Ecological Archives E096-161-A4

Jerod A. Merkle, Seth G. Cherry, and Daniel Fortin. 2015. Bison distribution under conflicting foraging strategies: site fidelity vs. energy maximization. Ecology 96:15031511. http://dx.doi.org/10.1890/14-0805.1

Appendix D. Detailed results of abundance model.

Minimum counts of bison during aerial surveys (n = 15) ranged from 89 to 389 individuals between 1996 and 2013. Mean counts over time for the northern, central, and southern sites were 48.5 (SD = 28.7), 122.9 (SD = 56.9), and 28.8 (SD = 25.9), respectively.

D.1 RSF for abundance model

RSFs were developed based on 46 bison GPS collared during 10 of 18 aerial surveys. In general, bison selected open areas and avoided coniferous forests during survey periods (Table D1). The probability of detecting a bison decreased with the distance from the survey line, as indicated by the majority of bison observations during the surveys being in areas closer to aerial survey lines than expected randomly within the bison range. Although strength of selection for these variables varied by year, we did not detect a general increasing or decreasing trend (Table D1).

D.2 Abundance model

Based on the N-mixture model, approximately 30 new individuals were counted at each site (i.e., apparent recruitment; Git) each year (Table C2). This rate was also dependent on the previous year’s population size, where apparent recruitment was positively related to the previous year’s population size. Approximately 30% of the individuals counted at each site survived and were recounted in each site the following year (i.e., apparent survival; Sit). A baseline of approximately 61% (p0 = 0.61, SE = 0.01) of animals were detected during each survey. However, detection probability increased when selection for open areas and areas closer to the aerial survey lines by bison was stronger, and when selection for coniferous forest was weaker (Table D2). In summary, as indicated by the posterior probability distributions of Nt, population size ranged from a low of 174 in 2011, to a high of 474 in 2005 (Table C3).

D.3 Validation of abundance model

During summers 2011, 2012, and 2013, we took 287, 300, and 461 high-quality photographs, respectively. Using likelihood-based matching, we identified 113, 122, and 144 unique adult bison in 2011, 2012, and 2013, respectively. Estimated population size from mark–recapture models was 152.8 (SE = 14), 158.2 (SE = 24.4), and 160.9 (SE = 10.8) adult bison, for 2011, 2012, and 2013, respectively (Table D4). Based on bootstrapping of the combined age and sex classes, population estimates for summers 2011 to 2013 were 202, 244, and 232, respectively (Table D4). Population estimates from the N-mixture model and combined photographic mark–recapture were similar given the confidence intervals. Estimates from photographic mark–recapture were consistently higher ( = 10% higher; Table D4), as expected due to an increase in population size after the calving season.

Table D1. Parameter estimates (± SE for fixed effect parameters) of a Resource Selection Function for five weeks before and after winter aerial surveys when radio collar data were available for plains bison in Prince Albert National Park, Canada. Models were parameterized using mixed effects logistic regression comparing observed GPS collar data with random locations sampled from the entire bison range. We specified a random intercept as well as random slopes on each variable based on the year the data were collected. Variables included in the model were coniferous forest (Conifer), open areas including meadows, water bodies and agricultural lands (Open), and distance from the aerial survey transect lines (Dist2line).

 

Year

Intercept

Conifer

Open

Dist2line

Fixed effects

 

 

 

 

All

 -0.05 ± 0.15

 -0.31 ± 0.12

1.64 ± 0.14

 -1.30 ± 0.37

Random effects

 

 

 

 

1998

0.06

-0.16

1.95

-1.77

 

2005

0.75

-1.24

1.56

-2.59

 

2006

-0.34

-0.08

1.84

-0.75

 

2007

0.45

-0.46

1.68

-2.42

 

2008

-0.89

-0.04

1.77

0.05

 

2009

0.46

-0.41

1.49

-2.02

 

2010

-0.26

-0.08

1.15

-0.14

 

2011

-0.60

0.00

1.51

-0.05

 

2012

-0.08

-0.55

0.93

-0.12

 

2013

-0.01

-0.10

2.55

-3.17

 

Table D2. Posterior parameter estimates for RSF-informed Generalized N-mixture model. Site specific parameters included baseline apparent recruitment (γ0), the impact of Nt-1 on apparent recruitment (γ1), mean abundance at t = 1 (λ), apparent survival (ω), base detection probability (p0), and the influence of selection for conifer (pconifer), distance to transect (pdist2line), and open areas (popen) on detection probability. Reported values for parameters associated with gains and detection probability are on the logit scale.

Variable

SE

L 95% CI

U 95% CI

γ0

3.382

0.073

3.233

3.518

γ1

0.007

0.000

0.007

0.008

λ

62.764

5.986

51.861

75.120

ω

0.289

0.045

0.201

0.378

p0

0.461

0.054

0.407

0.604

pconifer

-0.517

0.170

-0.868

-0.206

pdist2line

0.652

0.127

0.440

0.934

popen

0.757

0.167

0.473

1.139

 

Table D3. Posterior population size estimates and 95% confidence intervals from an RSF informed N-mixture model for plains bison in Prince Albert National Park, Canada, 1996–2013. Model was based on how bison habitat selection, during the 5 weeks before and after the survey, for open areas (easily detected), conifer stands (difficult detection), and distance from the transect (accounting for movement outside of survey area) influenced detection probability.

Year

SE

LCI

UCI

1996

187.1

11.9

166.0

213.0

1997

218.2

14.2

191.0

247.0

1998

231.4

11.8

208.0

255.0

1999

240.1

10.7

219.0

261.0

2000

246.0

15.5

216.0

276.0

2001

237.0

13.3

211.0

262.0

2002

328.8

12.0

306.0

353.0

2003

395.9

16.3

364.0

428.0

2004

470.5

13.6

445.0

497.0

2005

474.4

17.4

441.0

510.0

2006

460.1

16.4

430.0

494.0

2007

384.4

15.9

355.0

417.0

2008

334.7

13.4

310.0

363.0

2009

292.8

12.1

270.0

318.0

2010

181.3

13.6

156.0

209.0

2011

173.7

11.4

153.0

197.0

2012

220.3

10.3

201.0

241.0

2013

222.3

14.0

196.0

250.0

 

Table D4. Demographic parameters and 95% CI for plains bison in Prince Albert National Park, Canada, 2011–2013. Parameters estimated by photographic mark–recapture (females and males), field observation (proportion of juveniles to cows and proportion of calves to cows), a combination of the two based on bootstrapping (N photo), and an RSF-informed generalized N-mixture model based on annual resource selection coefficients and annual aerial survey counts (N-mix).

 

2011

 

2012

 

2013

Parameter

estimate

95% CI

 

estimate

95% CI

 

estimate

95% CI

Females

105.64

83.5–133.7

102.79

75.6–139.6

101.29

90.6–113.3

Males

47.42

36.2–62.2

55.63

29.5–104.9

58.89

43.8–79.2

Juv:cow

0.22

0.20–0.25

0.47

0.43–0.51

0.44

0.40–0.48

Calf:cow

0.24

0.22–0.27

0.36

0.31–0.40

0.28

0.24–0.31

N (photo)

201.58

172–231

243.75

191–294

232.44

210–255

N (N-mix)

173.67

153–197

220.27

201–241

222.28

196–250


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