1
1
Supplemental Tables
2
Table S1. Sampled species and populations, sample sizes for adults in the wild and common
3
garden seedlings (J=Jonaskop garden, K=Kirstenbosch garden), locality name, latitude,
4
longitude, rainfall, and elevation. H.H. = Hottentots Hollands. EC =Eastern Cape. KZN=Kwa-
5
Zulu Natal. All localities excluding those marked EC or KZN are in the Western Cape Province.
Sample
Mean
sizes,
Elevation
(mm/yr)
(m)
Species
Pop.
adult/J/K
Locality name
Latitude
P. aurea
DR
20/16/16
Doringrivier, Outeniqua
-33.87775
22.31026
669
792
aurea
LW
15/17/15
Langeberg-Wes, Robertson
-33.74354
19.90748
440
646
MP
40/14/13
Marloth, Langeberg-Wes
-33.99629
20.45651
882
239
RP
39/11/14
Robinson’s pass, Outeniqua
-33.90872
22.02348
723
544
RV
20/9/10
Riviersonderend
-34.06276
19.70707
473
584
P. aurea
KP
17/11/12
Klipspringer, De Hoop
-34.37912
20.58325
489
493
potbergensis
PB
18/13/22
Potberg, De Hoop
-34.42262
20.65524
420
228
P. lacticolor
GW
15/16/15
Grabouw, H.H.
-34.11947
18.97258
1218
618
LI
13/10/11
Limietberg, H.H.
-33.69506
19.13143
880
1263
LK
19/12/13
Landroskop, H.H.
-34.03944
18.99126
2069
1372
PK
40/15/16
Pofaddersnek, H.H.
-34.01826
19.07807
1260
836
PO2
23/15/15
Purgatory outspan, H.H.
-33.96764
19.14433
926
435
BS
18/5/4
Baviaanskloof, EC
-33.60970
24.50043
458
809
KM
13/16/16
Kleinmond, Kogelberg
-34.32715
19.00270
972
228
MS
20/12/16
Maanschynkop, Vogelgat
-34.38826
19.35095
534
866
OB
15/9/16
Oudebos, Kogelberg
-34.33402
18.93185
1089
403
TK
15/14/12
Tsitsikamma, EC
-33.94140
24.18693
784
251
P. mundii
Longitude
rainfall
2
P. punctata
BBP
13/2/8
Blesberg, Swartberg
-33.41927
22.68854
255
1959
CB
12/3/7
Cederberg
-32.51260
19.18215
414
1408
GB
27/3/3
Gydoberg, Ceres
-33.25397
19.48446
394
1363
JK
18/0/0
Jonaskop, Riviersonderend
-33.96950
19.50170
323
1396
KS
20/13/12
Kammanassieberg
-33.64508
22.95381
444
1105
SPP
20/12/11
Swartberg pass
-33.36256
22.06647
932
1208
P. hybrid
TW
17/13/11
Towerkop, Klein Swartberg
-33.44548
21.28841
348
975
P. subvestita
SE
15/6/10
Somerset East, Bosberg, EC
-32.69389
25.58685
543
1465
TD
20/7/10
Tor Doone, Hogsback, EC
-32.58046
26.93345
1169
1536
MC
16/4/0
Maclear, Potrivier Pass, EC
-30.92358
28.20812
905
1718
WZ
14/0/1
Near Weza, Kokstad, EC
-30.54535
29.6563
852
1638
SA
36/1/2
Sani Pass, KZN
-29.60925
29.36219
1063
1851
RN
35/0/0
Royal Natal, KZN
-28.68338
28.9178
969
1833
BBV
12/2/6
Blesberg, Swartberg
-33.41856
22.68702
255
2037
KSV
11/0/1
Kammanassieberg
-33.64890
22.78194
419
1833
MJV
8/0/0
Swartberg pass
-33.35318
22.05030
744
1522
SPV
17/1/2
Oliewenberg,Swartberg
-33.34692
22.09973
796
1848
WB
17/2/5
Waboomsberg, Swartberg
-33.35238
22.03304
679
1880
P. venusta
3
6
7
8
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Table S2. Regression coefficients from multiple regressions on traits of plants measured in the wild and in the Kirstenbosch and
Jonaskop common gardens. Inter-trait and trait-climate correlations in were tested in a multiple regression for each leaf trait (log
transformed and standardized), with random effects of species and population. See Fig. 2A-C for diagrams of analyses for wild
adults and common gardens seedlings. Numerator degrees of freedom = 1 for all. *** = p<0.01, ** = p ≤ 0.05, * = p < 0.1
Regression coefficients for each predictor (denominator degrees of freedom)
Location
Responses
Wild
(2008-2009)
SLA
Kirstenbosch
(Jan 2009)
Jonaskop
(Jan 2009)
SLA
-
LWR
Leaf area
Stomatal d.
DRYPCA
COLDPCA
PPTCON
FERTPCA
-0.019
(665)
0.113**
(494)
-0.0505
(664)
0.249**
(30)
0.220**
(31)
0.074
(30)
0.086
(31)
-0.386***
(630)
-0.104**
(674)
-0.015
(27)
0.208
(29)
-0.199
(32)
-0.173*
(28)
LWR
-0.023
(676)
Leaf area
0.050**
(674)
-0.150***
(668)
-
-0.0618**
(673)
0.152**
(23)
0.053
(24)
0.397***
(26)
0.089
(25)
Stomatal
density
-0.049
(668)
-0.094**
(657)
-0.138**
(612)
-
-0.167**
(26)
0.087
(28)
0.182
(23)
0.065
(30)
-
-0.002
(295)
-0.369***
(303)
0.259***
(309)
0.265**
(18)
0.238*
(24)
-0.101
(28)
-0.019
(18)
LWR
-0.003
(309)
-
0.161***
(316)
0.0599
(298)
-0.106
(15)
0.375**
(18)
-0.360**
(21)
-0.069
(17)
Leaf area
-0.240***
(304)
0.127**
(310)
-
-0.131***
(303)
0.312**
(16)
0.340*
(24)
0.384**
(19)
0.071
(24)
Stomatal
density
0.226***
(277)
0.073
(147)
-0.226***
(218)
-
0.027
(25)
-0.159*
(34)
0.245**
(20)
-0.052
(25)
-
-0.036
(276)
-0.258***
(270)
0.095*
(261)
0.040
(15)
0.283**
(21)
-0.271*
(25)
-0.017
(16)
LWR
-0.039
(276)
-
-0.089
(272)
-0.0004
(266)
-0.021
(21)
0.388***
(29)
-0.122
(35)
-0.113
(23)
Leaf area
-0.154***
(275)
-0.045
(273)
-
-0.147***
(262)
0.260**
(14)
0.308**
(25)
