Statistical Analyses
We used R version 4.0.2 for all analyses and visualization (R Core Team
2021), using the package ‘lme4’ to fit mixed effect models (Bates et al.
2015), the ‘Anova’ function from the ‘car’ package (Fox & Weisberg
2019) using type III sum of squares to test for significant terms, the
package ‘sjPlot’ (Lüdecke 2021) to calculate marginal and conditional
R2 values based on Nakagawa et al. (2017), and the
package ‘emmeans’ (Lenth 2020) to calculate model estimated marginal
means and conduct post-hoc tests for significant differences between
categorical variables with more than two levels. To accommodate the type
III sum of squares, we set contrasts = c(“contr.sum”,”contr.poly”).
We used the ‘ggplot2’ package for data visualization (Wickham 2016).
We first tested for background germination by modeling the number of
seedlings in each cell as a Poisson distribution, fitting the
interaction of common garden (HD, HR) and cell type (planted, control)
as fixed effects and quadrat as a random effect. To correct for the fact
that many cells contained zero seedlings, we included an observation
level random effect to account for overdispersion (Browne et al. 2005,
Harrison 2015).
We also performed an initial coarse test of our seed processing
techniques (soaked and sheathed) to see whether either technique
affected germination rates (across the two gardens). We fit binomial
logistic regressions separately for chasmogamous and cleistogamous
seeds, with soaked as a fixed effect for chasmogamous and both soaked
and sheathed as fixed effects for cleistogamous. Both models included
random effects for quadrat, maternal plant nested within source
population, and an observation level random effect for overdispersion.
To address our hypotheses, we fit a series of binomial logistic
regressions separately for each common garden. Each model included
average maternal seed weight as well as soaked and sheathed treatments
as covariates, but we dropped the soaked and sheathed treatments when
not significant (most often the case) to reduce model complexity. For
random effects, we included quadrat, maternal plant nested within source
population, and observation level random effects for overdispersion.
For hypotheses 1a-b regarding local adaptation, we fit a categorical
model with the interaction of seed origin (local, nonlocal to the south
of the garden, and nonlocal to the north of the garden) and seed type
(chasmogamous, cleistogamous) as fixed effects. We also ran models
separately for each pairwise combination of nonlocal source population
and common garden, with the interaction of seed origin (local, nonlocal)
and seed type as fixed effects. We then ran separate regression models
for hypotheses 2 and 3 to explore the possible mechanisms that could
explain the presence or absence of seed origin effects. These models
addressed the geographic and environmental distances (separately)
between source populations and common gardens and the latitudes of the
source populations. Each of these models included interactions with seed
type (cleistogamous, chasmogamous) and the geographic distance model
also included a quadratic distance term to allow for nonlinearity.
We calculated geographic distance between source populations and common
garden sites using NOAA’s Latitude and Longitude distance calculator
(Williams n.d.). We calculated environmental distance using the
Euclidean distance of a principal components analysis on a set of
environmental variables collected from each source population site in
the year of seed collection (2018). These variables included spring
precipitation, temperature (min, mean, and max), dew point (mean), vapor
pressure deficit (min and max), elevation, and plant density as
described in Mackin et al. (2021). We performed a principal components
analysis on this set of nine environmental variables and calculated the
Euclidean distance of each source population from each common garden
using the first two principal components. We also performed a simple
linear regression between geographic and environmental distance to see
whether the two were correlated.
Finally, we tested whether average maternal seed weight, a covariate in
all the germination rate models, could be explained by seed type, source
population, or source population latitude. We fit two linear mixed
effects models: the first including the interaction of source population
and seed type as fixed effects and maternal plant as a random effect,
and the second taking the average weight across cleistogamous and
chasmogamous seed types and fitting source population latitude as a
fixed effect and source population as a random effect.