1
2
Figure S1: Daily fluctuations in nighttime (3:00 am; a) and daytime (3:00 pm; b) soil temperature, and daytime soil volumetric water
3
content (c) from 0-5 cm depth from December 2011 through August 2012 (a and b) or November 2012 (c), at a thinned canopy block.
46
4
Manipulations in February and March 2012 affected the duration of snow cover, as evidenced by both daytime and nighttime
5
temperatures at zero when snow was on the ground, and above zero once snow melted. Manipulations did not directly affect soil
6
moisture (c).
47
7
Table S1: Annual mean snowfall total (in cm) and associated standard deviation (sd) for each
8
canopy class – snow treatment combination, across the three years of the study. Snow treatment
9
categories are reduced (-), increased (+) and ambient (A)
10
2011-2012 2012-2013 2013-2014
Canopy Snow mean sd
mean sd mean sd
152.4 14.4
62.2 1.8
14 1.8
Open +
344.2 16.2
188 3.6 100.3 1.8
A
212.1
9 104.1
0
48.3 3.6
106.4 2.5
28.9 1.3
8.6 1.3
Thinned +
241 8.3
78.1
4
53.7 5.8
A
150.8 3.6
42.5 2.6
26 3.5
114.3
18
25.4 3.6
6.3 1.8
Closed +
226.1 10.8
64.8
9
33 3.6
A
154.9 14.4
34.3 1.8
15.2 2.3
97.8 41.3
17.8 2.4
5.1 1.1
Dense +
172.7 61.1
33 1.2
17.8 7.2
A
124.5 46.7
21.6 1.8
7.6 3.6
11
46
12
Table S2: Structure of annual population projection matrix. Annual transition probabilities in
13
this matrix are given in Table S2.
14
Seed 1
Seed
B
Yr 1
Yr 2
Pre-A
A
Seed 1
0
0
0
0
0
Nas
Seed B
Pd2
PdB
0
0
0
0
Yr 1
Ps1y1
PsBy1
0
0
0
Nasdlg
Yr 2
0
0
Py1y2
0
0
0
Pre-A
0
0
0
Py2pa
Ppa
0
A
0
0
0
Py2a
Pmpa
Pa
47
15
Appendix S3
16
Statistical models of component probabilities
17
To model variation in component (i.e. sub-annual) probabilities as a function of canopy
18
closure, fire, and snowpack, we used a logistic regression approach. These probabilities included
19
germination and seasonal survival rates of seedlings. For canopy closure and fire, because the
20
treatments were imposed at the block level, we assumed independence between replicates and
21
used a generalized linear model structure:
22
𝑦~Bin(𝑛, 𝑝); 𝑙𝑜𝑔𝑖𝑡(𝑝) = 𝛽⃑ 𝑋̅
Eq. 1
23
where 𝑦 is the observed number of successful transitions to a given state, 𝑛 is the initial number
24
of individuals, 𝑝 is the component probability, and 𝛽⃑ is a vector of coefficients for design matrix
25
𝑋̅, which contains the different states of the treatment variable in question (canopy closure or
26
fire). We fit the models using maximum likelihood and calculated a standard deviation σ of each
27
element of 𝛽⃑ by sampling the posterior model fit 10,000 times to obtain a distribution of each 𝛽.
28
In the case of canopy closure, many of the transition probabilities had a strong unimodal
29
relationship to the continuous form of the variable (one minus proportion light transmittance),
30
rather than a linear relationship, so we chose to keep this variable as a categorical factor. Thus
31
the states of 𝑋̅ are Open, Thinned, Closed and Dense for canopy closure, and Unburned and
32
Burned for fire, which was only applied to the Thinned canopy class because of forest
33
regulations. Parameters 𝛽⃑ represent the logit of a given component probability 𝑝 in different
34
scenarios of 𝑋̅ (e.g. dense canopy closure, or thinned canopy closure with fire). For each
35
component probability, we used Akaike’s Information Criterion (AIC) to compare the model
36
described in Eq. 1 against a null model with no effect of 𝑋̅, using AICc to correct for small
37
sample sizes in cases where the initial species pool was low (Burnham & Anderson, 2004). We
48
38
used sequential model selection to determine the value of 𝛽 assigned to a particular treatment
39
combination: first we allowed 𝛽⃑ to vary among canopy classes if the canopy closure model had
40
more support than a null model with no canopy effect, indicated by ΔAICc >2 (Burnham &
41
Anderson, 2002). If the canopy closure model did not have more support than the null model, we
42
set the inverse logit of the null model parameter, 𝑖𝑛𝑣. 𝑙𝑜𝑔𝑖𝑡(𝛽0 ), as the baseline transition
43
probability across all canopy classes. Then, because fire only occurred in the Thinned canopy
44
class, we allowed the previously selected parameter estimates for the Thinned canopy class from
45
the canopy closure model to be replaced by separate burned and unburned estimates from the fire
46
model, if the fire model had more support than the null model. Unlike comparable methods of
47
estimating parameters from multiple models, such as stepwise regression, this information-
48
theoretic method of assigning parameter values to data allows for evaluation of non-nested
49
alternate models and incorporation of a priori information on the plausibility of certain model
50
combinations (Hegyi & Garamszegi, 2011).
