Appendix S1: Details of conceptual fitness model presented in Figure 1.
Our model simulates empirical estimates of natural selection using the Lande and Arnold
(1983) quadratic selection models on flowering time in a finite population undergoing a shift in
the adaptive landscape as a result of global climate change. We consider three scenarios: (A)
‘past conditions’ in which the population is at equilibrium, (B) ‘present conditions’ in which the
population is evolving to a new optimum, and (C) ‘future conditions’ in which the population is
far from the new optimum. Details of the model are provided as code for R (below) and briefly
summarized here.
In each scenario, we model the fitness surface for flowering time as a Gaussian function:
we

 z  z 2
2VS
(1)
where z is flowering time, 1/VS is the strength of stabilizing selection, and zɵ is the optimum
flowering time. A second Gaussian distribution, similar to Eq. (1), defines the distribution of
flowering time phenotypes in the population, but with z replacing zɵ in Eq. (1) and representing
the population mean flowering time. We also replace VS from Eq. (1) with VP to represent the
phenotypic variance. From this distribution, 50 individuals are sampled and their fitnesses are
estimated using Eq. (1) plus a normally distributed random error term to simulate experimental
and environmental deviations. Individuals with fitness < 0.01 are excluded from the analysis to
simulate dead individuals and individuals which survive but fail to flower or produce offspring.
To simulate a population whose rate of evolution lags behind the rate of climate change in
scenarios (B) and (C), we multiply z by 0.4 for each scenario relative to its preceding scenario,
representing a 60% shift in the mean towards the new optimum in each case. We also model a
reduction in phenotypic variance (VP) to account for the fact that the evolutionary response to
selection erodes standing genetic variation in a finite population. However, the resulting shift
from stabilizing to directional selection as shown in scenario B, and eventual extinction as shown
in scenario C, are both robust to any case in which z lags behind zɵ, even if there is no change in
VP.
A quadratic selection model is fit to the 50 randomly sampled individuals, following Lande
and Arnold (1983) as an empirical estimate of the fitness surface. The quadratic coefficient is
included in the fit only if significant, whereas the linear fit is included regardless of significance
to allow comparison of the slope between scenarios B and C.
References
Lande R & Arnold SJ (1983) The measurement of selection on correlated characters. Evolution
37:1210-26
1
R-code:
## Variables Defined below, AFTER function ###
## zopt == Optimum value of z-trait (i.e. z-value with highest fitness)
## Vs == Variance in selection; inversely proportional to strength of
stabilizing selection
## Vp == Variance in phenotypes on which seleciton is measured
## zmean == Mean z-score of population upon which selection is measured
## Plots fitness function graph given zopt, Vs, and Vp
fitnessplot<-function(zopt,Vs,zmean,Vp){
z<-c(-200:200)/20 ## Arbitrary z-values for plotting fitness function
w<-exp(-(z-zopt)^2 /(2*Vs)) ## Stabilizing selection equation from Johnson &
Barton (2005): PRSB 360:1411-1425
## Now randomly select n data points from the fitness surface
zdat<-rnorm(50,mean=zmean,sd=Vp)
wdat<-exp(-(zdat-zopt)^2 /(2*Vs))+rnorm(length(zdat))/20 ## And calculate
the fitness of each data point, with experimental error
zdat<-zdat[wdat>=0.01] ## Remove individuals with fitness~0 and recalculate
wdat<-wdat[wdat>=0.01] ## And calculate the fitness of each data point, with
experimental error
points(z,w,col=rgb(1-(z+10)/20,(z+10)/30,(z+10)/20,0.2),cex=1,pch=16) ##
Fitness function
points(zdat,wdat,col=rgb(0.4,0.4,0.4),cex=1.5)
mod<-lm(wdat~zdat+I(zdat^2)) ## Lande-Arnold estimate of fitness for sampled
individuals
zfit<-min(zdat)+c(0:100)/100*(max(zdat)-min(zdat)) ## increase number of z
values so that fitted curve will be smoother
quadtest<-anova(mod)[['Pr(>F)']][2] ## Is quadratic term significant?