0.316**
(27)
0.111
(19)
Stomatal
density
0.067
(184)
0.022
(113)
-0.295***
(123)
-
-0.058
(17)
-0.020
(38)
0.206***
(20)
-0.066
(22)
SLA
SLA
-
4
10
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Supplemental Appendices
12
APPENDIX 1 (A1)
13
The climate layers used in our study were extracted from the widely used and recently updated
14
South African Atlas of Agrohydrology and Climatology (Schulze 2007). Our focal layers were
15
interpolated from long-term records of daily rainfall and temperature from thousands of weather
16
stations throughout southern Africa. Data were available at a resolution of approximately 1.55 by
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1.85 km, or 1 by 1 minute. We extracted site-specific climate data for each sampled population,
18
and from these, we created three focal climate axes. The first axis (PPTCON) reflects the
19
percentage of total annual rainfall that falls during a single month. PPTCON was taken directly
20
from Schulze, and it was calculated from monthly rainfall data using Markham’s technique (see
21
Schulze 2007 for additional details).
22
The second axis (COLDPCA) serves as an index of winter cold stress, reflecting
23
limitations on growth during the winter and the severity of cold stress. COLDPCA is the first
24
axis of a PCA on two climate layers from Schulze (2007), TMINAV07C and HU10_WINC.
25
This PCA explains 89% of the variation in the two layers, and the loading for each climate layer
26
is 0.7. TMINAV07C is the average daily minimum temperature in the coldest winter month
27
(July). HU10_WINC is the number of heat units during the winter months. Winter heat units are
28
calculated as the number of degrees by which daily maximum temperature exceeded 10° C,
29
summed across the winter months. COLDPCA is strongly positively correlated with elevation
30
and the number of days above 0 C⁰, and it is negatively correlated with summertime
31
temperatures (see also Discussion).
32
33
The third axis (DRYPCA) serves as an index of the duration and severity of drought
during the dry season. This axis was created from two sets of monthly rainfall layers, which were
5
34
each combined into a single variable and then used in a PCA. DRYPCA is the first axis,
35
explaining 79% of variation, and again, each layer has a loading of 0.7. The first set of layers
36
was GMEDNRFL1-12, or the average median rainfall for each month. From these 12 layers, we
37
selected the driest 3 per site, and summed them. The second set of layers was RFLGE2MM, or
38
monthly averages of the number of days to receive fewer than 2 mm rainfall. We summed these
39
data for the driest 3 months per site as an estimate of the duration drought during the dry season.
40
Analysis of all of the above climate variables in a single PCA showed that the first three
41
components accounted for 93% of the variance. The first principal component (66% of the
42
variance) contrasted PPTCON against drought variables and winter temperatures. The second
43
principal component (17% of the variance) contrasted drought variables against winter
44
temperatures and PPTCON. The third principal component (10% of the variance) contrasted
45
winter temperatures against drought variables and PPTCON. In other words, each of the first
46
three components contrasted one set of climate variables with the other two. Hence we focus on
47
separate PCAs that individually describe each of those climate variables, making the results
48
easier to interpret.
49
50
51
52
53
54
55
56
57
6
58
APPENDIX 2 (A2)
59
To understand how local selection gradients are related to local environments, we performed a
60
hierarchical regression in which local selection gradients and their relationship to environmental
61
covariates were estimated in a single Bayesian model. We standardized the data within each
62
population prior to analysis (mean fitness equal to 1; mean of each trait equal to 0 and standard
63
deviation of each trait equal to 1). Thus, we were estimating standardized selection differentials
64
(Lande and Arnold 1983) separately within each population. Specifically, if wi is the fitness of
65
the ith individual in our sample, we assume that
2
w i  N( i , pop[i]
)
66
i  0, pop[i]  area, pop[i]area i  SLA, pop[i]SLA i  LW R, pop[i]LWR i  dens, pop[i]dens i
67
where 0, pop[i] is the intercept, the , pop[i] are the local selection gradients for each trait, and
68
 2pop[i] is the error variance associated with the multiple regression of fitness on traits within each
69
 70
71



