Assessing Cone-Warming Effects on Plant Responses

Multivariate and univariate models were used to investigate statistical relationships between the cone-warming treatment and response variables. Effect sizes of cone-warming on responses were then estimated as described below. All analyses were conducted in R (version 3.5.1, R Core Team 2018). Seedlings in the common garden demonstration from each type of cone-warming bag (glassine versus plastic bubble-wrap packaging material, both inside of a polyester pollination bag) were treated the same because there was no statistically significant difference between the effect of the two types of cone-warming bags on seedling traits. Multivariate models were built using both principal component analysis (PCA; via the function prcomp) and permutational multivariate analysis of variance (PERMANOVA; via the function adonis) separately for the following three categories of response variables: (1) plant growth traits including bud phenology, (2) foliar spectra, and (3) mycorrhizal assemblages. The first principal component of the PCA generated from variables, belonging to one response category at a time, was used as the response in linear mixed effect models. Next, PERMANOVAs were executed using Euclidean distance matrices composed of aggregated response variables for each of the three response categories (plant growth, spectra, and mycorrhizae), separately, specifying seed source tree as a random effect. Univariate linear mixed effect models were also fitted for all response variables, specifying seed source tree nested within stand, and raised-bed box (where models would allow), as random effects using functions from the R package lme4. In both multivariate and univariate models, seed mass was tested for inclusion as a covariate via AIC comparisons. Models with the smallest AIC were favored, and when models competed with AIC values within 2 AIC units of the smallest AIC, the simplest model structure with the least predictors was selected for subsequent ANOVAs. Satterthwaite approximation of denominator degrees of freedom was specified for all omnibus F-tests of fixed effects as well as type III sum of square ANOVAs for models that included interactions between seed mass and warming treatment. Type II sum of square ANOVAs were specified for models that included seed mass as an added covariate. The magnitude of the variance explained by the cone-warming fixed effect was estimated by Cohen’s Local f², which is suitable for use with mixed models for which denominator degrees of freedom must be approximated, and is suitable for use with unbalanced experimental designs [34 (link), 35 (link)]. Input for the calculation of Cohen’s Local f² includes marginal R² goodness-of-fit values both from models with and without the factor of interest, as follows: $$f^2=\frac{R_{\mathit{with}}^2-R_{\mathit{without}}^2}{1-R_{\mathit{with}}^2}$$
$R_{\mathit{with}}^2$ refers to the marginal coefficient of determination from a model containing a fixed factor of interest, and $R_{\mathit{without}}^2$ refers to the marginal coefficient of determination from the same model with the fixed factor of interest removed. For instance, in this study the warming treatment was present in the $R_{\mathit{with}}^2$ model and omitted from the $R_{\mathit{without}}^2$ model. Cohen’s Local f² effect sizes ≥ 0.02, ≥ 0.15, and ≥ 0.35 are respectively considered small, medium, and large [35 (link), 36 (link)]. Code and data related to this work are accessible through the Knowledge Network for Biocomplexity.