Evaluating Animal Space Use:

New Developments to Estimate Animal Movements, Home Range, and Habitat Selection

Dr. Jon S. Horne, University of Idaho

Central question:“Where do animals live… and why?”

• Space Use is Non-uniform

• Quantitative Description of Space Use

“Utilization Distribution”

The relative amount of time spent in an area

Biotelemetry • Cannot Monitor Animals Continuously

– Have locations at discrete intervals (e.g., telemetry)

• Describing and Understanding Animal Space Use is Important

• We Want an Estimate of the Utilization Distribution

• Obtain This Estimate Using Discrete Locations

New Developments

1) Objective Method for Choosing Among Home Range Models

2) Improve the Kernel – Likelihood-based smoothing parameter

3) Correct Home Range Models for Observation Bias4) The Brownian Bridge Movement Model 5) Incorporate Other Variables (e.g., habitat, other

organisms) Into Home Range Models

1) Selecting the Best Home Range Model

• How do we choose the best home range model?– Popularity– Evaluate using simulated data

• Shouldn’t we “Let the data speak”?– Information-theoretic model selection

Selecting the Best Model

• Selection Criteria– Akaike’s Information Criteria (AIC)

• Adjusts model likelihood for overfitting

– Likelihood Cross-validation Criteria (CVC)• Evaluates the predictive ability

• Stone (1977) Showed Asymptotic Equivalence

Applying Selection Criteria to Home Range Models

• Can we calculate likelihood?– Yes, if home range models estimate the

utilization distribution– No for minimum convex polygon (MCP)

• New model based on uniform distribution

Ecologically Based Shapesfor Territories (from Covich 1976)

Exponential Power Model

0

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0 2 4 6 8

Location (x)

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c = 1

c = 0.5

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Circular Uniform is a Particular Case3 parameters: location, scale, shape ( c )

Application: Home Range Model Selection

• Used location data from a variety of species

• Evaluated 6 home range models:– Bivariate normal– Exponential power– 2-mode circular normal mix– 2-mode bivariate normal mix– Fixed and adaptive kernels

• Calculated AIC and CVC

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Adaptive kernel 2-mode circular normal mix

2-mode bivariate mix Bivariate normal

Conclusions• AIC or CVC

– No strong arguments favoring one over the other– Must use CVC with kernel models

• No Single Model Was Always Best– Kernels performed quite well

• Goal of Model Selection– Find model closest to truth– “Test” hypotheses

Use model selection to understand home range

New Approaches

1) Develop Objective Method for Choosing Among Home Range Models

2) Improve the Kernel – Likelihood-based smoothing parameter

3) Correct Home Range Models for Observation Bias 4) The Brownian Bridge Movement Model 5) Incorporate Other Variables (e.g., habitat, other

organisms) Into Home Range Models

Influence of smoothing parameter (h) on kernel density

Smoothing parameter (h)

kernels Kernel estimate

Influence of smoothing parameter (h) on kernel density

Previously Recommended for Home Range Estimation

• Fixed Kernel Density– Least Squares Cross-validation (LSCVh)

• Drawbacks to LSCVh– High variablility– Tendency to undersmooth– Multiple minima in the LSCVh function

An Alternative

• Likelihood cross-validation (CVh)• Minimizes Kullback-Leibler Distance

• CVh outperforms LSCVh– Especially at smaller sample sizes (i.e., <~50)– Especially if you enjoy Kullback-Leibler

Influence of Smoothing Parameter

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CVh LSCVh

Beware of Your Home Range Program4 Programs All with LSCVh?

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KERNELHR(Seaman)

HOMERANGE(Carr)My Program(Horne)

AnimalMovement(Hooge)

New Approaches

1) Develop Objective Method for Choosing Among Home Range Models

2) Improve the Kernel – Likelihood-based smoothing parameter

3) Correct Home Range Models for Observation Bias 4) The Brownian Bridge Movement Model 5) Incorporate Other Variables (e.g., habitat, other

organisms) Into Home Range Models

3) Observation Bias of Locations• Home range models traditionally assumed

locations were obtained with equal probability

• Documented Unequal Observation Rates– Mostly for satellite telemetry

– Can be modeled across a study site

• Corrections Based on Probability Sampling– Weight locations by 1/probability of inclusion

Difference between corrected and uncorrected models

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Fixed Kernel Bias

-0.184 - -0.145

-0.145 - -0.106

-0.106 - -0.067

-0.067 - -0.028

-0.028 - 0.011

0.011 - 0.051

0.051 - 0.09

0.09 - 0.129

0.129 - 0.168

2-mode Bivariate Mix Bias

-0.142 - -0.105

-0.105 - -0.068

-0.068 - -0.031

-0.031 - 0.006

0.006 - 0.043

0.043 - 0.08

0.08 - 0.118

0.118 - 0.155

0.155 - 0.192

1.34 - 1.46#

1.46 - 1.58#

1.58 - 1.76#

1.76 - 1.98#

1.98 - 2.34#

Location Weights

Bivariate Normal Bias

-0.025 - -0.011

-0.011 - 0.003

0.003 - 0.017

0.017 - 0.031

0.031 - 0.044

0.044 - 0.058

0.058 - 0.072

0.072 - 0.086

0.086 - 0.1

Bivariate normal

2-mode BVN Mix

Locationweights

Fixed Kernel

Underestimate ~18%

Overestimate ~19%

Contributors to Magnitude of Bias

• Magnitude of differences in observation rates

• Aggregation of observation rates

• Home range model

• Sample size

• Intentional Differences (i.e., sampling design) – Diurnal vs. nocturnal locations

