1
APPENDICES
2
3
APPENDIX S1 Outline of the species distribution models used.
4
5
6
Species Distribution Models description (inspired by Thuiller et al. 2009 and Franklin
2010).
7
8
9
10
Random forests (RF): A machine-learning method – a combination of tree predictors in
which each tree depends on the values of a random vector sampled independently and
with the same distribution for all trees in the forest. (Breiman, 2001)
11
12
13
14
Classification tree analysis (CTA): A classification method – a 50-fold cross-validation
to select the best trade-off between the number of leaves of the tree and the explained
deviance. (Breiman et al., 1984)
15
16
17
Multivariate adaptive regression splines (MARS): A non-parametric regression method,
combining elements of CTA and GAM. (Friedman, 1991)
18
19
20
21
Generalized linear model (GLM): A regression method, with polynomial terms for
which a stepwise procedure is used to select the most significant variables. (McCullagh
& Nelder, 1989)
22
23
24
25
Generalized additive model (GAM): A regression method more flexible than GLM, we
used a spline of 4 degrees of freedom and a stepwise procedure to select the most
parsimonious model. (Hastie & Tibshirani, 1990)
26
27
28
29
Generalized Boosting Models (GBM): A method that fits a large tree of simple models,
together aimed at giving a more robust estimate of the response. Based on Boosted
Regression Tree algorithm. (Friedman, 2001)
30
31
32
33
Artificial neural networks (ANN): A machine-learning method, with the mean of three
runs used to provide predictions and projections. (Ripley, 1996)
34
35
36
Flexible discriminant Analysis (FDA):A supervised classification method based on a
mixture of normals obtain a density estimation of each class. (Hastie and Tibshirani,
1996)
37
38
39
40
REFERENCES
41
42
43
Breiman, L., Friedman, J.H., Olshen, R.A., & Stone, C.J. (1984) Classification and
regression trees. Chapman and Hall, New York.
44
45
Breiman, L. (2001) Random forests. Machine Learning, VOLUME? 5-32.
46
47
Breiman, L (2002).Manual On Setting Up, Using, And Understanding Random Forests
48
V3.1. http://oz.berkeley.edu/users/breiman/Using_random_forests_V3.1.pdf
49
50
51
Franklin, J. (2010) Mapping species distributions: Spatial inference and prediction.
Cambridge University Press, Cambridge, UK.
52
53
54
Friedman, J.H. (1991) Multivariate additive regression splines. Annals of Statistics, 19,
1-141.
55
56
57
Friedman, J.H. (2001) Greedy function approximation: A gradient boosting machine.
Annals of Statistics, 29, 1189-1232.
58
59
60
Hastie, T.J. and Tibshirani, R. (1990) Generalized additive models. Chapman and Hall,
London.
61
62
63
Hastie, T. and Tibshirani, R. (1996) Discriminant analysis by Gaussian mixtures.
Journal of the Royal Statistical Society Series B, 58, 155-176.
64
65
McCullagh, P. and Nelder, J.A. (1989) Generalized linear models. Chapman and Hall.
66
67
68
Ripley, B.D. (1996) Pattern recognition and neural networks. Cambridge University
Press, Cambridge.
69
70
71
72
Thuiller, W., Lafourcade, B., Engler, R. & Araújo, M. B. (2009) BIOMOD : A platform for
ensemble forecasting of species distributions. Ecography, 32, 369-373.
73
APPENDIX S2 Metrics of exposure to climate change
74
75
76
77
78
Broad species geographic attributes of conservation (range level or current distribution level).
Each metric is provided with its formula and a description. In grey, relevant studies using the
same or very similar metric/concept.
79
RANGE LEVEL
Conservation applied to potential suitable habitat; range-wide
ecosystem management perspective.
80
81
Species range change (SRC)
82
83
84
85
Differences in potential suitable area between two periods. Area Gained is the total area
predicted suitable at time 2 but not time 1, Area Lost is predicted suitable at time 1 but not
time 2.
86
87
𝑆𝑅𝐶 = 𝐴𝑔𝑎𝑖𝑛𝑒𝑑 − 𝐴𝑙𝑜𝑠𝑡 ,
88
89
90
where 𝐴 is area
91
92
Purpose: Indicates the degree of shrinkage or expansion of potential suitable habitat.
93
94
Range exposure to migration (REM)
95
96
97
98
99
100
101
Difference in habitat suitable area between full (𝐴𝑓𝑢𝑙𝑙 ) and null (𝐴𝑛𝑢𝑙𝑙 ) dispersal assumptions.
