Ecological Archives E096271A1
Geir Rune Rauset, Matthew Low, and Jens Persson. 2015. Reproductive patterns result from agerelated sensitivity to resources and reproductive costs in a mammalian carnivore. Ecology 96:3153–3164. http://dx.doi.org/10.1890/150262.1
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 zeroinflated 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 agerelated selective appearance and disappearance of phenotypes^{1}.
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 highestranked model without first & lastage terms had an AICc of 496.63)
Table A2. Candidate set of zeroinflated Poisson (ZIP) models to predict annual reproductive output (n = 174) in individual female wolverines (n = 41) based on the highestranked agespecific model in Table A1. Explanatory variables include environmental representation of individual home ranges: mean integrated NDVI (NDVI), and three seasonal densities of reindeer carcasses (FebMay: reindeerSPRING; Jun–Sep: reindeerSUMMER; OctJan: 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 highestranked zeroinflated Poisson (ZIP) mixedeffects model in Table A2 combining age and winter seasonal (OctJan) 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 zeroinflated 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 agefirst and agelast 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 markrecapture 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 
agevarying 
agevarying 
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. SpringerVerlag 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.
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