Miles Hemstrom
Elk Habitat Use Modeling
for the Blue Mountains
Ryan Nielson
Miles Hemstrom
Topics
• Analysis of Habitat Use
• Blue Mts. Modeling
Objectives
Covariate Reduction
Model Selection
Model Validation
Interpretation of Model Predictions
Comparing Management Alternatives
Jim Ward
Miles Hemstrom
Analysis of Habitat Use
• Objectives:
– Relate landscape characteristics to animal
distribution
– Interpret and predict the distribution of animals
– Distribution map
– Ideas for conservation or mitigation
– Forecast changes in habitat use based on potential
changes in land management
Habitat Use Model
Miles Hemstrom
Analysis of Habitat Use
Habitat Use Model:
“A statistical model with one or more covariates describing
landscape characteristics, and coefficients estimated from
spatially explicit location data that describe the relationships
between animal use and the landscape characteristics”
– Coefficients
• interpretation of relationships between use and the landscape
• make predictions to other areas / points in time
– Comparison of several different models (covariate
importance)
– Evaluation of goodness-of-fit
Blue Mts. Modeling
Jim Ward
Miles Hemstrom
Modeling Objectives
1. Model the probability of elk use within each
study area / year
2. Develop a regional model of elk use for the
region using a meta-analysis approach
3. Treat the collared elk as the primary sampling
unit within each study area / year
Miles Hemstrom
A Model for Probability of Use
Definition of Probability:
“Long-run Relative Frequency of Occurrence”
Miles Hemstrom
A Model for Probability of Use
Basic Sampling Situation…
3
7
5
1
7
8
2
4
9
0
3
3
Miles Hemstrom
A Model for Probability of Use
Relate counts to habitat characteristics
Habitat Use Model
Poisson or Negative Binomial (NB) Model:
log(counti) = β0 + β1X1i + …+ βpXpi + εi
We now have a model for counts of use, but NOT Probability of Use…
Miles Hemstrom
A Model for Probability of Use
3 /60
7/60
5/60
7/60
8/60
4/60
0/60
9/60
N=60
1/60
2/60
3 /60
3/60
Divide count by total = relative frequency = Probability of Use!
Miles Hemstrom
A Model for Probability of Use
Can we still use NB model to relate relative frequencies
to habitat characteristics?
YES, If we include an offset term = log(total):
log(counti) = log(total) + β0 + β1X1i + … + βpXpi + εi
log(counti/total) = β0 + β1X1i + … + βpXpi + εi
log(Relative Frequencyi) = β0 + β1X1i + … + βpXpi + εi
We now have a model for Probability of Use
Miles Hemstrom
Modeling Objectives
1. Model the probability of elk use within each
study area / year
2. Develop a regional model of elk use via a metaanalysis approach
3. Treat the collared elk as the primary sampling
unit
Miles Hemstrom
Regional Model Using Meta-analysis
• Develop a model for each study area / year
• Combine the estimated models to produce one
regional model representing use by the average
animal
• Averaged coefficients across study areas and years
– Treats the study-area specific estimates as
independent, replicate measures of habitat use
– Quantifies use by the average individual elk
Miles Hemstrom
Modeling Objectives
1. Model the probability of elk use within each
study area / year
2. Develop a regional model of elk use for the
region using a meta-analysis approach
3. Treat the collared elk as the primary sampling
unit
Miles Hemstrom
Primary Sampling Units
When estimating precision, it is important to recognize
that within each study area the elk were sampled
first. How do we account for variability between elk
in our final habitat use model?