population. To examine the relationship between local selection gradients and environmental
covariates we further assume that each of the , pop[i] is described by a regression on those
covariates. Specifically,

2
area,
pop[i]  N( area, pop[i], area )
2
SLA, pop[i]  N(SLA, pop[i], SLA
)
72
2
LW R, pop[i]  N( LW R, pop[i], LW
R)
2
dens, pop[i]  N(dens, pop[i], dens
)

7
73
area, pop[i]   0,area[sp[i]]   area,PPTCON PPTCON pop[i]   area,DRYPCADRYPCA pop[i]
 area,COLDPCA COLDPCA pop[i]   area,FERTPCAFERTPCA pop[i]
SLA, pop[i]   0,SLA[sp[i]]   SLA,PPTCONPPTCON pop[i]   SLA,DRYPCADRYPCA pop[i]
74
 SLA,COLDPCA COLDPCA pop[i]   SLA,FERTPCAFERTPCA pop[i]
LW R, pop[i]   0,LW R[sp[i]]   LW R,PPTCON PPTCON pop[i]   LW R,DRYPCADRYPCA pop[i]
 LW R,COLDPCA COLDPCA pop[i]   LW R,FERTPCAFERTPCA pop[i]
dens, pop[i]   0,dens[sp[i]]   dens,PPTCON PPTCON pop[i]   dens,DRYPCADRYPCA pop[i]
 dens,COLDPCA COLDPCA pop[i]   dens,FERTPCAFERTPCA pop[i]
75
76
where
 the  0, are the intercepts, the  ,env are the regression coefficients of local selection
77
gradients for each trait on environmental covariates, and the 2 are the error variances of each
78


regression. We complete the Bayesian model by specifying vague normal priors on the  0, and
79

the  ,env (mean = 0, s.d. = 1) and uniform priors (0, max.sd) on the standard deviation for
80

variance parameters (Gelman et al. 2004). The upper bound (max.sd) for the uniform distribution

