Appendix S1 Constructing a Stochastic Life Table Response Experiments (SLTRE) with IID rates
1. Construct P-by-P matrices of stage transition rates for each period (t) for each population (m).
Denote these transition rates by the symbols bij(m)(t) for periods t = 1, …,T periods and populations m
= 1,…,M;
2. Assume that transition rates are IID. For each population, calculate the mean (time-averaged)
transition rates (µij(m)) and their standard deviations (σij(m)) across the T observations;
3. Construct a reference population (ref) whose transition rates for every period (t) are averages across
the M observed populations:
Bijre f(t) = (1/K) ∑m bij(m) (t) .
4. Compute the means and standard deviations of the transition rates for the reference population;
denote these by µij(ref), σij(ref).
5. Calculate stochastic elasticities Eijµ, Eijσ of the stochastic growth rate (aref) of the reference
population to changes in the mean and the variability, respectively, for every one of the P2 transition
rates that has a nonzero mean in the reference population. Here,
Eijµ = ∂ log λS / ∂ log µij ; Eijσ = ∂ log λS / ∂ log σij.
6. Calculate differences, for each year, between the means and standard deviations, respectively, of the
vital rates of each population and the means and standard deviations, respectively, of the reference
population. Differences are log ratios of mean values (log [µij(m) / µij(ref)] = log µij(m) – log µij(ref)) and
of the standard deviations of those rates (log [σij(m) / σij(ref)] = log σij(m) – log σij(ref)).
7. Calculate contributions of each vital rate to overall differences, between populations, in the
stochastic growth rate. Contributions of mean values are the products of mean differences and
elasticities to µij, Cijµ = Eijµ (log µij(m) – log µij(ref)), while contributions of differential variability are
the products of standard deviations and elasticities to σij, Cijσ = Eijσ (log σij(m) – log σij(ref)). Summed
across both types of contributions and across elements (i,j), they estimate the total differences,
between populations, in the stochastic growth rate a, where
am – aref = Σij [log μij(m) – log μij(ref)] Eijμ + Σij [log σij(m) – log μij(ref)] Eij
Appendix S3 Weather conditions and microclimate in the study area.
Local climate is characterized by a yearly average temperature of 8.6°C (range: 1.2-16.2), a total
precipitation of 780 mm y-1 and a reference evapotranspiration of 740 mm y-1. During the
growing season (apr-sept), these figures are 13.2°C (range: 7.9-16.2), 408 mm y-1 and 560 mm y1
respectively (Belgian Royal Meteorological Institute). Soils of calcareous grasslands consist
mainly of unprofiled, shallowly (i.e. max 15 cm deep) weathered, calcareous rock material with
limited water retention capacity and are therefore subject to extreme temperatures and long
periods of drought. The hilly aspect of many grassland patches strengthens this sensitivity. Most
grasslands are south exposed and slopes range from 0 to 70%. Hence, vegetation suffers more
rapidly from drought compared with flat, well-developed and deeper soils.
To assess weather conditions during the sampling period, we obtained weather data from
the automated station of Dourbes, in the middle of the study area. Minimum, maximum and
mean temperatures, mean relative humidity, total precipitation, amount of sunshine and wind
speed were combined into an integrative measure of climate, i.e. the aridity index (AI). This
index is the proportion of measured precipitation and potential crop evapotranspiration (ET0):
precipitat ion (mm month 1 )
with ET0 being the reference evapotranspiration, i.e. the rate
AI 
ET0 (mm month 1 )
of evapotranspiration of an extended surface of green grass, 12 cm tall and actively growing. ET0
was calculated according to Allen et al. (1998) using the Penman-Monteith method. The lower
AI, the more the vegetation suffers from drought. If AI <1, there is water shortage and vegetation
experiences water stress.
The Figure S1 below shows that the monitoring period was characterized by 3 extreme
weather events: the summer heat wave of 2003 during August and September, the spring drought
from May till June 2005, and finally the most extreme heath wave of 2006 from June till July
and in September. Aridity indices of these periods seriously differed from normal and were
unprecedented in the past 10 years.
