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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0.1
0.15
0.2
0.25
0.3
0.35
0 2 4 6 8
Location (x)
Pro
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y d
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c = 1
c = 0.5
c = 0.1
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