Vincent de Leijster

42 Chapter 3 failed to meet one of these assumptions, we considered alternative distributions (Appendix Table A3-1). A negative binomial distribution (arthropod, pollinator and pest abundance), Poisson distribution (arthropod richness) and a zero inflated Poisson (natural enemies) were considered for count data and a gamma distribution for continuous data (soil K content, understory carbon, almond yield and fruit set). Non-Gaussian distributed models were tested for overdispersion using the method described by Zuur et al. (2013), which was not the case for any of the models. We calculated the models’ marginal R 2 to explain the variance of the fixed factor and the conditional R 2 for the variance of the fixed and random factors together, by using the MuMIn package (Nakagawa et al., 2017). Likelihood ratio test ( function drop1) was used to test for significant effects of the fixed factor. Tukey’s pairwise comparisons ( function glht) were applied to models that showed significant effects. Effects were considered significant at α<0.05. The GLMM analysis was conducted using the lme4 package and the functions glmer and lmer in R (Version 3.4.3). Principal Component Analysis We used a PCA to determine whether ecosystem services formed bundles or trade-offs and assess whether treatments would cluster based on their effects on ecosystem services. Bundles were defined as multiple ecosystem services that appear in the same quadrant defined by the first three PCA axes. To select which PCA axes were relevant, we used the contribution of each axis to variance explained and then picked the minimum number of axes that explains >70% of the variance. For display purposes, we choose 2D graphs with all PCA axes combinations (in our case 72% of the variance was explained by the first 3 PCA axes, and we plotted three 2D plots: PCA1-PCA2, PCA1-PCA3, and PCA2-PCA3). A trade-off occurred when one ecosystem service was on the positive side of a PCA axis and another ecosystem service on the negative side of that axis. When ecosystem services were related to different axes it was assumed that they did not interact because of the orthogonality imposed in the PCA. The abundance of natural enemies of pests was excluded from this analysis because the response variable had too little variance for rescaling. We applied the prcomp function in R (Version 3.4.3) on the rescaled ecosystem service indicators. 3.3 RESULTS We found that on average the overall ecosystem service index was highest in the compost treatment (CM), followed by green manure (GM) and no tillage (NT) and the lowest for conventional tillage (CT) treatments (Figure 3-2 and Appendix Table A3-2). Compared