if(quadtest>0.05){ ## If not, exclude from model fit
mod<-lm(wdat~zdat)
wfit<-mod$coefficients[1]+mod$coefficients[2]*zfit}
2
if(quadtest<0.05){wfit<mod$coefficients[1]+mod$coefficients[2]*zfit+mod$coefficients[3]*zfit*zfit}
## If so, include it
lines(zfit,wfit,col=rgb(0,1,0),lwd=3,lty=1)
}
## Create a blank plot with x-y labels
plot(0,0,col='white',xlab="Flowering
Time",ylab="Fitness",axes=FALSE,frame.plot=FALSE)
## Plot 3 separate graphs
par(mfcol=c(3,1),mar=c(0,0,0,0),oma=c(3,3,0,0),mfg=c(1,1))
## First Graph
plot(0,0,col='white',xlim=c(-10,10),ylim=c(0,1.2),axes=FALSE,frame.plot=TRUE)
zopt<-5 ## Optimum value of z-trait (i.e. z-value with highest fitness)
Vs<-10 ## Variance in selection; inversely proportional to strength of
stabilizing selection
zmean<-5 ## Mean z-score of population upon which selection is measured
Vp<-Vs/10 ## Variance in phenotypes on which seleciton is measured
fitnessplot(zopt,Vs,zmean,Vp)
text(-10,1.1,"A",cex=1.5)
## Second Graph
plot(0,0,col='white',xlim=c(10,10),ylim=c(0,1.2),axes=FALSE,frame.plot=TRUE,xlab="Flowering
time",ylab="Fitness")
zopt<- -2 ## Optimum value of z-trait (i.e. z-value with highest fitness)
Vs<-10 ## Variance in selection; inversely proportional to strength of
stabilizing selection
zmean<- 3 ## Mean z-score of population upon which selection is measured
Vp<-Vs/15 ## Variance in phenotypes on which seleciton is measured
fitnessplot(zopt,Vs,zmean,Vp)
text(-10,1.1,"B",cex=1.5)
3
## Third Graph
plot(0,0,col='white',xlim=c(10,10),ylim=c(0,1.2),axes=FALSE,frame.plot=TRUE,xlab="Flowering
time",ylab="Fitness")
zopt<- -10 ## Optimum value of z-trait (i.e. z-value with highest fitness)
Vs<-10 ## Variance in selection; inversely proportional to strength of
stabilizing selection
zmean<- 1.8 ## Mean z-score of population upon which selection is measured
Vp<-Vs/20 ## Variance in phenotypes on which seleciton is measured
fitnessplot(zopt,Vs,zmean,Vp)
text(-10,1.1,"C",cex=1.5)
4
Appendix S2: Year-level analyses of long-term flowering phenology data. For these
analyses, we calculated yearly averages (LSMEANS) for the timing of first flowering in mixed
models (Proc Mixed) that included plot as a random effect. As with the plot-level analyses (see
main text), we ran one model including all predictors, and then three separate models for each
predictor to address possible problems with multicollinearity. The results presented here are
virtually identical to the plot-level analyses in the main text.
The results in this table use data from 1975-2011 because snowmelt data are not available for
1973 and 1974. However, flowering time data are available from 1973-2011. A univariate
model with data from 1973-2011 shows a significant advancement in the timing of first
flowering (β=-0.35 ±0.15, F1,34=5.84, p=0.0212).
Full model
β
F1,30 p-value
Intercept
514.8 ± 137.8
Year
-0.20 ±0.07
8.74
0.006
Snowmelt date
0.45 ±0.09
22.98 <0.0001
Temperature*
-2.35 ± 0.9
6.97
0.013
*Average April and May temperature
5
Each predictor independently
β
F1,32
p-value
-0.37 ±0.16
0.69±0.065
-6.2 ± 0.7
5.23
111.6
81.2
Intercept β
0.029 904.7± 323.7
<0.0001 67.6 ± 9.2
<0.0001 183.8± 2.3
Appendix S3: Relationship between the peak mean daily runoff in the East River (x) and
snowmelt date in Gothic, the site of the Rocky Mountain Biology Laboratory (y), based on
data from 1975-2011, with 2003 removed as an outlier. This relationship was used to estimate
snowmelt date from 1935-1974. See main text for details.
6
Appendix S4: Selection analysis using raw data (not family means) for the recombinant
inbred lines (RILs). In this dataset, the number of fruits (the fitness component) followed a
zero-inflated Poisson distribution. We conducted this analysis using Proc NLMIXED, which can
only accommodate one random effect. We incorporated family as the random effect, and block
as a fixed effect.