51
For snowpack, because treatments were nested within blocks, we quantified the effect of
52
snowpack on each component probability p using a multilevel regression (i.e. mixed-effects)
53
approach (Gelman & Hill, 2007). We used a modified version of Eq. 1 such that 𝑙𝑜𝑔𝑖𝑡(𝑝) =
54
𝛽𝑋 + (1|𝐵𝑙𝑜𝑐𝑘), which we fit using the lmer package in R (Bates et al., 2013). The (1|𝐵𝑙𝑜𝑐𝑘)
55
syntax specifies that Block is a random-intercept term. The model therefore accounts for overall
56
variation among blocks prior to assigning a parameter 𝛽 to the fixed-effects term 𝑋, which in this
57
case represents total winter snowfall total. These multilevel models of snowpack effects were fit
58
to data that was first subset into the five unique disturbance classes (Open, Thinned+Burned,
59
Thinned+Unburned, Closed and Dense), thereby allowing snowpack effects to vary depending
60
on the canopy and fire condition. Within each disturbance class, if the snowpack effects model
49
61
had more support than a null model of the same data (Δ AICc>2), we replaced the previous
62
estimate of p for that disturbance class with three estimates of p calculated as 𝑝 = 𝑙𝑜𝑔𝑖𝑡 −1 (𝛽𝑋),
63
where 𝑋 represents three different scenarios for annual snowfall total. We calculated a standard
64
deviation for each estimate of p, based on uncertainty in the multilevel model estimates of 𝛽, by
65
bootstrapping the multilevel model 10,000 times for each value of 𝑋 using the ez package in R
66
(Lawrence, 2012).
67
To get a clearer picture of the relative magnitudes of variation within treatment plots and
68
among blocks – i.e. how important among-block variation was in our experiment, we compared
69
the block-level variance in our study to the within-plot variance, for each parameter that was
70
estimated statistically. To assess block-level variance, we calculated an among-block variance
71
for each combination of snowpack level-fire-canopy cover. For instance, for the Open canopy
72
class we calculated the variance in percentage of first-year germinants for a given species,
73
separately for the increased snow, ambient snow, and decreased snow treatments (among two
74
blocks in each case). To assess plot-level variance, we calculated the variance in the same
75
parameter of interest, among the seven rows per plot, for each combination of snowpack level-
76
fire-canopy cover-block. We then took the average value of these plot-level variances across all
77
blocks. Ultimately, therefore, we obtained both plot-level variance and block-level variance for
78
each combination of snowpack level-fire-canopy cover. We found that for every parameter of
79
interest except for the probability of maturity (Pm3), the variance within plots was higher than
80
the variance among blocks. That Pm3 was the only parameter to have greater among-block
81
variance than within-block variance is not surprising, as only two of the eight blocks in the
82
Thinned canopy class had any individuals that reached maturity during year 3. Overall, the
83
relatively low among-block variation supports the formal statistical analysis in the paper, which
50
84
found significant treatment effects for many parameters, but relatively small block random
85
effects.
51
86
Appendix S4: Sensitivity and elasticity scores for Scotch and Spanish broom under different
87
climate-canopy disturbance scenarios.
88
Table S4.1: Elasticity scores for Scotch broom (a) and Spanish broom (b) in the open canopy
89
class scenario under intermediate snowfall scenario (100 cm).
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
0
0
0
0
0
0.073
Seed1
0
0
0
0
0
0.024
SeedB
0
0
0
0
0
0
SeedB
0.008
0.006
0
0
0
0
Yr1
0.073
0
0
0
0
0.16
Yr1
0.016
0.008
0
0
0
0.135
Yr2
0
0
0.233
0
0
0
Yr2
0
0
0.159
0
0
0
PreA
0
0
0
0.039
0.027
0
PreA
0
0
0
0.159
0.163
0
A
0
0
0
0.194
0.039
0.161
A
0
0
0
0
0.159
0.163
90
91
Elasticity Scotch O.100
a
Elasticity Spanish O.100
b
92
93
Table S4.2: Sensitivity scores for Scotch broom (a) and Spanish broom (b) in the open canopy
94
class scenario under intermediate snowfall scenario (100 cm).
