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SUPPLEMENTARY MATERIAL
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Appendix S1. Model Specification and Fitting
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Though we described the prediction of species probability of occurrence using a Bayesian
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logistic regression in greater detail elsewhere (Bell et al., 2013), we will briefly describe our
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methodology. For each forested FIA plot i in the study area, we modeled the probability of
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species occurrence as a Bernoulli process with a logit link function
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yi ~ Bernoulli (qi )
(S1)
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i = logit-1(xi) = (1 + exp[xi])-1
(S2)
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where yi = 1 if the species was present at plot i and zero otherwise, i was the probability of
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species occurrence on plot i, xi was the 1 by k vector of covariates with main effects, quadratic
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terms, and interaction terms for mean winter temperature, the difference between summer and
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winter temperature, winter precipitation, and summer precipitation for plot i, and  = [0, 1, …,
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k] was the k by 1 vector of associated parameters for the logistic regression. An weak prior
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distribution for  was assumed to be multivariate normal with mean vector b = [0, …, 0] and
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covariance matrix Vb, where diagonal values (i.e., variances) equaled 1000 and off-diagonal
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values (i.e., covariances) equaled zero. Thus, the conditional posterior for the logistic regression
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parameters  was
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p ( b y, x, b,Vb ) ~ Õ Bernoulli yi logit -1 ( xi b ) ´ Õ N k ( b b,Vb )
i
(
)
(S3)
k
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where y was the n by 1 vector of observations yi, and xi was the n by k matrix of covariates for
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plot i. The model was fit with a Gibbs sampler with an adaptive Metropolis algorithm (Shaby &
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Wells, 2010). MCMC simulations were allowed to run for 125,000 steps. The first 75,000 steps
Bell et al. Supplement -- 1
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were discarded before posterior parameter estimates were constructed. Mean parameter estimates
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and standard deviations are reported in (Bell et al., 2013).
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Predictions of current and future probability of species occurrence were based on 2000
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realizations of the parameter estimates. First, 2000 realizations of the parameters were randomly
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sampled from the MCMC output. Then, the probability of species occurrence at each plot was
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calculated for each climate change scenario based on the 2000 parameter realizations. We
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averaged the 2000 estimates to calculate the mean predicted probability of occurrence at each
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plot i. These predictions incorporate parameter uncertainty, though this uncertainty is not
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explicitly explored in further detail in this paper.
Bell et al. Supplement -- 2
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Appendix S2: Additional comparisons of contemporary and future climatic suitabilities for
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different species and climate change scenarios.
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Fig. S1. High (red), intermediate (blue), and low (gray) suitability plots for (a) A. lasiocarpa, (b)
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P. engelmannii, (c) P. contorta, and (d) P. ponderosa as well as plots outside the predicted
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climate envelope (light gray). Only plots currently occupied by the focal species were plotted.
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State boundaries are outlined by dashed, black lines and the study region is outlined by the bold,
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black line.
Bell et al. Supplement -- 3
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(b)
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
(d)
(c)
current
A1B
A2
B1
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
current
A1B
A2
B1
proportion of plots
(a)
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Fig. S2. Proportion of FIA plots currently occupied by each species categorized as high (red),
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intermediate (blue), and low (dark gray) suitability as well as plots outside the climate envelope
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(light gray) for current climate compared to the future climatic suitabilities under three climate
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change scenarios for (a) A. lasiocarpa, (b) P. engelmannii, (c) P. contorta, and (d) P. ponderosa.
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Bell et al. Supplement -- 4
(a)
(b)
p(occurrence) under A1B scenario
1
0
0
0
1
4
0
0
0
5
0
0
4
11
0
0
4
15
0
1
10
14
0
7
21
13
9 23 19
6
6 20
7
1
(c)
(d)
1
0 0
0
1
5 6 13
15
0 0
1
8
0 1 8
0 5 27 24
22
3
3 4 4
1 1 2
7 7 14
7
4
9
0
1
0
p(occurrence) under current climate
1
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Fig. S3. Implications of changing climate for abundance of suitable areas assuming no migration
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(i.e., persistence), presented as the probability of species occurrence for (a) A. lasiocarpa, (b) P.
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engelmannii, (c) P. contorta, and (d) P. ponderosa under current vs. future climate (based on
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scenario A1B) are presented (gray points) with the percentage of plots transitioning between
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each suitability category (blue indicates increases, red indicates decreases, and black indicates no
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change) overlaid. Solid lines separate low suitability plots from plots outside the climate
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envelope, the dashed lines separate intermediate and low suitability plots, and the dotted line
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separates high and intermediate suitability plots.
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Bell et al. Supplement -- 5
(a)
(b)
p(occurrence) under B1 scenario
1
0
0
0
0
6
0
0
0
6
0
0
4
12
0
0
3
17
0
1
10
13
0
3
23
10
9 23 19
4
6 24
6
0
(c)
(d)
1
0 0
0
3
5 4 9
15
0 0
2
10
0 2 14
0 5 25 16
21
0
3 3 5
1 1 3
7 9 15
8
3
8
0
1
0
p(occurrence) under current climate
1
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Fig. S4. Implications of changing climate for abundance of suitable areas assuming no migration
58
(i.e., persistence), presented as the probability of species occurrence for (a) A. lasiocarpa, (b) P.
59
engelmannii, (c) P. contorta, and (d) P. ponderosa under current vs. future climate (based on
60
scenario B1) are presented (gray points) with the percentage of plots transitioning between each
61
suitability category (blue indicates increases, red indicates decreases, and black indicates no
62
change) overlaid. Solid lines separate low suitability plots from plots outside the climate
63
envelope, the dashed lines separate intermediate and low suitability plots, and the dotted line
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separates high and intermediate suitability plots.
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Bell et al. Supplement -- 6
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Table S1. FIA plot sample size and probability of species occurrence thresholds used to define
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high, intermediate, and low suitability as well as outside the climate envelope (based on true skill
69
statistics; see Methods).
total sample
high-intermediate
intermediate-low
low-outside
size
threshold
threshold
threshold
Abies lasiocarpa
4235
0.680
0.443
0.180
Picea engelmannii
4186
0.639
0.405
0.110
Pinus contorta
4013
0.533
0.371
0.110
Pinus ponderosa
5732
0.591
0.376
0.265
species
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