Statistical methods
The mean annual fruit production (F_mean), our response variable, had a negative exponential probability distribution pattern. Three observations with disproportionally large fruit yield were excluded, to keep the distribution continuous (see the Supplementary Fig.S1). All statistical analyses were performed using the R software \cite{computing2023}. The preliminary analyses confirmed high co-linearities within the 15 architectural traits, and two separate scaled principal component analyses (PCAs) were conducted, following similar studies \cite{Martin_Ducup_2020,K_dra_2022}, to reveal orthogonal trait dimensions, for both the size (PCAabs) and proportions (PCArel) traits. Several PCA axes, with the highest variation explained, were further used as the explanatory variables. The names of the PCA axes were: PCabs1, PCabs2, ..., PCabs7; and PCrel1, PCrel2, ..., PCrel8, for the absolute and the relative trait dimensions, respectively. The contributions of individual architectural traits to the PCA axes were analysed and visualized using the R package "corrplot" \cite{2021}. Two-dimensional heat-maps of F_mean were created, along the major PCA axes, using the kriging interpolation with the R package "kriging" \cite{e2022}. We used the height values of the kriging rasters (F_mean_kriging) to search for local maxima (or architectural optima) in rowan fruit production. The interaction effects between the architectural PCA axes and canopy openness (C_Open), possibly contributing to the variability in architecture-fecundity relations, were analysed using the novel R package "diversityForest" \cite{n2023}. The algorithm implements ensembles of decision trees, to model interaction effects using bivariable splitting \cite{Hornung_2022}, and quantifies interaction importance by the Effect Importance Measure (EIM); it also enables a two-dimensional LOESS (Local Polynomial Regression) fitting. We used such contour plots to represent the change of our response, depending on two interacting explanatory variables (one of the structural dimensions and C_Open). The cross-sections of the LOESS fits served as the architecture-fecundity trajectories, for the given C_Open levels (deciles). We then tested for significance (α = 0.05) of the linear interaction effects between architecture and C_Open, for the most important interactions.
3 RESULTS
The two multivariate analyses (PCAabs, PCArel) together revealed five considerable trait dimensions (Fig. \ref{154230}), reducing the number of included structural variables (Tab. \ref{591913}) to one third. Two of the major trait dimensions were the first PC axes in the absolute traits PCA (Fig. \ref{154230}a), primarily driven by crown size (PCabs1, 61.7% variance explained), but also by asymmetry (PCabs2, 16.5% variance explained), jointly explaining 78.2% of the total PCAabs inertia. There were no strong trade-offs identified within the first PCAabs axes (Fig. \ref{553668}a). However, multiple traits contributed unidirectionally to PCabs1 (all the absolute traits, except asymmetry), with tree height (H) and crown width (CW) forming both the peripheries of PCabs1 and a slight trade-off within PCabs2. Specifically, higher trees had narrower crowns, and were less asymmetric (Fig. \ref{553668}a). The variation in PCAabs was driven by both large-crowned and highly asymmetric trees, with disproportionally little variation among the small and symmetrical trees.