Statistical analyses for both experiments
Analyses were conducted with R 4.0.4 (R Core Team, 2018). Linear mixed effects models (LMMs) were fitted using the “lme4” package (version 1.1-20, Bates, Mächler, Bolker, and Walker (2014)). Eta-squared (η2) values (see below) were calculated from marginal models. LMMs were subjected to type III ANOVAs with Satterthwaite’s method to produce a summary of the F and p statistics. Eta-squared (η2) values, which are measures of effect sizes quantifying the proportion of marginal model variance explained by each variable, were calculated using the “sjstats” package (version 0.17.6, (Lüdecke, 2019)). The significance of random effects was tested with log-likelihood-ratio tests using the ranova function of the “lmerTest” package (v.3.1-3 ) (Kuznetsova, Brockhoff, & Christensen, 2017). Weibull curve parameters were generated in Excel solver.
We used two sets of LMMs to address the questions posed for Experiment 1. The first set of models evaluated the impacts of the explanatory variables (ploidy, drought, defoliation, and their interactions) on the various tree traits while ignoring genotypic effects (i.e., we determined average ploidy effects). A second set assessed the effects of the explanatory variables, and their interactions, on the same tree traits while incorporating genotypic variation. For the first set of models, we separately calculated average values for diploid and triploid genotypes in each mesocosm and used these averaged trait values as experimental units. Mesocosm and block were used as random intercepts. For the second set of models, individual trees were used as experimental units. Genotype, all possible genotype × stress interactions, as well as mesocosm and block were used as random intercepts.
Individual values of final tree dry weights were normalized for initiald 2h . The normalized values were then used as model response variables. The response variables SWR and LWR were normalized for final tree dry weight. To quantify how much stem mass a tree allocated to height growth (i.e., how “lanky” a tree was), final height values were normalized for total final stem dry weight. Prior to any normalization, the relationship between the response and the normalizing variable was explored and, if necessary, ln- or square root transformed to meet the model assumptions of normality and homoscedasticity.
For some LMMs, we found significant (p ≤ 0.100) ploidy × drought or ploidy× defoliation interactions, indicating differences in stress-related plastic responses between diploid and triploid trees. We further explored the relevance of these interactions by calculating ratios between stressed and control plants growing in the same experimental block using normalized values (described in Appendix 1).
The impact of ploidy, genotypic effects and defoliation on leaf physiology on well-watered trees was explored with the two model sets as described above. Because physiological trait measurements were taken multiple times from each tree, average values across all measurements per tree were calculated and used for statistical analyses. For well-watered trees, we examined the relationship betweenA area and ΨPD for each genotype in both defoliation treatments using a three-parameter, Weibull-type vulnerability curve with the equation:
\begin{equation} \text{fi}\left(y\right)=A_{\max}e^{-\left(\frac{x}{b}\right)^{c}}\nonumber \\ \end{equation}
where x is the absolute value of the difference between ΨPD corresponding to a particular photosynthetic measurement and the least negative ΨPD observed during the study. The difference was used to avoid potential overestimation ofA max (or g max). Multi-parameter Weibull-type vulnerability curves are typically used to describe how tree trait respond to changes in drought stress, as they account for the often-observed relative unresponsiveness of trees when experiencing mild stress (Bateman, Lewandrowski, Stevens, & Muñoz‐Rojas, 2018; Vico & Porporato, 2008; Wolfe, Sperry, & Kursar, 2016). We calculated for each genotype the curve parameter valuesA max , b and c based on minimization of the sum of squared differences between the observed and predicted values for A area at different stages of drought stress. We then generated LMMs with curve parameter values as response variables and ploidy, defoliation and their interaction as explanatory variables and genotype as random intercepts. If necessary, response variables were transformed to meet model assumptions as described above.
In Experiment 2, the effects of ploidy, genotype, and defoliation on tree growth and leaf morphology were evaluated using two sets of LMMs as described above. Individual values of final tree dry weights and dry weight of newly produced tissue were normalized for initiald 2h. In cases of significant (p ≤ 0.1) ploidy× defoliation interactions, we further explored differences in plasticity between ploidy levels calculating trait ratios by dividing trait values of stressed trees by trait values of control trees (Appendix 1). In cases were ratios were calculated based on genotype averages, Kruskal-Wallis tests were used to characterize the relationship between trait ratios and ploidy levels.