Statistics
All statistical analyses were performed using R version 3.5.1 (R Core Team, 2019). The data visualization was done with the package ‘ggplot2’ (Wickham, 2016).
Mass flow, volumetric flow rate, morphology data and functional/physiological parameters: Linear mixed effect (LMM) or generalized linear mixed models (GLMM) were used to determine the effect of phytoplasma infection on phloem mass flow, volumetric flow rates and morphological and functional parameters (phloem sap viscosity and density) in M. domestica , P. persica and P. communis leaves. To account for non-independent errors, which may occur due to repeated measurements at each tree, trees were specified as a random factor in all models. Models with different error distributions and link-functions were compared by AICc (Akaike information criterion with correction for small sample size) with the AICctab function from the ‘bbmle’ package (Bolker & R Development Core Team, 2017). Models with the lowest AICc values were used if model assumptions were valid. LMMs were fitted with the lmer function from the ‘lme4’ package (Bates et al. , 2015), and Typ III analysis of variance (ANOVA) with Satterthwaite’s method, which was calculated with theanova function from the ‘lmerTest’ package (Kuznetsova et al. , 2017). GLMMs were fitted with the glmer function from the ‘lme4’ package, and Typ II analysis of variance was calculated with the Anova function from the ‘car’ package (Fox & Weisberg, 2019) to determine treatment effects. Used error distribution, link-function and ANOVA results were specified in the Tables S3-S5 in the Supporting Information.
Phytohormone data and Brix values: Linear models were fitted to determine the influence of phytoplasma infections on the concentration of phytohormones and the relative density of phloem sap in M. domestica , P. persica and P. communis plants. In case of non-normality of the residuals the data was log, square root or box-cox transformed as specified in the Table S6. Variance heterogeneity was detected in abscisic acid content in samples from P. communis . In this case the generalized least squares method (GLS) was applied with the gls function from the ‘nlme’ package (Pinheiro et al., 2019). The different variance in the treatments was incorporated into the model with the varIdent variance structure. Treatment effects were calculated by Typ I analysis of variance.
Callose deposition: Linear models were fitted with the GLS method, to model the different variance structures of the data with the varIdent function. Treatment effects were calculated by Typ I analysis of variance and were reported in Table S7.
General procedure: For all models, the estimated marginal means (EMMs) and corresponding 95% confidence intervals were calculated and used to determine differences between treatment levels with the ‘emmeans’ package (Lenth, 2019). All model assumptions were validated graphically as recommended by (Zuur et al. , 2009).