Area of suitable habitat assuming full dispersal is the total area predicted suitable at time 2;
area assuming null (no) migration is the area of intersection of habitat predicted suitable at
time 1 and time 2 (stable habitat).
102
𝑅𝐸𝑀
=
(𝐴𝑓𝑢𝑙𝑙 −𝐴𝑛𝑢𝑙𝑙 )
𝐴𝑛𝑢𝑙𝑙
,
103
104
where 𝐴 is area
105
106
107
Purpose: Assess the degree of disparity between assumption of full migration and no
migration. REM represents the potential role of migration on filling potential suitable habitat.
108
109
(Araújo & New, 2007 suggest bounding boxes between these assumptions;
110
Svenning & Skov 2004 use current to potential distribution)
111
112
113
Range change velocity (RCV)
114
115
116
Differences the velocity of climatic exposure between leading edge (unsuitable cells in t0
becoming suitable in t1) and trailing edge (suitable cells in t0 becoming unsuitable in t1).
117
118
𝑁
RCV = (𝑣̅𝑔𝑎𝑖𝑛𝑒𝑑 − 𝑣̅𝑙𝑜𝑠𝑡 ) =
119
𝑁
𝑐;𝑢→𝑠
𝑐;𝑠→𝑢
∑𝑐=1
𝑣𝑐;𝑢→𝑠 ∑𝑐=1
𝑣𝑐;𝑠→𝑢
−
𝑁𝑐;𝑢→𝑠
𝑁𝑐;𝑠→𝑢
120
121
122
123
124
and 𝑣𝑐;𝑢 →𝑠 is the bioclimatic velocity in cell c and Nc is the number of cells changing from
unsuitable to suitable (𝑢 → 𝑠). Conversely, 𝑣𝑐;𝑠 →𝑢 is the bioclimatic velocity in cell c and Nc is
the number of cells changing from suitable to unsuitable (𝑠 → 𝑢) .
125
126
Velocity is calculated as follows:
127
128
129
𝑣𝑐 =
Δ𝑇𝑐
,
Δ𝑆𝑐
130
where Δ𝑇𝑐 is the temporal gradient of probabilities 𝑃 between 𝑡1 and 𝑡0,
131
132
Δ𝑇𝑐 =
𝑃𝑐,𝑡1 − 𝑃𝑐,𝑡0
,
Δt
133
134
and 𝑆𝑐 is the spatial gradient of probabilities in cellc. Gradients are defined as:
135
136
2
2
𝑆𝑖,𝑗 = √(Sc;horizontal
+ Sc;vertical
),
137
138
139
140
where Sc;horizontal is spatial gradient of probabilities in horizontal direction for a target cell c,
and i and Sc;vertical is spatial gradient of probabilities in vertical direction for a target cell c
(see figure)
141
142
Cell position scheme (target cell in bold):
143
Pa
Pd
Pg
Pb
𝒄 = 𝐏𝐜
Ph
Pj
Pf
Pi
144
145
146
𝑆c;horizontal =
ΔPc;horizontal (Pj + 2Pf + Pi ) – (Pa + 2Pd + Pg )
=
Δ𝑥
8 × cell size
147
ΔPc;vertical
Δ𝑥
𝑆c;vertical =
149
150
Where Pc is the probability in cell c, and so for.
151
152
Purpose: To assess the balance between the velocity of trailing edge and leading edge in order
to determine which one is faster in acquiring or losing suitable conditions.
153
154
=
(Pa +2Pb +Pj ) – (Pg + 2Ph + Pi )
8 ×cell size
148
155
Range spatial fragmentation (RSF)
156
157
Number of discrete habitat patches at a given time period.
158
159
160
Purpose: To assess spatial fragmentation of potential suitable habitats. (Opdam & Wascher,
2004)
161
162
163
Range Spatial Aggregation (RSA)
164
165
Percent of total suitable habitat occupied by the largest (suitable) patch at a given time period.
166
167
168
𝐿𝑃𝐼 =
𝐴𝑙𝑎𝑟𝑔𝑒𝑠𝑡_𝑃𝑎𝑡𝑐ℎ
× 100,
𝐴𝑠𝑢𝑖𝑡𝑎𝑏𝑙𝑒
169
170
where 𝐴 is area
171
172
173
174
175
176
177
178
179
180
181
182
Purpose: To assess spatial aggregation of potential suitable habitats. (Opdam & Wascher,
2004)
POPULATIONS
LEVEL
Conservation applied to current known distribution (species plots);
local management strategies and in situ conservation.