Zero-inflated Poisson analysis account for excess zeros by modeling the probability that
fitness=0 in a logistic model, and then separately modeling the number of fruits >0 using a
Poisson distribution. We used the same predictors in the zero and count components of this
analysis: linear and quadratic effects of the timing of first flowering, plant size at flowering
(height and leaf number), block, and covariates for initial plant size and density of neighboring
plants, with a random effect for family. SAS code is presented after the figure.
Zero-inflation parameter estimates were non-significant for all traits in our multivariate and
univariate models (p-values ranging from 0.11 to 0.67). The following table contains maximum
likelihood parameter estimates for the count component of the model.
Please note that the general patterns presented here are qualitatively similar to the analysis
conducted at the family level (main text), but this analysis was conducted using absolute fitness
and the family-level analysis was done with relative fitness. We used absolute fitness here
because relative fitness was not normally distributed and could not be fit using Poisson models.
As with other analyses, this analysis shows directional selection for earlier flowering.
The following table contains results from multivariate models to estimate standardized selection
gradients in the presence of other traits (β'), as well as univariate models of each trait separately
to estimate standardized selection differentials (S'). Univariate analyses included the specific
trait (flowering time, height at flowering, or leaf number at flowering), as well as the covariates
(plant density, and size at first flowering), block, and the random effect of family. There are 95
degrees of freedom for all analyses. Comparing selection gradients (β') to selection differentials
(S') can expose the extent of direct and indirect selection on a given trait.
Significant p-values are highlighted in bold.
The unstandardized selection coefficient for flowering time from this analysis was -0.035 ±
0.004 relative fitness unit/day, t=-8.82, p<0.0001. This value is nearly identical to the
unstandardized selection coefficient for the family-level analysis presented in the main text.
7
Univariate analyses
Multivariate analysis
β'
Day of first flowering: Linear
effect
Day of first flowering:
Quadratic effect
Height at first flowering
Number of leaves at first
flowering
t-value p-value
-0.27 ±0.07
-3.80
0.0003
-0.013 ±0.08
0.34 ± 0.07
-0.17
4.59
0.87
<0.0001
0.125 ± 0.06
2.12
0.037
Plant density
-0.13 ± 0.05
-2.55
0.0123
Initial plant size
0.099 ±0.04
2.28
0.025
-1.85
0.067
3.32
0.0013
Block (fixed effect)
Genotype (random effect)
S'
t-value p-value
-0.47±0.053
-8.85 <0.0001
0.038 ±0.08
0.5
0.62
0.51 ±0.055
-0.063 ± 0.056
9.21
-1.11
<0.0001
0.27
Values changed slightly for each
phenotypic trait
Values changed slightly for each
phenotypic trait
Values changed slightly for each
phenotypic trait
Values changed slightly for each
phenotypic trait
Analyses were conducted with standardized phenotypic data (mean=0, standard deviation=1),
but the figure below illustrates the relationship using raw data on the timing of first flowering.
8
SAS code for Zero inflated Poisson regression. Trait values were standardized prior
to analysis
FT=flowering time
veg= density of neighboring plants
initW= initial rosette width (at planting)
LFN= leaf number at flowering
Height_at_flr= Height at flowering
Siliques = Number of fruits = Fitness component
bFT, bveg, bFT2, binitW, bheight, bLFN, bblock - > These will give parameter
values for the associated predictors for the count component of the analysis
(respectively: flowering time, density of neighboring plants, quadratic effect of
flowering time, initial plant size, height at flowering, leaf number at flowering, block)
inf0 – inf7 will provide the parameter estimates for the logistic regression component
of the analysis.:
proc nlmixed data=work.Traits;
/* starting values */
parms b0=0 bFT=0 bveg=0 bFT2=0 binitW=0 bheight=0 bLFN=0 bblock=0 inf0=0
inf1=0 inf2=0 inf3=0 inf4=0 inf5=0 inf6=0 inf7=0 s2u1=1 s2u2=1;
/* zero inflation model (including all traits) */
zeromodel = inf0 + inf1*FT+ inf2*FT*FT + inf3*veg +
inf4*initW+inf5*height_at_flr + inf6*LFN + inf7*block +U1;
infprob = 1/(1+exp(-zeromodel));
/* poisson model (including all traits) */
lambda
= exp(b0 + bFT*FT + bFT2*FT*FT + bveg*veg + binitW*initW +
bheight*height_at_flr + bLFN*LFN + bblock*block + U2);
/* define ZIP log likelihood */
if siliques=0 then ll = log(infprob + (1-infprob)*exp(-lambda));
else ll = log((1-infprob)) + siliques*log(lambda) lgamma(siliques+1) - lambda;
model siliques ~ general(ll);
/* request predicted counts */
predict (1-infprob)*lambda out=nout;
/* establish family as a random effect */
Random U1 U2~N([0,0],[s2u1,0,s2u2]) subject=family;
run;
9
Appendix S5:
(A) SAS code for calculating the genetic covariance between relative fitness and flowering
time (the Robertson-Price identity) for the RILs. Here, we provide code for standardizing trait
values to a mean of 0 and standard deviation of 1, but we used unstandardized values in our
analyses to obtain results with the relevant phenotypic units (days of flowering time per
generation, as opposed to standard deviation change per generation).
