t-locoh: a spatiotemporal method for analyzing movement data andy lyons, wendy turner & wayne...

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