New Approaches

1) Develop Objective Method for Choosing Among Home Range Models

2) Improve the Kernel – Likelihood-based smoothing parameter

3) Correct Home Range Models for Observation Bias 4) The Brownian Bridge Movement Model5) Incorporate Other Variables (e.g., habitat, other

organisms) Into Home Range Models

0.5 Kilometer0.5 Kilometer

From: Stokes, D. L., P. D. Boersma, and L. S. Davis. 1998. Satellite tracking of Megellanic Penguin migration. Condor 100:376-381.

Probabilistic model of the movement path?

“Brownian Bridge”

Brownian Bridge Movement Model

• Can we model the probability of occurrence?

• Given:– Known locations– Time interval between locations

2-location BrownianBridge

Shape dependent on:

1. Distance2. Time interval3. Animal mobility

Brownian Bridge Applications

• Estimate movement paths– Home range– Migration routes– Resource utilization/selection

Kilometer

• Black bear

• Satellite telemetry

• 1470 locations

• 20-min. intervals

• ~1 month

Home range of a male black bear

Brownian bridge

Probability

low

high

Fixed Kernel

Probability

low

high

Advantages of Brownian Bridge Home Range

• ASSUMES serially correlated data

• Models the movement path

• Location error explicitly incorporated

Caribou Migration

• Fall migration in southwestern Alaska

• 11 female caribou with GPS collars

• Locations every 7 hours

Probability

Low

High

Fine-scale Resource Selection

• Why did the bear cross the road…

where it did?

Probability of crossing

Probability of Crossing

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 0.5 1 1.5 2 2.5 3 3.5

Road kilometer

Prob

abil

ity

New Approaches

1) Develop Objective Method for Choosing Among Home Range Models

2) Improve the Kernel – Likelihood-based smoothing parameter

3) Correct Home Range Models for Sampling Bias 4) The Brownian Bridge Movement Model5) Incorporate Other Variables (e.g., habitat, other

organisms) Into Home Range Models

Ecological Factors Affecting Space Use

– Site Fidelity (i.e., home range)

– Habitat Selection

– Interrelations with Other Organisms

5) A Synoptic Model of Space Use

• Space Use Generally Estimated Using Discrete Locations (x-y coordinates)

• Can we get a better model and learn more by incorporating additional variables?

– Distribution of…• Important resources

• Avoided areas

• Other animals

Synoptic Approach… Multiple Competing Models

Initial/Null Model(site fidelity)

Habitat Inter/Intraspecific Relationships

Model Assessment

“Best” Model(s)

Prediction and Inference

Example: Space Use of Male White Rhinos

• Location Data: 3 Adult Males, Matobo National Park, Zimbabwe

Candidate Models… Covariates

• Park boundary

• 3 Environmental Covariates H(x)

0 2 Kilometers

Percent slopeGrassland/openwoodland Female Density

Candidate Models… Hypotheses

• Null model: no environmental covariates– Exponential Power + Park boundary

• Habitat model:– Null + open covertype + percent slope

• Social model:– Null + female density

• Combined model:– Null + habitat + social

AIC Model Selection

Best Model

slope

0 2 Kilometers

OPEN femaleslope

Interpretation of Best Model

• Best Model Can Be Used to:– Estimate space use– Define home range– Determine factors affecting space use– Infer importance of these factors

• Answers not only “Where?” but “Why?”

M05 was 3 times more likely to be in an area: 2% slope, 0.5 relative female density, and open covertype10% slope, 0.7 relative female density, and not open

To Summarize

• Information theoretic criteria for choosing among home range models

• Use likelihood cross-validation choice of smoothing parameter

• Home range models can be corrected for observation bias

• Brownian bridge for serially correlated data• Synoptic models answer “where?” and “why?”

Publications

Horne, J. S. and E. O. Garton. 2006. Likelihood Cross-validation vs. Least SquaresCross-validation for Choosing the Smoothing Parameter in Kernel Home Range Analysis. Journal of Wildlife Management 70:641-648

Horne, J. S., E. O. Garton, and K. A. Sager. 2007. Correcting Home Range ModelsFor Sample Bias. Journal of Wildlife Management 71:996-1001

Horne, J. S. and E. O. Garton. 2006. Selecting the Best Home Range Model: AnInformation Theoretic Approach. Ecology 87:1146-1152

Horne, J. S., E. O. Garton, and J. L. Rachlow. 2008. A Synoptic Model of AnimalSpace Use: Simultaneous Analysis of Home Range, Habitat Selection, and Inter/Intra-specific Relationships. Ecological Modelling 214:338-348.

Horne, J. S., E. O. Garton, S. M. Krone, and J. S. Lewis. 2008. Analyzing AnimalMovements using Brownian Bridges. Ecology 88:2351-2363