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 Type 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 Type 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 are 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 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 of 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 Type 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 Type I analysis of
variance (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).