh ”” parameter parameter controls width of controls width of kernels kernels smoothingsmoothing
output: raster output: raster surfacesurface
Classic Home Range MethodsClassic Home Range MethodsLocal Probability FunctionsLocal Probability Functions
CharacteristCharacteristic Hullic Hull
create Delaunay create Delaunay trianglestriangles
start peeling start peeling them off, them off, longest longest perimeter firstperimeter first
pause when N% of pause when N% of points are points are enclosed, call enclosed, call that the N% that the N% utilization utilization distributiondistribution
output: polygonsoutput: polygons
Home Range Hull Home Range Hull MethodsMethods
Local PolygonsLocal Polygons
Local Convex Hull Local Convex Hull (LoCoH)(LoCoH)
create a little create a little MCP or hull around MCP or hull around each pointeach point
sort those sort those smallest to smallest to largestlargest
start mergingstart merging pause when N% of pause when N% of points are points are enclosed, call enclosed, call that the N% that the N% utilization utilization distributiondistribution
output: polygonsoutput: polygons
Hull Home Range Hull Home Range MethodsMethods
Local Convex HullsLocal Convex Hulls
Brownian BridgeBrownian Bridge
New Home Range MethodsNew Home Range MethodsLocal Probability FunctionsLocal Probability Functions
Brownian BridgeBrownian Bridge output: raster output: raster probability surfaceprobability surface
RecentRecentImprovementsImprovements
New Home Range MethodsNew Home Range MethodsLocal Probability FunctionsLocal Probability Functions
omission errorsomission errors commission errorscommission errors
hugs the data, defines boundarieshugs the data, defines boundariessmoothed: obscures smoothed: obscures boundariesboundaries
‘‘automaticautomatic’’tailored parameterstailored parameters
Trade-offs among methodsTrade-offs among methods
LoCoH Algorithm1. 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 LoCoH =Local Convex HullHull
LoCoH Algorithm1. 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 LoCoH =Local Convex HullHull
3
4
12
5
6
7
LoCoH Algorithm1. 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 LoCoH =Local Convex HullHull
LoCoH Algorithm1. 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 LoCoH =Local Convex HullHull
Σd ≤a
LoCoH Algorithm1. 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 LoCoH =Local Convex HullHull
LoCoH Algorithm1. 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 LoCoH =Local Convex HullHull
7.
3.
2.
4.
8.
5.
6.
1.
LoCoH Algorithm1. 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 LoCoH =Local Convex HullHull
LoCoH Algorithm1. 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 LoCoH =Local Convex HullHull
LoCoH Algorithm1. 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 =Local Convex LoCoH =Local Convex HullHull
LoCoH Algorithm1. 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.
3.
2.
4.
8.
5.
6.
1.
T-LoCoH Algorithm1. 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”
Sort hulls by a time-dependent metric: elongation, revisitation index, duration / intensity of use
New visualization tools
T-LoCoH ApproachT-LoCoH Approach
Time Scaled DistanceTime Scaled Distance
Want the Want the ““distancedistance”” to reflect both to reflect both how far apart two points are in space how far apart two points are in space as well as timeas well as time
We transform the time difference We transform the time difference between two points to spatial between two points to spatial units by asking:units by asking:
how far would the animal have how far would the animal have traveled had it been moving at traveled had it been moving at
maximum speed in same direction?maximum speed in same direction?
This time-distance becomes This time-distance becomes a third axis in a third axis in ““space timespace time””
x
y
time
Time-Scaled Distance (TSD)Time-Scaled Distance (TSD)
space-selections=0
time-selections ≈ 1
points fromother visits to this area
Sorting Hulls in a Sorting Hulls in a Meaningful Way: Time-Meaningful Way: Time-
UseUse revisitation raterevisitation rate duration or intensity duration or intensity of useof use
revisitation index
dura
tion
of u
se
importantseasonal resources
year- longresources
infrequentlyused resources
Sorting Hulls in a Sorting Hulls in a Meaningful Way:Meaningful Way:
Identify Canonical Identify Canonical Activity ModesActivity Modes
Sorting Hulls in a Sorting Hulls in a Meaningful Way: Meaningful Way:
ElongationElongation eccentricity of bounding eccentricity of bounding ellipsoidellipsoid
perimeter : area ratioperimeter : area ratio
Sorting Hulls in a Sorting Hulls in a Meaningful Way: Hull Meaningful Way: Hull
MetricsMetrics DensityDensityareaareanumber of nearest number of nearest neighborsneighbors
number of enclosed number of enclosed pointspoints
Time UseTime Userevisitation ratesrevisitation rates mean visit durationmean visit duration
TimeTime (parent point)(parent point)hour of dayhour of daymonthmonth datedate