– Bootstrapping individual elk to produce 1,000
estimates of model coefficients for each study
area / year and the regional model
– 90% Confidence Intervals using ‘percentile
method’ from the 1,000 estimates for each model
coefficient
Miles Hemstrom
Modeling Objectives
1. Model the probability of elk use within each
study area / year
2. Develop a regional model of elk use for the
region using a meta-analysis approach
3. Treat the collared elk as the primary sampling
unit
Miles Hemstrom
Covariates Considered
Nutrition
Dietary digestible energy (DDE)
Accepted biomass (AB)
Total forage biomass (FB)
EVI (Enhanced Vegetation Index)
Human
Disturbance
Distance to:
any road
open road
closed road
class 1 road
class 2 road
class 3 road
class 4 road
class 4 or greater road
class 1 or 2 road
class 3 or 4 road
Density of:
all roads
open roads and trails
Vegetation
Physical/
Other
Proportion of vegetation classes
Percent slope
Overstory canopy cover (CC)
Dominant slope class
Dominant CC class
Percent area in:
flat to gentle slopes
moderate to steep slopes
very steep slopes
Cover/forage ratio
Percent area in cover
Distance to:
cover-forage edge
cover patch (3 patch sizes)
agricultural land
Cosine and sine of aspect
Convexity
Solar radiation
Soil depth
Distance to:
water
pond
stream
Dominant landowner
Cattle RSF
Miles Hemstrom
Covariate Reduction
Each covariate was examined for:
• Relevance to elk use
• Relevance to management
• Ease of calculation
• Consistency in distributions
• Consistency in relation to elk habitat use
• Multicolinearity
Miles Hemstrom
Covariates Considered
Human
Disturbance
Nutrition
Dietary digestible energy (DDE)
Accepted biomass (AB)
Total forage biomass (FB)
EVI (Enhanced Vegetation Index)
Distance to:
any road
open road
closed road
class 1 road
class 2 road
class 3 road
class 4 road
class 4 or greater road
class 1 or 2 road
class 3 or 4 road
Vegetation
Physical/
Other
Proportion of vegetation classes
Percent slope
Overstory canopy cover (CC)
Dominant slope class
Dominant CC class
Percent area in:
flat to gentle slopes
moderate to steep slopes
very steep slopes
Cover/forage ratio
Percent area in cover
Distance to:
cover-forage edge
cover patch (3 patch sizes)
agricultural land
Density of:
all roads
open roads and trails
Reduced Sets of
Nutrition, Human Disturbance, Vegetation, &
Physical/other Covariates in Competing Models
Cosine and sine of aspect
Convexity
Solar radiation
Soil depth
Distance to:
water
pond
stream
Dominant landowner
Cattle RSF
Miles Hemstrom
Model Selection
Modeling started with:
1) Nutrition model set:
1) Dietary digestible energy (DDE)
2) Accepted biomass
3) Total forage biomass (excluding conifers &
herbaceous annuals)
Miles Hemstrom
Model Selection
Process:
1. Fit each model in Set 1 (Nutrition Models) to each
study area / year
2. Calculated AIC values and AIC weights for each
model in each study area / year
3. Ranked each model within each study area / year
according to AIC weights (lower rank better)
4. Summed the ranks for each model among the study
areas / years
The Nutrition Model with the
lowest sum of ranks was brought forward
Miles Hemstrom
Model Selection
Example…
Data
Model #
2
Starkey 2006
1
3
2
Starkey 2008
1
3
2
Starkey 2010
1
3
3
Sled 2005 South
1
2
2
Sled 2006 South
3
1
2
Sled 2006 North
1
3
AIC AIC weight Rank
2885.26
0.96
1
2892.08
0.03
2
2893.95
0.01
3
3934.45
1.00
1
3957.03
0.00
2
3957.82
0.00
3
3914.32
1.00
1
3927.58
0.00
2
3929.44
0.00
3
6992.96
1.00
1
7016.88
0.00
2
7016.93
