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.