In these models:
w=relative fitness = fitness of an individual/average fitness of population
FT= flowering time (day of first flowering)
ID = unique number for each individual plant.
Height=height at flowering
Veg= Density of neighboring plants
LFN=leaf number at flowering
More complex models produced quantitatively very similar results, so we elected to use a simple
model that converged more rapidly. The first data steps put the data into the correct format, and
create dummy variables (“Trait” with associate numbers in “Value”) necessary to model genetic
covariances. Here we show the proc mixed code for the reduced model (“data=reduced”), but the
full model can be obtained by running the same code with “data=full.”
data
data
data
data
w; set selection_final; Trait="1"; Value=w; run;
FT; set selection_final; Trait="2"; Value=FT; run;
height; set selection_final; Trait="3"; Value=height; run;
LFN; set selection_final; Trait="4"; Value=LFN; run;
*The following data step creates the data file for the univariate model to
assess the genetic covariance of relative fitness and flowering time;
data reduced; set w FT; keep ID family block veg Trait Value; run;
*The following data step creates the data file for the multivariate model to
assess the genetic covariance of relative fitness, flowering time, plant
height at flowering and leaf number at flowering;
data full; set w FT height LFN; keep ID family block veg Trait Value; run;
*Here is the model statement. Substituting “data=full” for “data=reduced”
will give the output of the full model. The univariate (data=reduced) model
runs relatively quickly. The full model took 9.5 days to converge;
ods output CovParms=Covs_reduced FitStatistics=LogLik_red;
proc mixed data=reduced lognote covtest;
Class ID family block Trait site cohort;
model Value = Trait*veg Trait*site/ddfm=satterthwaite;
random Trait /type=VC subject=block*site group=trait ;
10
random Trait /type=UN subject=family ;
repeated Trait /type=UN subject=ID(family);
run;
To test the effect of the genetic covariance component in the reduce model, we simply
constrained the covariance to 0, and used a likelihood ratio test :
ods output CovParms=Covs_reduced FitStatistics=LogLik_red;
proc mixed data=reduced lognote covtest;
Class ID family block Trait site cohort;
model Value = Trait*veg Trait*site/ddfm=satterthwaite;
random Trait /type=VC subject=block*site group=trait ;
random Trait /type=UN(1) subject=family ;
repeated Trait /type=UN subject=ID(family);
run;
In the SAS output file for the reduced model, the genetic covariance between relative
fitness and flowering time (highlighted for results of the reduced model, below) can be found in
the covariance parameters. Trait 1= relative fitness, and trait 2 = unstandardized flowering time:
Covariance Parameter Estimates
Cov Parm
Trait
Trait
UN(1,1)
UN(2,1)
UN(2,2)
UN(1,1)
UN(2,1)
UN(2,2)
Subject
block*Site
block*Site
family
family
family
ID(family)
ID(family)
ID(family)
Group
Trait 1
Trait 2
Standard
Estimate
Error
Z-Value
0.02841
0.01885
1.51
80.2976
24.1446
3.33
0.06176
0.02708
2.28
0.2347
-2.2
-0.5165
5.4951
3.2123
1.71
0.7111
0.04412
16.12
-2.7539
0.3627
-7.59
82.1731
5.2221
15.74
11
Pr Z
0.0659
0.0004
0.0113
0.0277
0.0436
<.0001
<.0001
<.0001
(B) Genetic Variance-Covariance Matrix from full model (genetic variances are on the
diagonals, covariances are below). The Robertson-Price identity predicts response to selection as
the genetic covariance of a trait with relative fitness, so the response to selection for flowering
time would be -0.52 days/generation, for height at flowering would be 1.69 mm/generation, and
for leaf number at flowering would be 0.135 leaves/generation.
