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Supporting information
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Appendix Table S1: Fixed effects of canopy openness and understory vegetation cover
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on the probability of seed caching, seedling establishment and seed pilferage based on
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generalized linear mixed-effects models with binomial error distribution (library
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MCMCglmm in R, Hadfield (2010)). Caching models also include sample type
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(observation versus random sample) as fixed effect. Not shown, but also included in all
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models were random effects for elevation level and study region. In the establishment and
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pilferage models, we also included random effects for experimental cache ID (see main
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text). Significant P values are shown in boldface. The Deviance Information Criterion
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indicates difference to the respective null model (ΔDIC).
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Model
Source of variation
Estimate
DIC
ΔDIC
pMCMC
Caching
~Vegetation cover
+Soil moisture
-0.03
-0.04
251
26
<0.001
<0.001
+Sample
18.25
~ Vegetation cover
0.01
+Soil moisture
0.02
~ Vegetation cover
0.01
+Soil moisture
0.01
Establishment
Pilferage
<0.001
370
7
0.090
0.020
813
1
0.201
0.864
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13
14
1
***
0.5
0.0
Caches observed per hour
(b)
Prob. of caching (ran.sam.)
Prob. of caching (obs. & ran.sam.)
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(a)
1.0
1.0
***
0.5
0.0
(c)
4
3
2
***
1
0
1850
2000
2150
Elevation (m)
2300
1850
2000
2150
Elevation (m)
2300
1850
2000
2150
2300
Elevation (m)
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Appendix Figure S1: Comparison of different methods to detect the probability of seed
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caching by nutcrackers, here depicted as a function of elevation. While in (a) 119 seed-
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caching observations and 360 random samples (79 samples with caches and 281 without
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caches) are combined, (b) shows the probability of caching based on random samples
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only (79 samples with caches and 281 without caches). Both figures show similar pattern
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with highest caching rates at intermediate observations. Also, unbalanced sampling of
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seed-caching observations across the elevational gradient (i.e., more observations at
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intermediate elevations compared to the balanced random sampling) did not affect the
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results. Generalized linear mixed effects models with binomial errors that are fitted in (a)
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and (b) include the study region as random effect. In both models a linear and a quadratic
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term are fitted. Significance level: *** = p < 0.001.
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Appendix Figure S2: Generalized linear mixed-effects models showing the effect of
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understory vegetation cover and soil moisture on the probability of (a) seed caching by
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Spotted nutcrackers (Nucifraga caryocatactes), (b) seedling establishment of Swiss stone
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pine (Pinus cembra) and (c) Swiss stone pine seed cache pilferage by rodents. While
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effects of environmental variables on seed caching and seedling establishment were
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significant and opposed to each other, there was no significant effect on cache pilferage.
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For model details, please see Table S1. Significant effects are shown in colour, non-
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significant effects in grey.
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Appendix Figure S3: Relationship between predicted probabilities of seed caching and
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seedling establishment as a function of understory vegetation cover and soil moisture.
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The negative relationship indicates that the probability of seedling establishment
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decreases with increasing probability of seed caching. For visualization purposes, a
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negative exponential curve has been fitted.
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