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
0
0
0
0
0
0.001
Seed1
0
0
0
0
0
0
SeedB
0
0
0
0
0
0
SeedB
0.013
0.014
0
0
0
0
Yr1
2.769
0
0
0
0
0.038
Yr1
8.932
9.758
0
0
0
0.094
Yr2
0
0
0.752
0
0
0
Yr2
0
0
0.437
0
0
0
PreA
0
0
0
0.501
0.066
0
PreA
0
0
0
0.252
0.322
0
A
0
0
0
0.753
0.099
0.395
A
0
0
0
0
0.254
0.322
95
96
a
Sensitivity Scotch O.100
Sensitivity Spanish O.100
b
52
97
Table S4.3: Elasticity scores in the thinned canopy class scenario under 25, 100 and 175 cm
98
annual snowfall for Scotch broom (a=25 cm, c=100 cm, e=175 cm) and Spanish broom (b=25
99
cm, d=100 cm, f=175 cm)
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
0
0
0
0
0
0.084
Seed1
0
0
0
0
0
0.04
SeedB
0.008
0.001
0
0
0
0
SeedB
0.004
0.001
0
0
0
0
Yr1
0.076
0.008
0
0
0
0.079
Yr1
0.036
0.004
0
0
0
0.143
Yr2
0
0
0.163
0
0
0
Yr2
0
0
0.183
0
0
0
PreA
0
0
0
0.096
0.12
0
PreA
0
0
0
0.183
0.111
0
A
0
0
0
0.067
0.096
0.203
A
0
0
0
0
0.183
0.111
100
101
a
b
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
SeedB
Yr1
Yr2
PreA
A
0
0
0
0
0
0.073
Seed1
0
0
0
0
0
0.041
SeedB
0.008
0.002
0
0
0
0
SeedB
0.008
0.003
0
0
0
0
Yr1
0.064
0.008
0
0
0
0.052
Yr1
0.032
0.008
0
0
0
0.066
Yr2
0
0
0.125
0
0
0
Yr2
0
0
0.107
0
0
0
PreA
0
0
0
0.088
0.189
0
PreA
0
0
0
0.107
0.261
0
A
0
0
0
0.036
0.088
0.266
A
0
0
0
0
0.107
0.261
Elasticity Scotch T.UB.100
c
Elasticity Spanish T.UB.100
d
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
0
0
0
0
0
0.041
Seed1
0
0
0
0
0
0.018
SeedB
0.006
0.002
0
0
0
0
SeedB
0.005
0.002
0
0
0
0
Yr1
0.035
0.006
0
0
0
0.022
Yr1
0.013
0.005
0
0
0
0.019
Yr2
0
0
0.062
0
0
0
Yr2
0
0
0.036
0
0
0
PreA
0
0
0
0.055
0.331
0
PreA
0
0
0
0.036
0.415
0
A
0
0
0
0.008
0.055
0.379
A
0
0
0
0
0.036
0.415
104
105
Elasticity Spanish T.UB.25
Seed1
102
103
Elasticity Scotch T.UB.25
e
Elasticity Scotch T.UB.175
Elasticity Spanish T.UB.175
f
53
106
Table S4.4: Sensitivity scores in the thinned canopy class scenario under 25, 100 and 175 cm
107
annual snowfall for Scotch broom (a=25 cm, c=100 cm, e=175 cm) and Spanish broom (b=25
108
cm, d=100 cm, f=175 cm)
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
0
0
0
0
0
0.002
Seed1
0
0
0
0
0
0.002
SeedB
0.015
0.009
0
0
0
0
SeedB
0.01
0.005
0
0
0
0
Yr1
0.595
0.363
0
0
0
0.016
Yr1
0.799
0.374
0
0
0
0.034
Yr2
0
0
0.335
0
0
0
Yr2
0
0
0.546
0
0
0
PreA
0
0
0
0.229
0.216
0
PreA
0
0
0
0.392
0.294
0
A
0
0
0
1.821
1.719
0.366
A
0
0
0
0
0.397
0.294
109
110
a
b
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
SeedB
Yr1
Yr2
PreA
A
0
0
0
0
0
0.002
Seed1
0
0
0
0
0
0.001
SeedB
0.013
0.01
0
0
0
0
SeedB
0.011
0.011
0
0
0
0
Yr1
0.457
0.354
0
0
0
0.01
Yr1
0.38
0.392
0
0
0
0.009
Yr2
0
0
0.751
0
0
0
Yr2
0
0
0.984
0
0
0
PreA
0
0
0
0.172
0.278
0
PreA
0
0
0
1.485
0.367
0
A
0
0
0
0.808
1.305
0.391
A
0
0
0
0
0.122
0.367
Sensitivity Scotch T.UB.100
c
Sensitivity Spanish T.UB.100
d
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
0
0
0
0
0
0.001
Seed1
0
0
0
0
0
0
SeedB
0.007
0.008
0
0
0
0
SeedB
0.005
0.007
0
0
0
0
Yr1
0.226
0.233
0
0
0
0.004
Yr1
0.116
0.174
0
0
0
0.002
Yr2
0
0
3.212
0
0
0
Yr2
0
0
3.919
0
0
0
PreA
0
0
0
0.084
0.386
0
PreA
0
0
0
1.05
0.451
0
A
0
0
0
0.137
0.628
0.441
A
0
0
0
0
0.032
0.451
113
114
Sensitivity Spanish T.UB.25
Seed1
111
112
Sensitivity Scotch T.UB.25
e
Sensitivity Scotch T.UB.175
Sensitivity Spanish T.UB.175
f
54
115
Table S4.5: Elasticity scores for Scotch broom (a) and Spanish broom (b) in the closed canopy
116
class scenario under intermediate snowfall scenario (100 cm).
