Ecological Archives E096-271-A1

Geir Rune Rauset, Matthew Low, and Jens Persson. 2015. Reproductive patterns result from age-related sensitivity to resources and reproductive costs in a mammalian carnivore. Ecology 96:31533164. http://dx.doi.org/10.1890/15-0262.1

Appendix A. Mapping of spatial variation in resource availability.

For the modeling of spatial variation in resource availability, we employed data on the spatial distribution of reindeer carcasses; (see details in Mattisson et al. 2011) to derive three maps of seasonal distributions of reindeer carcasses (winter/spring: Feb–May, summer: Jun–Sept, autumn/winter: Oct–Jan).

Reindeer carcasses were detected by the identification of spatiotemporal clustering of GPS locations of individual lynx and wolverines, which were later visited in the field (see details in Mattisson et al. 2011). We excluded carcasses belonging to multiple kills and other tied death events (e.g., avalanches killing several reindeer). This left us with 492 reindeer carcasses, of which the origins were: lynx kills (64%), wolverine kills (6%), unknown carnivore (6%), avalanche (2%), and unknown (21%). The seasonal distribution of the carcasses was: winter/spring (53%), summer (22%), and autumn/winter (26%). We generated 5 random locations conditional on the location of each carcass, using a buffer distance of 6000 m (corresponding to mean daily displacement in wolverines; Rauset 2013), and sampled habitat and landscape features at each point (see Rauset et al. 2013). For the three seasons, we built separate suits of competing models, using logistic discriminant functions (use vs. availability). We assessed model performance by small sample corrected Akaike’s Information Criterion (AICc; Burnham and Anderson 2002). To avoid multicollinearity among many potentially correlated environmental variables, we evaluated suites of potential variables by Variance Inflation Factor (VIF; (Zuur et al. 2009) in the R package “AED” (Zuur 2010). We did not include variables with a VIF ≥ 3 in the same models. Spatial predictions from the best models were interpolated into density surfaces by kriging regression in ArcGIS 9.3™ (©1999–2013 ESRI Inc.)).

Table A1. Candidate set of zero-inflated Poisson (ZIP) models using combinations of age structures to predict annual reproductive output (n = 205) in individual female wolverines (n = 53). ∆AICc = difference in AICc relative to the best model; wi = AICc weight of the model; K = number of parameters in the model. All models contained 2 additional variables in the count process part of the model describing the first and last ages each individual occurred in the data set to account for the possibility of biases arising from age-related selective appearance and disappearance of phenotypes1.

Binomial process

Count process

K

AICc

ΔAICc

wi

 

 

 

 

 

 

age + age²

age

7

495.65

0.0

0.47

age

age

6

496.48

0.83

0.31

age + age²

age + age²

8

497.40

1.75

0.19

age + age²

intercept only

6

501.44

5.79

0.03

age

intercept only

5

504.62

8.97

0.0

intercept only

age + age²

6

514.93

19.28

0.0

intercept only

age

4

522.10

26.45

0.0

intercept only

intercept only

5

522.30

26.65

0.0

1 Note that the inclusion of first and last ages in these models had very little effect on model fit, no effect on absolute model rankings and very little effect on relative rankings compared to the same set of models that did not include these first & last age terms (e.g., the highest-ranked model without first- & last-age terms had an AICc of 496.63)

 

Table A2. Candidate set of zero-inflated Poisson (ZIP) models to predict annual reproductive output (n = 174) in individual female wolverines (n = 41) based on the highest-ranked age-specific model in Table A1. Explanatory variables include environmental representation of individual home ranges: mean integrated NDVI (NDVI), and three seasonal densities of reindeer carcasses (Feb-May: reindeerSPRING; Jun–Sep: reindeerSUMMER; Oct-Jan: reindeer WINTER). ∆AICc = difference in AICc relative to the best model; wi = AICc weight of the model; K = number of parameters in the model.

Binomial process

Count process

K

AICc

ΔAICc

wi

age + age²

age + reindeer WINTER

6

423.05

0.00

0.37

age + age²

age + NDVI

6

423.11

0.06

0.36

age + age²

age + reindeerSPRING

6

425.30

2.24

0.12

age + age²

age + reindeerSUMMER

6

425.76

2.70

0.10

age + age²

age

5

426.79

3.73

0.05

 

Table A3. Parameter estimates from the highest-ranked zero-inflated Poisson (ZIP) mixed-effects model in Table A2 combining age and winter seasonal (Oct-Jan) distribution of reindeer carcasses in individual home ranges to predict annual reproductive output (n = 174) in individual female wolverines (n = 41). The estimates are means, standard deviations and 95% credible intervals from the posterior distributions generated from a zero-inflated Bayesian hierarchical model implemented in JAGS, with individual wolverine identity included as a random effect in both the binomial and count process models. The minimum and maximum ages for each individual were used to control for potential biases relating to selective (dis)appearance based on individual quality of breeding phenotype*.

