Vincent de Leijster

97 Ecosystem services trajectories in coffee agroforestry in Colombia over 40 years 5 service indicators. We selected the orthogonal axes that together explained more than 50% of the variance and used these axes (principal components; PCs) to identify which biotic and abiotic factors best explain them in a multiple regression model (OLR). To do so, we used as biotic and abiotic conditions vegetation, soil, micro-climate, farm and management characteristics that were independently measured from the ecosystem services indicators (Table 5-1). These biotic and abiotic conditions were included as fixed factors to explain the PCs as response variables. First, we tested for correlations among the biotic and abiotic variables, using Spearman correlation, to not include variables with high collinearity and chose one representative variable of correlated biotic and abiotic variables that best correlated to the response variable. Therefore, one variable was chosen as a representative for vegetation characteristics, soil conditions, and for farm and management characteristics the individual indicators were not correlated so they were all included. Then, we used the multiple regression analysis and included a maximum of three abiotic and biotic variables as fixed factors, as our sample size did not allow for more fixed factors. We compared the models with different fixed factor combinations based on Akaike Information Criterion (AIC), which is an estimate for likelihood of the model with lower values indicating a better model fit. This process resulted in one final model that best explained a single PC. Moreover, for each variable in the model we tested whether the estimate of the coefficient was significant, and its confidence interval did not cross zero, indicating a reliably estimated coefficient. We visually assessed whether the residuals of the final model met the assumptions of homoscedasticity and normal distribution by inspecting density plots and residuals vs. fitted values plots. Similarly, we separately assessed how the biotic and abiotic conditions influenced the provisioning of coffee (coffee yield and coffee productivity). The multiple regression analysis was performed using the R packages ‘lme4’ and ‘stats’. Additionally, we related each ecosystem service indicator of all the farms to their biotic and abiotic factors by using Spearman correlations. 5.2.5.4 Agroforestry tree planting arrangement effect on ecosystem service supply We tested whether the tree spatial arrangement in the agroforestry farms influenced supply of ecosystem services, as well as vegetation and soil characteristics, and general farm and management characteristics (Table 5-1). We used either OLR or GLM, depending on the distribution and/or the characteristics of the response variable. We did this by including tree arrangement as a categorical fixed factor. The residuals of the OLR models were evaluated for their ability to meet the assumptions of homoscedasticity and normal distribution. If