Relative
fitness
Flowering time
Height at flowering Leaf number at
flowering
Relative fitness
0.059
Flowering time
-0.5186
5.37
Height at
flowering
1.69
-11.68
357.9
Leaf number at
flowering
0.135
-2.10
-8.46
12
3.64
(C) Response to selection via the breeder’s equation.
(1) The univariate breeder’s equation (R=H2S) says that the response to selection is equal to
heritability multiplied by the selection differential. The unstandardized selection differential is
calculated by multiplying the total phenotypic variance in flowering time by the unstandardized
regression coefficient for the regression of relative fitness on flowering time. We calculated the
breeder’s equation from the recombinant inbred line experiment, using 2 datasets: (1) a reduced
data set containing only data from the Colorado common garden in 2010, and (2) a combined
dataset with data from Colorado in 2010 and the Montana common garden in 2009 and 2010.
Unstandardized regression coefficients presented here come from the individual level
data, and include random effects for family and block (Colorado dataset only) and family, family
by site and block by site (combined dataset, Colorado and Montana). Analyses at the family
level produced nearly identical parameter estimates (combined dataset: -0.035 ± 0.005 relative
fitness units per day, F1,46=61.2, p<0.0001; Colorado dataset: -0.036 ± 0.007 relative fitness units
per day, F1,95=26.1, p<0.0001), and would result in a response to selection of -0.20 (combined
dataset) and -0.32 days per generation (Colorado dataset only).
The calculations follow. We evaluated statistical significance for the regression
coefficient, variance components and broad sense heritability only. *** p<0.0001, **p<0.01, *
p<0.05, N.S.=Not significant:
Combined dataset
Unstandardized regression coefficient (relationship between
flowering time and fitness). This is the covariance of relative
fitness and flowering time divided by the variance in flowering
time.
Total phenotypic variance in flowering time
Selection differential (S=Covariance of relative fitness and
flowering time= regression coefficient × Variance in flowering
time)
Genetic variance in flowering time
Residual variance in flowering time
Block variance in flowering time
Broad-sense heritability (H2)
Response to selection (R=H2S). The units are days/generation
13
Reduced dataset
(Colorado only)
-0.035 ± 0.003 *** -0.038 ± 0.005 ***
118.1
-4.13
191.7
-7.35
5.77 ± 3.3*
82.0 ± 5.2 ***
30.34 ± 10.4 **
0.049± 0.028*
9.06 ± 11.5 N.S.
98.8 ± 15.7 ***
83.8 ± 50.7 *
0.047 ± 0.06N.S.
-0.20
-0.35
(2) The multivariate breeder’s equation predicts the response to selection based on multivariate
selection gradients and the genetic variance-covariance matrix:
R=Gβ
We calculated unstandardized multivariate selection gradients for a regression of relative fitness
on flowering time and plant height at flowering in a model with family and block by site as
random effects and plant density as a covariate.
G matrix (genetic variances are on the diagonals, and covariances are beneath). For the
Colorado dataset, a full model with flowering time, plant height at flowering and leaf number at
flowering did not converge. Since the number of leaves at flowering was nonsignificant in the
multivariate selection analysis (Table 2 of main text), we eliminated leaf number at flowering,
and the genetic covariances converged.
Trait
Combined dataset (Colorado and
Montana)
Colorado dataset only
Flowering Height at Leaf number
time
flowering at flowering
Flowering
time
Flowering 5.37
time
Height at -11.68
flowering
-2.10
Leaf
number at
flowering
Height at
flowering
Leaf number at
flowering
10.19
357.9
-8.46
3.64
-16.94
1204.6
Did not
converge
Did not
converge
Did not converge
Multivariate selection gradients and predicted response to selection from the multivariate
breeder’s equation. The multivariate selection analyses here used unstandardized data from
individual-level analyses that included random effects for block and family (Colorado only, zeroinflated Poisson regression in NLMIXED), and block by site, family and family by site
(combined Colorado and Montana dataset; a normal distribution in Proc Mixed produced
reasonable residuals for these data). The family level analyses using LSMEANS produced
nearly identical multivariate selection gradients for flowering time and height at flowering, but
different results for leaf number at flowering in the Colorado and Montana dataset. For the
combined dataset (Colorado and Montana), the selection gradients from family-level analyses
14
are: flowering time= -0.032 ± 0.006 relative fitness units/ day (p<0.0001); height at
flowering=0.00515± 0.0008 relative fitness units/mm (p<0.0001); leaf number at flowering=0.004 ± 0.008 relative fitness units per leaf (p=0.63). For the Colorado dataset alone, the
selection gradients from family-level analyses are: flowering time= -0.017 ± 0.007 relative
fitness units/ day (p=0.0205); height at flowering=0.0045± 0.001 relative fitness units/mm
(p<0.0001). *p<0.05, ** p<0.001, ***p<0.0001
Combined dataset (Colorado and
Montana)
Colorado dataset only
Trait
Multivariate
selection
gradient (β)
Response to selection
Multivariate
selection gradient
(β)
Response to selection
Flowering time
-0.029 ±
0.0045***
-0.24 days/ generation
-0.018 ± 0.005 **
-0.23 days/generation
Height at
flowering
0.0052 ±
0.0006***
2.10 mm/generation
0.003 ± 0.0008***
3.92 mm/generation
Leaf number at
flowering
0.012 ±
0.005*
0.0606
leaves/generation
Not included in the
model
15
Appendix S6: Sample sizes of individuals from each family and 4 cohorts planted at
different dates in the greenhouse.