183
184
185
Population migration effort (PME)
186
187
188
189
190
Average distance along the most climatically suitable route for current woodland locations
(plot) to reach a suitable patch. Cost resistance surface is determined by probabilities of
presence.
191
192
𝑁
193
PME =
𝑝
∑𝑝=1
l(cp,c
final ,f(P))
𝑁𝑝
194
195
196
197
198
199
where 𝑝 is species plot, and 𝑙 is the distance between the cell matching the species plot cp and
the nearest suitable cell cfinal determined by the function of probability of occurrence f(P) and
𝑁𝑝 is the total amount of plots.
200
201
202
203
Purpose: to incorporate a surrogate metric of meta-population persistence and potential
connectivity processes.
204
205
206
207
208
209
210
(Skov & Svenning 2004, use tree cover for resistance, Wang et al. 2008 found significant
relationship between habitat suitability resistance and gene-flow; Blaum et al. 2012)
211
Populations climate-site exposure (PCS)
212
213
214
Percentage of current woodland locations (plots) changing from suitable in t0 to unsuitable
conditions in t1.
215
216
217
𝑃𝐶𝑆 =
𝑁𝑝;𝑠→𝑢
× 100,
𝑁𝑝
218
219
220
221
where 𝑁𝑝;𝑠→𝑢 indicating the number of plots of decreasing suitability in time and 𝑁𝑝 is the
total amount of plots.
222
223
224
Purpose: to assess the extent of current species woodlands exposed to new environmental
conditions.
225
226
(Thomas et al. 2004; Thuiller et al. 2005)
227
228
229
Populations change in velocity (PCV)
230
231
Mean bioclimatic velocity of woodland plots in decline.
232
233
𝑁
234
𝑃𝐶𝑉 =
𝑝;𝑠→𝑢
∑𝑝=1
𝑣𝑝
𝑁𝑝;𝑠→𝑢
235
236
237
238
where 𝑣𝑝 is velocity 𝑣 in plot 𝑝 is assigned as the velocity in matching cell, and 𝑁𝑝;𝑠→𝑢
indicating plots of decreasing suitability in time.
239
240
Purpose: to assess the speed of change in exposure of current woodlands.
241
REFERENCES
242
243
244
245
Araújo, M. B. & New, M. (2007) Ensemble forecasting of species distributions. Trends in
Ecology and Evolution, 22, 42-47.
246
247
248
249
250
Blaum, N., Schwager, M., Wichman, M.C. & Rossmanith, E. (2012) Climate induced changes in
matrix suitability explain gene flow in a fragmented landscape – the effect of interannual
rainfall variability. Ecography, 35, 650–660.
251
252
253
254
Opdam, P. & Wascher, D. (2004) Climate change meets habitat fragmentation: Linking
landscape and biogeographical scale levels in research and conservation. Biological
Conservation, 117, 285-297.
255
256
257
Skov, F. & Svenning, J. (2004) Potential impact of climatic change on the distribution of forest
herbs in Europe. Ecography, 27, 366-380.
258
259
260
Svenning, J. & Skov, F. (2004) Limited filling of the potential range in European tree species.
Ecology Letters, 7, 565-573.
261
262
263
264
265
266
Thomas, C. D., Cameron, A., Green, R. E., Bakkenes, M., Beaumont, L. J., Collingham, Y. C.,
Erasmus, B. F. N., de Siqueira, M. F., Grainger, A., Hannah, L., Hughes, L., Huntley, B., van
Jaarsveld, A. S., Midgley, G. F., Miles, L., Ortega-Huerta, M., Townsend Peterson, A.,
Phillips, O. L. & Williams, S. E. (2004) Extinction risk from climate change. Nature, 427,
145-148.
267
268
269
270
Thuiller, W., Lavorel, S., Araújo, M. B., Sykes, M. T. & Prentice, I. C. (2005). Climate change
threats to plant diversity in Europe. Proceedings of the National Academy of Sciences
USA, 102, 8245-8250.
271
272
273
Wang, Y. H., Yang, K. C., Bridgman, C. L. & Lin, L. K. (2008) Habitat suitability modelling to
correlate gene flow with landscape connectivity. Landscape Ecology, 23, 989-1000.
274
275
276
APPENDIX S3 Maps of range change dynamics for the each combination of
species, periods and general circulation models analyzed.
277
278
PER1= Mid-21st century projections (2041-2070)
279
PER2= Late-21st century projections (2071-2100)
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
APPENDIX S4 Maps of bioclimatic velocity for the each combination of species,
periods and general circulation models analyzed.
307
PER1= Mid-21st century projections (2041-2070)
308
PER2= Late-21st century projections (2071-2100)
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331