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.