Development of an
Elk Habitat Use Model
for the Westside
by Ryan Nielson (WEST, Inc.)
Photo by Scott McCorquodale
Overview
• Analysis of Habitat Use
• Westside Modeling
Objectives
Covariate Reduction
Model Selection
Model Validation
Interpretation of Model Predictions
Evaluating and Comparing Landscapes
Analysis of Habitat Use
Objectives:
– Distribution map
– Relate landscape characteristics to distribution
– Interpret and predict the distribution of animals
across the landscape
– Ideas for conservation or mitigation
– Forecast changes in habitat use based on potential
changes in land management
Analysis of Habitat Use
Produce a 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 (variable
importance)
– Evaluation of goodness-of-fit
Westside Modeling
Photo by Rachel Cook (NCASI)
Westside Modeling Objectives
1. Model the probability of elk use within
each study area
2. Develop a regional model of elk use for
western OR and WA using a meta-analysis
approach
3. Treat the collared elk as the primary
sampling unit within each study area
A Model for Probability of Use
Definition of Probability:
“Long-run Relative Frequency of Occurrence”
A Model for Probability of Use
Basic Sampling Situation…
3
7
5
1
7
8
2
4
9
0
3
3
A Model for Probability of Use
Relate counts to habitat characteristics
Habitat Use Model
Poisson or Negative Binomial Model:
log(counti) = β0 + β1X1i + …+ βpXpi + εi
We now have a model for counts of use, but
NOT Probability of Use…
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!
A Model for Probability of Use
Can we still use Negative Binomial 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
Westside Modeling Objectives
1. Model the probability of elk use within
each study area
2. Develop a regional model of elk use for
western OR and WA using a meta-analysis
approach
3. Treat the collared elk as the primary
sampling unit
Regional Model Using Meta-analysis
• Develop a model for each year/study area
• Combine the estimated models to produce one
regional model representing use by the average
animal
• Averaged coefficients across study areas
– Treats the study-area specific estimates as independent,
replicate measures of habitat use
– Quantifies use by the average individual elk
Westside Modeling Objectives
1. Model the probability of elk use within
each study area
2. Develop a regional model of elk use for
western OR and WA using a meta-analysis
approach
3. Treat the collared elk as the primary
sampling unit
Treat Collared Elk as
Primary Sampling Units
When estimating precision, it is important to
recognize that within each study area the elk
were sampled first
– Bootstrapping individual elk to produce 1000
estimates of model coefficients for each study
area and the regional model
– 90% Confidence Intervals using ‘percentile
method’ from the 1000 of estimates for each
model coefficient
Westside Modeling Objectives
1. Model the probability of elk use within
each study area
2. Develop a regional model of elk use for
western OR and WA using a meta-analysis
approach
3. Treat the collared elk as the primary
sampling unit
Covariate Reduction
Covariates calculated for each circular sampling unit:
Nutrition
DDE (continuous)
DDE (categorical)
Accepted Biomass (AB)
Distance to:
High DDE
Mod DDE
Percent area in M to H DDE
Quadratic, Cubic forms
Human
Disturbance
Vegetation
Physical/
Other
Density of & Distance to:
Open Roads
Closed Road
High Traffic Roads
Low Traffic Roads
Public Use Roads
Administrative Use Only
Motorized Use Trails
Overstory CC
Slope (continuous)
Dominant CC
Slope (categorical)
Cover-Forage Ratio
Percent Area in:
Flat to Gentle Slope
Mod to Steep Slope
Very Steep Slope
Quadratic, Cubic forms
Distance to:
Forage
Cover
Cover-Forage Edge
Optimal Cover
Thermal Cover
Hiding Cover
Habitat Effectiveness of
size/spacing of Cov & For
Cover Quality
Aspect
Convexity
Curvature
Soil Depth
Solar Radiation
Distance to Water
Land Ownership
Covariate Reduction
Each covariate was examined for:
• Relevance to elk use
• Relevance to management
• Consistency in distributions
• Ease of calculation
• Multicolinearity
Nutrition
DDE (continuous)
DDE (categorical)
Accepted Biomass (AB)
Distance to:
High DDE
Mod DDE
Percent area in M to H DDE
Quadratic, Cubic forms
Human
Disturbance
Vegetation
Physical/
Other
Density of & Distance to:
Open Roads
Closed Road
High Traffic Roads
Low Traffic Roads
Public Use Roads
Administrative Use Only
Motorized Use Trails
Overstory CC
Slope (continuous)
Dominant CC
Slope (categorical)
Cover-Forage Ratio
Percent Area in:
Flat to Gentle Slope
Mod to Steep Slope
Very Steep Slope
Quadratic, Cubic forms
Distance to:
Forage
Cover
Cover-Forage Edge
Optimal Cover
Thermal Cover
Hiding Cover
Habitat Effectiveness of
size/spacing of Cov & For
Cover Quality
Aspect
Convexity
Curvature
Soil Depth
Solar Radiation
Distance to Water
Land Ownership
Reduced Sets of
Nutrition, Human Disturbance, Vegetation, & Physical
Covariates in Competing Models
Model Selection
Model Sets Started with:
1) Nutrition Model Set
1)
Dietary Digestible Energy (DDE)
2)
Accepted Biomass
3)
DDE in MGE + % Area in MGE + Interaction
Model Selection
Process:
1. Fit each model in Set 1 (Nutrition Models) to each study
area
2. Calculated AIC values and AIC weights for each model in
each study area
3. Ranked each model within each study area according to
AIC weights (lower rank better)
4. Summed the ranks for each model among the study
areas
The Nutrition Model with the lowest sum of
ranks was brought forward
Model Selection
Example…
Data
Elwha 2009
White River 2004
White River 2005
White River 2007
Green/Cedar 2008
Model #
1
2
3
3
1
2
1
2
3
2
3
1
1
2
3
AIC AIC weight Rank
1081.37
0.39
1
1081.61
0.35
2
1082.13
0.27
3
5142.44
1.00
1
5153.92
0.00
2
5182.87
0.00
3
2207.98
0.53
1
2208.69
0.37
2
2211.22
0.10
3
5474.73
0.56
1
5475.26
0.43
2
5483.61
0.01
3
5132.19
0.45
1
5132.94
0.31
2
5133.43
0.24
3
Sum of Ranks
Model 1: 8
Model 2: 10
Model 3: 12
Model 1
Brought Forward
Model Selection
Process (cont’d):
5.