0.00
3
5986.47
0.61
1
5987.47
0.37
2
5993.53
0.02
3
7842.03
1.00
1
7867.13
0.00
2
7868.10
0.00
3
Sum of Ranks
Model 1: 13
Model 2: 8
Model 3: 15
Model 2
Brought Forward
Miles Hemstrom
Model Selection
Process (cont’d):
5. Went through same procedure for:
– Human disturbance models (Set 2)
– Vegetation models (Set 3)
– Physical/other models (Set 4)
6. Combined “best” models from each model set,
requiring that each contained the best human
disturbance and/or nutrition model
Miles Hemstrom
Model Selection
Process (cont’d):
6. “Best of the best” models:
Nutrition
Human Disturbance
Vegetation
Physical/other
Final Models
Nutrition
Human disturbance
Miles Hemstrom
Model Selection
Process (cont’d):
6. “Best of the best” models:
Nutrition
Human Disturbance
Vegetation
Physical/other
Final Models
Nutrition
Human disturbance
Nutrition + human disturbance
Miles Hemstrom
Model Selection
Process (cont’d):
6. “Best of the best” models:
Nutrition
Human Disturbance
Vegetation
Physical/other
Final Models
Nutrition
Human disturbance
Nutrition + human disturbance
Nutrition + vegetation
Miles Hemstrom
Model Selection
Process (cont’d):
6. “Best of the best” models:
Nutrition
Human Disturbance
Vegetation
Physical/other
Final Models
Nutrition
Human disturbance
Nutrition + human disturbance
Nutrition + vegetation
Nutrition + physical/other
Miles Hemstrom
Model Selection
Process (cont’d):
6. “Best of the best” models:
Nutrition
Human Disturbance
Vegetation
Physical/other
Final Models
Nutrition
Human disturbance
Nutrition + human disturbance
Nutrition + vegetation
Nutrition + physical/other
Nutrition + vegetation + physical/other
Miles Hemstrom
Model Selection
Process (cont’d):
6. “Best of the best” models:
Nutrition
Human Disturbance
Vegetation
Physical/other
Final Models
Nutrition
Human disturbance
Nutrition + human disturbance
Nutrition + vegetation
Nutrition + physical/other
Nutrition + vegetation + physical/other
Human disturbance + vegetation
Miles Hemstrom
Model Selection
Process (cont’d):
6. “Best of the best” models:
Nutrition
Human Disturbance
Vegetation
Physical/other
Final Models
Nutrition
Human disturbance
Nutrition + human disturbance
Nutrition + vegetation
Nutrition + physical/other
Nutrition + vegetation + physical/other
Human disturbance + vegetation
Human disturbance + physical/other
Miles Hemstrom
Model Selection
Process (cont’d):
6. “Best of the best” models:
Nutrition
Human Disturbance
Vegetation
Physical/other
Final Models
Nutrition
Human disturbance
Nutrition + human disturbance
Nutrition + vegetation
Nutrition + physical/other
Nutrition + vegetation + physical/other
Human disturbance + vegetation
Human disturbance + physical/other
Human disturbance + vegetation +
physical/other
Miles Hemstrom
Model Selection
Process (cont’d):
6. “Best of the best” models:
Nutrition
Human Disturbance
Vegetation
Physical/other
Final Models
Nutrition
Human disturbance
Nutrition + human disturbance
Nutrition + vegetation
Nutrition + physical/other
Nutrition + vegetation + physical/other
Human disturbance + vegetation
Human disturbance + physical/other
Human disturbance + vegetation +
physical/other
Nutrition + human disturbance +
vegetation
Miles Hemstrom
Model Selection
Process (cont’d):
6. “Best of the best” models:
Nutrition
Human Disturbance
Vegetation
Physical/other
Final Models
Nutrition
Human disturbance
Nutrition + human disturbance
Nutrition + vegetation
Nutrition + physical/other
Nutrition + vegetation + physical/other
Human disturbance + vegetation
