A model-based approach to estimating the Landowner Incentive Tag Award

A summary to the Incentive Tag Arbitration Panel

27 June 2016

Area of Interest

Incentive Tag Estimate: 3 Simple Steps

1. Develop a habitat model of elk in Unit 121.

2. Construct a map of predicted elk habitat in Unit 121 using parameters from habitat model.

3. Estimate number of elk expected to use property for 365 days given habitat suitability. Insert estimate into formula to estimate incentive tag award.

Habitat Model

• Analyzed resource selection by season using a use/availability design (Manly et al. 2002, McKee et al. 2015). • “Used” Data: GPS collar data from n = 15 elk, 2011-2014, 2016 • “Available” Data: An equal number of randomly generated locations

occurring within the known seasonal distribution of radiocollared elk.

• Extracted habitat characteristics (e.g., elevation, distance to nearest road, etc.) to used and available data that are known to influence habitat selection by elk in non-forested systems (Sawyer et al. 2007).

• Constructed various models of resource selection using derived habitat characteristics and analyzed relative importance of those components using a statistical computing package (R Core Team 2016).

Map of Predicted Habitat

• Divide Unit 121 into a grid of > 3 million cells, each cell measuring 30m by 30m .

• Apply habitat model best supported by data to each cell to calculate a value ranging from 0-1 that represents habitat quality for elk. Larger values represent habitat of higher quality.

• Output map is a spatial representation of predicted habitat of elk occurring in Unit 121.

Example of Predicted Habitat

Satellite Imagery Predictive Map

Estimating Incentive Tag Award 1. Estimate proportion of elk occurring in Unit 121:

• Multiply proportion of elk encountered in Unit 121 during aerial survey by the annual estimate of population size.

2. Estimate proportion of elk habitat on property:

• Sum total of predicted values occurring within property and divide by the sum of predicted values occurring in all of Unit 121.

3. Property estimate of population size (for incentive tag

formula): • Multiply proportion of elk habitat on property by population

estimate in Unit 121. Adjust for seasonal contribution (x/365) and sum adjusted values.

Habitat Model Components

Parameter Fall

Model Winter Model

Spring Model

Summer Model

Elevation² (m) Nonlinear Nonlinear Nonlinear Nonlinear

Slope² (°) Nonlinear Nonlinear Nonlinear Nonlinear

Northeastness Cooler, wetter Cooler, wetter Cooler, wetter *

Nearest Road (m) * Further Further Closer

Nearest Water (m) Further Further Further *

Habitat Class % % % sig * Parameter is not a significant component of resource selection % Parameter not included in model due to insufficient sample size

Model Effects

-3

0

3

Habitat Effect in Summer Model Parameter Estimates (+ 95% CI)

Parameter estimates of habitat effects are comparisons to shrubland habitat

Model Effects

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1750 2250 2750 3250

Rela

tive

Prob

abili

ty o

f Sel

ectio

n (p

i)

Elevation (m)

Elevation Effect in Summer Model Response 95% Confidence Interval

Model Effects

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35 40

Rela

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Prob

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f Sel

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n (p

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Slope (°)

Slope Effect in Summer Model Response 95% Confidence Interval

Predicted Habitat

Population Estimate Unit 121 Estimate = Population in Management Area x Proportion Encountered on Survey in Unit 121

• 700 elk estimated in Management Area (Units 121, 108, 104)

• 397 out of 466 or 85% of elk encountered on most recent survey

occurred in Unit 121.

• Unit 121 Estimate for Calculation: 700 x 0.85 = 595 elk

Elk Estimate

Season Seasonal Immigration

Unit 121 (∑Pi)

Property (∑Pi)

Unit 121 Estimate

(N)

Annual Property Estimate

(N)‡

Season Length (Days)

Seasonal Contribution

(N)†

Summer 0% 1212051 12928 595 6.35 92 1.60

Spring 0% 1244796 9645 595 4.61 92 1.16

Fall 0% 1530203 10905 595 4.24 91 1.06

Winter 0% 1295467 6557 595 3.01 90 0.74 ‡Annual property estimate assumes season is 365 days long (i.e., January 1-December 31st). Value is subsequently adjusted for season length to determine seasonal contribution to N. †The seasonal contribution provides a corrected N estimate based on season length. Summing the seasonal contributions provides a robust representation of elk use occurring for 365 days and accounts for differences in resources among seasons.

1.60 + 1.16 + 1.06 + 0.74 = 4.56 elk using property for 365 days

Incentive Tag Award • Incentive Tag Formula: (NP ÷ NE) × (DP ÷ 365) × (NT + TSH)

• NP – Number of elk using the private land (4.56) • NE – Elk estimate in the use area where private land is located (595) • DP – Number of days the elk use the private land during the year (365) • NT – Total number of antlered tags issued in previous year (68) • TSH – Total number of spikes harvested in previous year (0)

• Incentive Tag Estimate:

• (4.56/595) x (365/365) x 68 = 0.52 • 0.52 rounds up to 1 tag

Other Scenarios • Using the Management Area Population Estimate (n = 700):

• (5.36/700) x (365/365) x 68 = 0.52 or 1 tag • True population is double the estimate (n = 1400). Antlered

tags would also be double (n = 136): • (10.73/1400) x (365 x 365) x 136 = 1.04 or 1 tag

• 50% of population emigrates from 104 & 108 to Unit 121

during spring and summer (additional n = 53 elk): • (4.81/595) x (365/365) x 68 = 0.55 or 1 tag