6.
Went through same procedure for Human Disturbance Models
Best Nutrition Model + physical/vegetation covariates:
Model 1
Best Nutrition Model +
% Slope
7.
Model 2
Best Nutrition Model +
Dist. to Edge
Model 3
Best Nutrition Model +
% Slope
Dist. to Edge
Best Human Disturbance Model + physical/vegetation covariates:
Model 1
Best Human Disturbance +
% Slope
Model 2
Best Human Disturbance +
Dist. to Edge
Model 3
Best Human Disturbance +
% Slope
Dist. to Edge
Model Selection
Process (cont’d):
8. Best Nutrition Model + Best Human Disturbance Model +
physical/vegetation covariates:
Model 1
Best Nutrition Model +
Best Human Disturbance +
% Slope
Model 2
Best Nutrition Model +
Best Human Disturbance +
Dist. to Edge
Model 3
Best Nutrition Model +
Best Human Disturbance +
% Slope +
Dist. to Edge
9. New Versions of 1986 Westside Model
Model 1
Size and Spacing +
Density of Public Roads +
Optimal Cover +
Accepted Biomass
Model 2
Size and Spacing +
Density of Public Roads +
Optimal Cover
Model 3
Size and Spacing +
Density of Public Roads
Accepted Biomass
Model Selection
Process (cont’d):
10. Best from each of the Model Sets:
1.
2.
3.
4.
5.
6.
Best Nutrition Model
Best Human Disturbance Model
Best Nutrition + Human Disturbance Model
Best Nutrition + Physical/Vegetation Model
Best Human Disturbance + Physical/Vegetation Model
Best Nutrition + Human Disturbance +
Physical/Vegetation Model
7. Best 1986 Westside Model
Validation
• Predictions of elk use
based on regional
model for
independent data
• Divided into 20 classes
– each with equal area
• Count the total
number of elk
locations within each
class
• Correlation Analysis
Summary of Westside 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
Photo by Scott McCorquodale
Interpretation of Westside
Elk Habitat Use Model Predictions
• Modeled Probability of Use within each study
area (5 study areas)
(
Pˆ2 = exp(βˆ0
Pˆ3 = exp(βˆ0
Pˆ4 = exp(βˆ0
Pˆ5 = exp(βˆ0
)
+ 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 )
Pˆ1 = exp βˆ0 + βˆ1 x1 + βˆ2 x2 + ... + βˆ p x p
1
2
3
4
5
1
1
1
2
2
2
3
3
3
4
4
4
5
5
5
Interpretation of Westside
Elk Habitat Use Model Predictions
• Unique situation – data from multiple study areas
• Averaged coefficients across the 5 study areas
1
βˆi = ∑ βˆi
5 j =1
5
(
j
Pˆr = exp βˆ0 + βˆ1 x1 + βˆ2 x2 + ... + βˆ p x p
)
• Predictions represent relative probability of use (aka
“Predicted Level of Use” – e.g., Sawyer et al. 2009)
Interpretation of Westside
Elk Habitat Use Model Predictions
Comparing 2 sites within 1 regional landscape
application
Prediction(1)
0.04
vs.
Prediction(2)
0.02
Predicted Elk Use is 2 x higher for site 1 compared to site 2
Evaluating Elk Habitat Use Predictions
Across a Landscape
Predictions come from an exponential model, so the
distribution is likely highly skewed
Relative Probability of Use
• Means are sensitive outliers and large numbers
• Equal-interval binning doesn’t work
Evaluating Elk Habitat Use Predictions
Across a Landscape
Prediction
Relative Prob.
Percent of Study Area
Class
of Use
Existing
<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
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
Considering Management Options
Considering Management Options
Table showing acres in each Prediction Class under Existing
Conditions and under the ‘Alternative’ scenario
Alternative
Existing
Low
Medium-low
Medium
Medium-high
High
Total
12887
698
125
40
17
13767
Medium-low
4
12488
799
284
192
13767
Medium
0
3
12326
1142
295
13766
Medium-high
0
0
2
13029
735
13766
High
0
0
0
3
13764
13767
13190
13252
14499
15003
68833
Low
Total: 12890
Thank You
Photo by Scott McCorquodale