Elongation / Movement Elongation / Movement PhasePhaseeccentricityeccentricity of of ellipsoid bounding the ellipsoid bounding the hullhullperimeter / area ratioperimeter / area ratioaverage speedaverage speed of of nearest neighborsnearest neighborsstandard deviationstandard deviation of of nearest neighbor speedsnearest neighbor speeds
Ancillary VariablesAncillary Variablesancillary variables ancillary variables associated with hullsassociated with hullsproportion of enclosed proportion of enclosed points that have points that have property Xproperty X
Simulated Data• 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 frequencyof patch use varied
PatchPatch VisitsVisits Total PtsTotal Pts
p1p1 2 x 1202 x 120 240240
p2p2 4 x 604 x 60 240240
p3p3 1 x 2401 x 240 240240
p4p4 6 x 406 x 40 240240
p5p5 12 x 2012 x 20 240240
p6p6 4 x 604 x 60 240240
p7p7 6 x 406 x 40 240240
p8p8 4 x 604 x 60 240240
p9p9 2 x 1202 x 120 240240
1. spatially overlappingbut temporally separate
resource edges
2. gradient ofdirectionality
3. varied frequencyof use
T-LoCoH General WorkflowT-LoCoH General Workflow
1.1.Select a value of Select a value of ss based on the based on the time scale of interesttime scale of interest
2.2.Create density isopleths that do a Create density isopleths that do a ““good jobgood job”” representing the home representing the home rangerangee.g., no spurious crossoverse.g., no spurious crossovers
3.3.Compute hull metrics for elongation Compute hull metrics for elongation and/or time-useand/or time-use
4.4.Visualize isopleths and/or hull Visualize isopleths and/or hull pointspoints
5.5.Interpret and/or plot against Interpret and/or plot against environmental variablesenvironmental variables
s = 0.1 s = 0
k = 3With Time Without Time
Isopleth level indicates the proportion of total points enclosed along a gradient of point density
(red highest density, light blue lowest).
s = 0.1 s = 0Isopleth level indicates the proportion of total points enclosed along a gradient of point density
(red highest density, light blue lowest).
k = 7With Time Without Time
s = 0.1 s = 0Isopleth level indicates the proportion of total points enclosed along a gradient of point density
(red highest density, light blue lowest).
k = 15With Time Without Time
Simulated Data:Simulated Data:
Density IsoplethsDensity Isopleths
Hulls sorted from most number of points per unit area (red) to least (blue)
Simulated Data:Simulated Data:
Elongation IsoplethsElongation Isopleths
Hulls sorted by eccentricity of bounding ellipse (left) or perimeter/area ratio (right) from most (red) to least (blue) elongated.
Simulated Data:Simulated Data:
Revisitation IsoplethsRevisitation Isopleths
Hulls sorted by number of separate visits (inter-visit gap = 24 time steps)
Simulated Data:Simulated Data:
Duration IsoplethsDuration Isopleths
Hulls sorted by mean number of locations per visit (inter-visit gap = 24 time steps).
Etosha Etosha National National Park,Park,NamibiaNamibia
Female Female springbokspringbok
Text
Female springbok: density isopleths
Female Springbok:Female Springbok:
Hull revisitation rate and Hull revisitation rate and duration over timeduration over time
Female Springbok: Female Springbok: Directional Directional RoutesRoutes
Map of directional routes formed by identifying hulls with a perimeter area ratio value in the top 15%. Blue dots are known water points.
hour0 240
1
speed
Hour of dayvs
Avg. Speed
Hour of day
TerritoTerritorial rial malemale
a = 3700
Male Springbok: Male Springbok: Hulls in Time-Hulls in Time-Use SpaceUse Space
Male Springbok: Male Springbok: Hulls in Time-Hulls in Time-Use SpaceUse Space
Next step to include Next step to include Environmental VariablesEnvironmental Variables
Association Association
Hull Hull MetricsMetrics
count of count of spatially spatially overlapping overlapping hulls for two hulls for two individualsindividuals
number of number of separate separate visits in visits in overlapping overlapping hullshulls
time lag of time lag of overlapping overlapping hullshulls
T-LoCoH for RT-LoCoH for R Pre-processingPre-processing
remove burstsremove bursts sub-samplesub-sample animationsanimations
Feature CreationFeature Creation hulls hulls isoplethsisopleths directional directional routesroutes
Hull metric Hull metric creationcreation time usetime use elongationelongation
PlottingPlotting hull and isopleth hull and isopleth mapsmaps
pair-wise hull pair-wise hull metric metric scatterplotsscatterplots
hull-scatter hull-scatter plotsplots
support for support for shapefiles & shapefiles & imageryimagery
Export formatsExport formats R formatR format csvcsv shapefilesshapefiles
http://locoh.cnr.berkeley.edu/tlocoh
AcknowledgementsAcknowledgements
Andy LyonsAndy Lyons Scott Fortmann-Scott Fortmann-RoeRoe
Wendy TurnerWendy Turner Chris WilmersChris Wilmers George WittemyerGeorge Wittemyer Sadie RyanSadie Ryan Werner Kilian Werner Kilian
Namibian Ministry Namibian Ministry of Environment of Environment and Tourismand Tourism
staff of the staff of the Etosha Ecological Etosha Ecological Institute Institute
Berkeley Berkeley Initiative in Initiative in Global Change Global Change Biology Biology
NIH Grant GM83863 NIH Grant GM83863 http://locoh.cnr.berkeley.edu/tlocoh