## 2 Materials and Methods
### Statistical Analysis  
Statistical analysis was performed with the statistical software R, version 3.6.1 [35]. Data for all continuous numerical measures from the berry and bunch analysis were tested for each variety (Riesling, Cabernet Sauvignon) using Bayesian generalized linear mixed model analyses (R-package brms, version 2.10.0) [36; 37; 38] accounting for the sampling structure and pseudo replications (block, ring) and their respective repeated measures in time (year or date). Fixed effect estimation included treatment (aCO\({}_{2}\), eCO\({}_{2}\)), time (year or date), and their interaction. Focusing on the estimation of differences between treatments, time points were treated as factorial variables. For these measures, a Gamma distribution likelihood with a log-link function was assumed, accounting for deviations from a normal distribution, i.e., skewness, and the fact that all measures are restricted to positive values only, while assuming the variance to increase with the mean, which is typical for ecological data [39]. Weakly informative priors were set for the intercept and effect sizes. Each model was set up to run four Markov chains of 8000 iterations each. With a warm-up phase of 4000 iterations, each posterior included 16,000 samples in total. Posterior predictions were used for both treatments to estimate the difference between aCO\({}_{2}\) and eCO\({}_{2}\) measures for each time point. Results included the probability (%) of the treatment effect being larger than zero by estimating the proportion of posterior predicted differences between eCO\({}_{2}\) and aCO\({}_{2}\) that was greater than zero. A significant difference, i.e., a high probability of a difference, was attested when this probability of the treatment effect was estimated to be above 90% (positive difference) or below 10% (negative difference). In addition, information was provided on the most probable point estimate by calculating the median difference and the 50% posterior highest density interval (HDI) that stands for the 50% most probable point estimates. Count data on berry size classes were analyzed by Bayesian ordinal regression applying a mixed effects adjacent category model with category specific effects and a probit-link function [40]. Each analysis was based on the data of sampled bunches and split into yearly data sets. Again, controlling of sampling structure (block, ring, and bunch) was performed to estimate the treatment effect on the berry size distribution. By using default, uninformative priors, models were run with four chains each, with a total of 8000 iterations with 4000 warm-up iterations which were not included in the final samples. From model results, posterior predictions were calculated to estimate probabilities for sampling specific differences in categories between aCO\({}_{2}\) and eCO\({}_{2}\) single berry samples. In addition, the median of this difference is provided. No HDI was estimated for this discrete ordinal data. Model quality and convergence were checked by visual comparison of the posterior distributions and the data, visual inspection of well-mixedness from trace plots of the Markov chains, and controlling a Rhat measure of below 1.01 [41]. The length of the Markov chains guaranteed adequate multivariateeffective sample sizes [42] for a Monte Carlo standard error of below 5% for all models [43]. The ratio of estimated bulk and tail effective sample sizes (ESS) to the total number of samples was consistently kept above 0.1 for all model parameters. Limiting the model complexity by only including CO\({}_{2}\) treatment and year effects came with the consequence that other environmental factors, i.e., annual temperature cycle, precipitation, etc., might be confounded within the year effect and, thus, possible interactions could not be detected. Hence, higher residual errors are to be expected, which can cause higher uncertainties in posterior predictions.