Aridity index
1
0.5
0
JA JO JA JO JA JO JA JO JA JOJA JO JA JO JA JO JA JO JA JO
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
Fig. S1. Aridity index for the ten-year study period, based on the meteorological data of the
station of Dourbes located in the center of the study area. Values lower than 1 indicate a
precipitation shortage. The more the index falls below 1, the higher the precipitation deficit.
Climatic extreme values are highlighted with arrows. Months are indicated each three months,
starting with January.
Appendix S4 Population matrices for nine Anthyllis vulneraria populations sampled annually between 2003 and 2006.
Population
2003-2004
2004-2005
2005-2006
C (n = 216)
0
0.208
0.042
0.083
0
0
0.077
0.077
1.740
0
0
0.067
1.740
0.057
0
0.029
0
0.322
0.161
0.253
0
0.143
0.286
0.286
0.300
0
0
0.500
0.600
0
0
0.600
0
0
0.100
0.300
0
0
0.069
0.138
0.506
0
0.063
0.000
0.675
0.036
0.107
0.071
E (n = 277)
0
0.196
0.125
0.161
0
0
0.500
0.500
2.44
0
0
0.133
6.569
0
0
0.077
0
0.066
0.033
0.049
0
0.091
0
0
0.450
0.125
0.125
0.125
0.646
0
0.077
0.231
0
0.083
0
0.417
0
0
0
0.100
2.850
0
0
0
3.990
0
0
0.100
F (n = 464)
0
0.076
0.139
0.076
0
0
0
0
1.815
0.050
0
0
7.058
0.083
0.250
0.083
0
0.224
0.134
0.119
0
0
0.273
0.364
1.233
0.111
0.167
0.056
7.400
0.143
0.143
0.143
0
0.073
0.037
0.061
0
0.025
0.150
0.225
1.060
0.033
0.100
0.167
3.373
0
0.136
0.273
G (n = 68)
0
0
0.125
0.125
0
0
0
0
0.245
0.045
0.091
0.091
2.100
0
0
0.333
0
0.111
0
0.111
0
0
0
0
1.100
0
0
0
1.540
0
0
0
0
0
0.091
0.545
0
0
0
0.500
0
0
0
0
1.500
0
0
0.500
L (n = 682)
0
0.129
0.029
0.014
0
0
0
0
1.785
0
0
0
1.857
0.011
0
0.022
0
0.131
0.144
0.093
0
0.057
0
0.200
14.250
0
0
0
16.625
0.250
0
0.250
0
0
0.021
0.021
0
0
0.019
0.019
0.595
0.018
0.036
0.036
1.766
0
0.045
0.068
O (n = 523)
0
0.600
0.040
0.160
0
0.286
0.143
0.286
11.500
0.333
0
0
2.776
0.241
0
0.172
0
0.284
0.085
0.139
0
0.171
0.026
0.447
3.780
0
0
0
1.225
0.167
0.056
0.306
0
0.127
0.095
0.111
0
0.105
0.158
0.224
1.543
0.048
0.190
0
1.036
0.055
0.082
0.356
Q (n = 29)
0
0
0
1.000
0
0
0
0
0.150
0
0
0
0.175
0
0
0
0
0
0
1.000
0
0
0
0.667
0
0
0
0
0.250
0
0
1.000
0
0
0.250
0.250
0
0
0
0
0
0
0
0
1.429
0.143
0
0.571
R (n = 42)
0
0.250
0
0.250
0
0
0
0.167
0.700
0
0
0
0.613
0.125
0
0.250
0
0.286
0.286
0.286
0
0
0.333
0.333
0
0
0
0
0.600
0
0
1.000
0
0
0
0.333
0
0
0
0
0.700
0
0
0.333
0.613
0
0
0.625
S (n = 51)
0
0.167
0
0
0
0
0
0
2.100
0
0
0
0.817
0
0
0.167
0
0.333
0
0.333
0
0.500
0
0
0
0
0
0
7.000
0
0
1.000
0
0
0
0.111
0
0
0
0.750
0
0
0
0
1.400
0
0.200
0.200