81
on the standard deviation was chosen as 4 times the observed maximum within population
82
standard deviation for fitness (max.sd = 6.35 for the analysis with fitness as seed heads, max.sd =
83
9.87 for the analysis with fitness as total fecundity). The code and data used in the Bayesian
84
selection analysis are available through Kent Holsinger’s website (http://darwin.eeb.uconn.edu/).
85
8
86
APPENDIX 3 (A3)
87
To calculate standardized selection gradients and differentials within each garden, first we
88
standardized all trait variables to a mean of 0 and a standard deviation of 1. We then analyzed
89
trait-survival associations in a multiple logistic regression on a binary response. Because we used
90
a logistic regression, the standardized regression coefficient we obtained for each trait was not
91
directly comparable to a standardized selection gradient as originally defined by Lande and
92
Arnold (1983). A Lande-Arnold coefficient corresponds to the change in trait value given that
93
all other traits are at the mean, whereas the logistic coefficient corresponds to the change in log
94
odds of survival –i.e., log(p/(1-p))– for a unit change in that trait, again with all other traits held
95
at their mean. To convert the logistic coefficients into standardized selection gradients, we use a
96
method similar to the one originally proposed by Janzen and Stern (1998). We also converted
97
standardized selection differentials, which correspond to the observed change in the trait value.
98
Details on our models and conversions are as follows:
99
The multiple logistic regression focused on the four traits (SLA, LWR, leaf area, and
100
stomatal density), but we included home environment characteristics (PPTCON, DRYPCA,
101
COLDPCA, FERTPCA) as covariates and population nested within species to control for
102
unmeasured among-population differences that might bias the estimates. In short, the multiple
103
logistic model is given by
9
104
 p 
log  i    0   SLA SLAi   LW RLWRi   areaareai   densdensi
 1  pi 
  PPTCON PPTCON pop[i ]   DRYPCADRYPCA pop[i ]
  COLDPCACOLDPCApop[i ]   FERTPCAFERTPCApop[i ]
  pop[i ]   sp[i ]   i
105
We illustrate the calculations by focusing on the relationship between SLA and the
106
corresponding selection gradient and selection differential. The selection gradient for SLA, bSLA,
107
is given by
b SLA 
108


1
 SLAi pˆ i
N i
 pˆ 
log  i   ˆ0  ˆSLA SLAi  ˆPPTCON PPTCON pop[i ]  ˆDRYPCADRYPCA pop[i ]
 1  pˆ i 
 ˆCOLDPCACOLDPCApop[i ]  ˆFERTPCAFERTPCApop[i ]  ˆ pop[i ]  ˆsp[i ]
109
where hats refer to estimates derived from fitting the multiple logistic regression model.
110
Coefficients for LWR, leaf area, and stomatal density are not included in the gradient
111
calculation, because the corresponding means are zero as a result of standardizing the data prior
112
to analysis. The selection differential is calculated using a similar approach. pˆ i is calculated
113
using all trait covariates for each individual and used to obtain a mean trait value after selection,
114
x after 
115
the mean trait value before any individuals have died.

1
SLAi pˆ i , and the selection differential is calculated as x after  x before , where x before is

N i
 116


117
Literature cited for appendices:
118
Gelman, A., J. B. Carlin, H. S. Stern, and D. B. Rubin. 2004. Bayesian Data Analysis, 2nd ed.
119
Chapman & Hall, Boca Raton, FL.
10
120
121
122
123
124
125
Janzen, F. J., and H. S. Stern. 1998. Logistic regression for empirical studies of multivariate
selection. Evolution 52:1564-1571.
Lande, R., and S. J. Arnold. 1983. The measurement of selection on correlated characters.
Evolution 37:1210-1226.
Schulze, R. E. 2007. South African atlas of climatology and agrohydrology: WRC Report
1489/1/06. Water Research Commission, Pretoria, RSA.