family
CME10
CME12
CME6
CME7
CME9
CMEA
CMEB
CMEC
CMED
CMEE
CMEG
CMEH
CMEI
3/5/2010 3/12/2010 3/19/2010 3/25/2010
18
9
17
10
14
12
11
16
16
23
11
17
26
17
14
25
17
13
22
20
12
12
7
15
0
5
3
9
12
8
14
15
17
18
5
5
16
21
12
9
22
18
11
17
22
18
19
19
21
16
14
8
16
Appendix S7: Family-level analysis of selection on flowering time: Local genotypes.
To analyze the data at the genotypic-level, we calculated family-level means (LSMEANs) for
flowering time and fitness for each cohort in separate mixed model analyses (Proc Mixed), in
which block was included as a random effect and the number of leaves at planting (initial plant
size) was a covariate.
At the family-level, we detected significant directional selection for earlier flowering (F1,15=34.9,
p<0.0001, β'= -0.45 ± 0.08), with slight curvature to the relationship (F1,15=4.75, γ'=0.18± 0.08,
p=0.045). This positive quadratic term does not represent stabilizing selection, but indicates
minimal disruptive selection. This analysis found no effect of cohort age on fecundity
(F3,15=0.76, p=0.53). Analyses used day of first flowering data standardized to a mean of 0 and
standard deviation of 1. The figure here plots raw day of first flowering data.
The unstandardized regression coefficient for a univariate analysis of flowering time and relative
fitness was -0.026 ± 0.004 relative fitness unit/day, F1,19=35.1, p<0.0001. This value is similar to
the unstandardized regression coefficient for the family-level analysis of recombinant inbred
lines (RILs) presented in the main text.
17
Appendix S8: Changes in the timing of peak flowering from 1975-2011 in full and reduced
models. Separate figures for each of these predictors are presented in Appendix S8. The
results presented in this table use data from 1975-2011 because snowmelt data are not
available for 1973 and 1974. However, peak flowering data are available from 19732011. A univariate model with data from 1973-2011 shows a significant advancement in
the timing of peak flowering (β=-0.296 ±0.1, F1,26=8.67, p=0.0038). Significance of the
random effect (plot) was determined by a likelihood ratio test with 1 d.f. Plot was nonsignificant for the reduced models (p-values for plot were 0.21, 0.17, 0.09 respectively
for separate models of year, snowmelt date and temperature).
Full model
Each predictor independently
Partial
β
F1,119
Year
-0.20 ±0.09
4.77
Snowmelt day
0.25 ±0.12
4.33
Temperature*
-3.11 ±1.17
Plot
R2
β
F1,121
0.016
-0.32 ±0.1
8.85
0.0035
0.04
0.026
0.54 ±0.07
53.5
<0.0001
0.28
7.05
0.009
0.039
-5.4 ±0.7
59.9
<0.0001
0.30
χ2=3.8
0.051
p-value
0.0309
*Average April and May temperature.
18
p-value
R2
0.048
Appendix S9: Long term trends in peak flowering in Boechera stricta. The timing
of peak flowering has advanced significantly since 1973 (a), and is tightly related to the timing
of snowmelt (b), and late winter temperatures (average April and May temperatures, c). Grey
bands represent confidence intervals. See Appendix S8 for statistics.
(a)
19
(b)
20
(c)
21