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
0
0
0
0
0
0.045
Seed1
0
0
0
0
0
0.028
SeedB
0.011
0.012
0
0
0
0
SeedB
0.008
0.005
0
0
0
0
Yr1
0.034
0.011
0
0
0
0.084
Yr1
0.02
0.008
0
0
0
0.145
Yr2
0
0
0.129
0
0
0
Yr2
0
0
0.173
0
0
0
PreA
0
0
0
0.129
0.209
0
PreA
0
0
0
0.173
0.133
0
A
0
0
0
0
0.129
0.209
A
0
0
0
0
0.173
0.133
117
118
Elasticity Scotch C.100
a
Elasticity Spanish C.100
b
119
120
Table S4.6: Sensitivity scores for Scotch broom (a) and Spanish broom (b) in the closed canopy
121
class scenario under intermediate snowfall scenario (100 cm).
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
0
0
0
0
0
0.001
Seed1
0
0
0
0
0
0.001
SeedB
0.016
0.023
0
0
0
0
SeedB
0.015
0.012
0
0
0
0
Yr1
0.519
0.745
0
0
0
0.013
Yr1
1.397
1.143
0
0
0
0.049
Yr2
0
0
0.273
0
0
0
Yr2
0
0
0.552
0
0
0
PreA
0
0
0
0.253
0.338
0
PreA
0
0
0
0.319
0.306
0
A
0
0
0
0
2.089
0.338
A
0
0
0
0
0.324
0.306
122
123
a
Sensitivity Scotch C.100
Sensitivity Spanish C.100
b
55
124
Table S4.7: Elasticity scores for Scotch broom (a) and Spanish broom (b) in the dense canopy
125
class scenario under intermediate snowfall scenario (100 cm).
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
0
0
0
0
0
0
Seed1
0
0
0
0
0
0.018
SeedB
0
0
0
0
0
0
SeedB
0.008
0.009
0
0
0
0
Yr1
0
0
0
0
0
0.107
Yr1
0.01
0.008
0
0
0
0.121
Yr2
0
0
0.107
0
0
0
Yr2
0
0
0.14
0
0
0
PreA
0
0
0
0.107
0.287
0
PreA
0
0
0
0.14
0.203
0
A
0
0
0
0
0.107
0.287
A
0
0
0
0
0.14
0.203
126
127
Elasticity Scotch D.100
a
Elasticity Spanish D.100
b
128
129
Table S4.8: Sensitivity scores for Scotch broom (a) and Spanish broom (b) in the dense canopy
130
class scenario under intermediate snowfall scenario (100 cm).
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
SeedB
Yr1
Yr2
PreA
A
Seed1
0
0
0
0
0
0
Seed1
0
0
0
0
0
0.001
SeedB
0
0
0
0
0
0
SeedB
0.011
0.011
0
0
0
0
Yr1
0
0
0
0
0
0.035
Yr1
0.38
0.392
0
0
0
0.009
Yr2
0
0
0.192
0
0
0
Yr2
0
0
0.984
0
0
0
PreA
0
0
0
0.178
0.393
0
PreA
0
0
0
1.485
0.367
0
A
0
0
0
0
1.494
0.393
A
0
0
0
0
0.122
0.367
131
132
a
Sensitivity Scotch D.100
Sensitivity Spanish T.UB.100
b
133
134
135
136
137
138
139
140
141
Literature Cited
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using Eigen and S4. R package version 1.0-5. CRAN.R-project.org/package=lme4.
Burnham KP, Anderson DR (2002) Model selection and multimodel inference. A practical
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