Fertilization using manure minimizes the trade-offs between biodiversity and forage production in agri-environment scheme grasslands

of indicators (i.e. plant community, insect community and forage). Randomization tests com- pare observations to a probability distribution based on randomizations of the observed values under the single assumption that all randomizations have the same probability to be selected [37]. These tests do not rely on parametric assumptions regarding the distribution of the data, and so are especially useful for complex designs and low number of samples that reduce statis- tical power [38]. Hypothesis testing is similar to other statistical tests with the only difference that the probability value is estimated using the distribution created with the randomized observations. This type of analysis is widely used in ecology including estimation of species importance and ecosystem function [39,40]. Randomization was done as follows; we randomly shuffled the values of each indicator within blocks, but between treatments to retain the spatial correlation structure of the data. We then randomly selected one value for a pair of treatments and calculated the difference in mean between the two treatments carrying out a total of 54 comparisons con- sidering the possible treatments combinations and the three blocks design. We then repeated the process 10,000 times to build a reference distribution. Finally, the observed mean difference between the same pair of fertilizer regimes was compared to the reference distribution. The P value represents the proportion of times the value of each observed test

statistic was greater or equal to each randomized test statistic. Thus significant P values fall within the 97.5 or the 2.5% tails of the reference distribution, leading us to reject the null hypothesis of no difference between the observed and randomized test statistics for the pair of treatments. In practice, we use the absolute difference between the observed and ran- domized statistic so that P values are deemed statistically significant if < = 0.05. This pro- cess was repeated for all the fertilizer treatment combinations, so all fertilizers were compared between each other. The randomization testing scheme is illustrated in Fig 1 in S1 File for one of the three experimental blocks and for one pair of treatments only. Analy- ses used the vegan [41], dtplyr [42], plyr [43] ggplot2 [44] and Hmisc [45] packages embed- ded in a workflow written in R version 4.1.3 [46]. The R code is provided as supplementary information (S2 File) Identification of the optimum fertilizer regime supporting forage, plant communities and insect communities. Fertilization drives trade-offs in grasslands. This is because increas- ing productivity drives changes in the plant community that ultimately affect positively or neg- atively insect communities [33]. Therefore, we defined the optimum fertilizer regime not only as the one with the highest mean value across all the indicators from all group of indicators but also the one with the lowest variation across all indicators. In this sense, the optimum regime

is the one that minimizes the trade-off between group averages and maximizes their average values. As a result, the range of the indicators associated with the optimum treatment may well be greater than the observed maximum or minimum of any one indicator observed across the experiment (Fig 2 in S1 File). We again used randomization tests to assess for differences between treatments. However, instead of comparing mean differences for each indicator individually. We built distributions and compared differences between pair of treatments for the weighted mean and weighted standard deviation calculated across all indicators (group average); that is instead of the mean being derived from one indicator we calculate a weighted mean across all 12 indicators. In both cases, statistical weighting was established as explained in the first section. We repeated the process for each pair of fertilizers and estimated P values as explained in the previous sec- tion. However, for weighted standard deviation a significantly lower observed indicator is interpreted as better performance because it indicates that the mean is derived from indicators that vary less across the optimum treatment. PLOS ONE Manure minimizes trade-offs between biodiversity and forage production in agri-environment scheme PLOS ONE | https://doi.org/10.1371/journal.pone.0290843 October 4, 2023 6 / 18