Model parameters

Mean

SD

95% CIs

Binomial process (logit)

 

 

 

   intercept

-421

165

[-733, 141]

   age

57

68

[-106, 163]

   age²

76

36

[12, 130]

Count process (log)

 

 

 

   intercept

0.20

0.26

[-0.33, 0.72]

   age

-0.11

0.04

[-0.03, -0.19]

   reindeer WINTER

0.21

0.14

[-0.07, 0.48]

   age first breed

0.09

0.06

[-0.02, 0.2]

   age last breed

0.02

0.03

[-0.04, 0.08]

*Note that without the inclusion of the age-first and age-last breed parameters in the model, the age effect in the count process was qualitatively similar (-0.09 ± 0.03). Inclusion of these terms showed that the selective (dis)appearance of different phenotypes from the population partly masked the magnitude of the senescence effect.

 

Table A4. Candidate set of multistate mark-recapture models showing relative support for different age structures for the transition parameters of ψB→B & ψNB→B. The survival and resighting parameters were held constant (ФSTATE+AGE & pSTATE) in all models. Age was modeled as constant, linear, quadratic or age varying. ∆AICc = difference in AICc relative to the best model; wi = AICc weight of the model; K = number of parameters in the model.

ψB→B

ψNB→B

K

AICc

ΔAICc

wi

 

 

 

 

 

 

quadratic

constant

10

301.9

0

0.47

constant

constant

8

304.3

2.38

0.14

quadratic

linear

11

304.3

2.39

0.14

linear

constant

9

305.2

3.29

0.09

quadratic

quadratic

12

306.2

4.25

0.06

constant

linear

9

306.6

4.69

0.04

linear

linear

10

307.6

5.64

0.03

constant

quadratic

10

308.4

6.47

0.02

linear

quadratic

11

309.4

7.46

0.01

age-varying

age-varying

30

346.4

44.5

0.00

 

 

 

 

 

 

 

Table A5. Candidate set of multistate mark–recapture models showing relative support for different variable structures for the transition parameters of ψB→B & ψNB→B. The survival and resighting parameters were held constant (ФSTATE+AGE & pSTATE) in all models; the ψNB→B transition was modelled as a simple intercept for all ψB→B models; the ψB→B transition was modelled with its age dependent structure (age + age²) for all ψNB→B models (see also Table A4). The covariates were: female age (age = linear, age² = quadratic [age + age²]), winter reindeer carcass availability (reindeer), number of cubs weaned the previous year (cubs), the North Atlantic Oscillation index (NAO) and an index of rodent density (rodent). ∆AICc = difference in AICc relative to the best model; wi = AICc weight of the model; K = number of parameters in the model.

Transition (ψ) parameter

K

AICc

ΔAICc

wi

 

 

 

 

 

ψB→B

 

 

 

 

     age² + reindeer + cubs + NAO

13

296.3

0

0.24

     age² + reindeer + cubs

12

296.8

0.56

0.18

     age² + reindeer

11

297.4

1.13

0.13

     age² + reindeer + cubs + rodent

13

297.6

1.36

0.12

     age² + reindeer + NAO

12

298.2

1.91

0.09

     age² + reindeer + cubs + NAO + rodent

14

298.5

2.22

0.08

     age² + reindeer + rodent

12

298.8

2.56

0.07

     age² + reindeer + NAO + rodent

13

300.4

4.18

0.03

     age²

10

301.9

5.69

0.01

     age² + cubs

11

302.4

6.08

0.01

     age² + cubs + NAO

12

302.6

6.33

0.01

     age² + NAO

11

302.8

6.50

0.01

     age² + rodent

11

303.5

7.19

0.01

     age² + cubs + rodent

12

303.8

7.53

0.01

     intercept only

8

304.3

8.07

0.00

     age² + cubs + NAO + rodent

13

304.9

8.73

0.00

     age² + NAO + rodent

12

305.1

8.79

0.00

     age

9

305.2

8.90

0.00

 

 

 

 

 

ψNB→B

 

 

 

 

     intercept only

10

301.9

0

0.39

     reindeer

11

303.4

1.49

0.19

     NAO

11

304.1

2.11

0.14

     age

11

304.3

2.39

0.12

     rodent

11

304.4

2.40

0.12

     age²

12

306.2

4.25

0.04

 

Literature sited

Burnham, K. P., and D. R. Anderson. 2002. Model selection and multimodel inference. Second edition. Springer-Verlag New York, New York, USA.

Mattisson, J., H. Andren, J. Persson, and P. Segerstrom. 2011. Influence of intraguild interactions on resource use by wolverines and Eurasian lynx. Journal of Mammalogy 92:1321–1330.

Rauset, G. R. 2013. Life and death in wolverines - linking demography and habitat for conservation. PhD thesis. Swedish University of Agricultural Sciences, Uppsala.

Rauset, G. R., J. Mattisson, H. Andren, G. Chapron, and J. Persson. 2013. When species' ranges meet: assessing differences in habitat selection between sympatric large carnivores. Oecologia 172:701–711.

Zuur, A. 2010. AED: Data files used in Mixed effects models and extensions in ecology with R (in Zuur et al. 2009). R package version 1.0.

Zuur, A. F., E. N. Ieno, N. J. Walker, A. A. Saveliev, and G. M. Smith. 2009. Mixed effects models and extensions in ecology with R. Springer Science + Buisness Media, New York, USA.


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