Human disturbance + physical/other
Human disturbance + vegetation +
physical/other
Nutrition + human disturbance +
vegetation
Nutrition + human disturbance +
physical/other
Miles Hemstrom
Model Selection
Process (cont’d):
6. “Best of the best” models:
Nutrition
Human Disturbance
Vegetation
Physical/other
Final Models
Nutrition
Human disturbance
Nutrition + human disturbance
Nutrition + vegetation
Nutrition + physical/other
Nutrition + vegetation + physical/other
Human disturbance + vegetation
Human disturbance + physical/other
Human disturbance + vegetation +
physical/other
Nutrition + human disturbance +
vegetation
Nutrition + human disturbance +
physical/other
Nutrition + human disturbance +
vegetation + physical/other
Miles Hemstrom
Model Validation
• Predictions of elk
use from regional
model using
independent data
• Divided into 20
classes – each with
equal area
Miles Hemstrom
Model Validation
• Predictions of elk
use from regional
model using
independent data
• Divided into 20
classes – each with
equal area
• Count the total
number of elk
locations within
each class
• Correlation Analysis
Miles Hemstrom
Summary of Blue Mts. Modeling
• Modeled Probability of Use
– NB Regression has passed many peer reviews and
has been previously published
• Covariate selection was logical and based on the
study objectives
• a priori group of model sets
• Logical, a priori model selection protocol was
followed
• Created a regional model using a meta-analysis
approach
• Validation run on the regional model
Rachel Cook
Miles Hemstrom
Interpretation of Model Predictions
(
Pˆ2 = exp(βˆ0
Pˆ3 = exp(βˆ0
Pˆ4 = exp(βˆ0
Pˆ5 = exp(βˆ0
Pˆ = exp(βˆ
)
+ βˆ1 x1 + βˆ2 x2 + ... + βˆ p x p )
+ βˆ1 x1 + βˆ2 x2 + ... + βˆ p x p )
+ βˆ1 x1 + βˆ2 x2 + ... + βˆ p x p )
+ βˆ1 x1 + βˆ2 x2 + ... + βˆ p x p )
+ βˆ x + βˆ x + ... + βˆ x )
Pˆ1 = exp βˆ0 + βˆ1 x1 + βˆ2 x2 + ... + βˆ p x p
6
1
2
3
4
5
06
1
1
1
2
2
2
3
3
3
4
4
4
5
5
5
16 1
26
2
p6
p
Miles Hemstrom
Interpretation of Model Predictions
• Unique situation – data from multiple study areas /
years
• Averaged coefficients across the 6 study areas / years
1 6 ˆ
ˆ
βi = ∑ βi j
6 j =1
PˆOverall = exp βˆ0 + βˆ1 x1 + βˆ 2 x 2 + ... + βˆ p x p 


• Predictions represent relative probability of use (aka
“Predicted Level of Use”)
Miles Hemstrom
Interpretation of Model Predictions
Comparing 2 sites within 1 regional landscape
application
Prediction(1) vs. Prediction(2)
0.04
0.02
Predicted Elk Use is 2 x higher for site 1 compared to
site 2
Miles Hemstrom
Interpretation of Model Predictions
Predictions come from an exponential model, so the
distribution is likely highly skewed
Relative Probability of Use
• Means are sensitive to outliers and large numbers
• Equal-interval binning doesn’t work
Miles Hemstrom
Interpretation of Model Predictions
Prediction
Relative Prob.
Class
of Use
% of Study Area
<0.0094
20%
Medium-low
0.0094 to 0.0165
20%
Medium
0.0166 to 0.0270
20%
Medium-high
0.0271 to 0.0501
20%
>0.0501
20%
Low
High
Miles Hemstrom
Considering Management Options
E.g., Compare ‘Existing’ conditions to a silviculture
treatment (Alternative)
– Bin the predictions for the existing landscape
– Use same bin cut-points for predictions based on
an ‘Alternative’
Prediction
Relative Prob.
Class
of Use
Existing
Alternative
<0.0094
20%
18.7%
Medium-low
0.0094 to 0.0165
20%
19.2%
Medium
0.0166 to 0.0270
20%
19.3%
Medium-high
0.0271 to 0.0501
20%
21.1%
>0.0501
20%
21.8%
Low
High
Percent of Study Area
Thank You
Miles Hemstrom