Data analyses
We used generalised linear mixed‐effects models to test the interactive effects of herbivory and pollination treatments on: (a) proportion damaged beans per plant (beans with B. rufimanus emergence holes) (b) faba bean yield components (individual bean weight, total bean weight per plant, number of beans per pod, number of beans per plant, number of pods (mature, immature and unfertilized) per plant, proportion of mature pods per plant, and yield (kg.ha-1), and (c) plant growth components (plant height and aboveground biomass, root length and biomass). Normal distributions were used except for number of pods and beans per plant, where a Poisson distribution was used or a negative binomial when data was overdispersed, and for proportion of damaged beans and mature pods per plant where a binomial distribution was used (see Table 1 for model structures). The explanatory variables in all models included the H+/H- and P+/P- treatments and their interaction term. Despite the care taken to remove B. rufimanusfrom the H- cages at the beginning of the experiment, beans with emergence holes were also found in these cages, and there was a large variation in damage between plants within each H+/H- cage (Fig. S3). We therefore, in addition to the main H+/H- treatment effect (i.e. plant-stand scale, measured by averaging individual plant scale responses in each cage), investigated the effect of herbivory damage at the plant scale, measured as percentage of damaged beans per plant within cage (% Damage). Proportion of damaged beans did not vary with pollination treatment levels (Table 1, p=0.09). We tested all plant yield and growth variables, and used P+/P- treatment and % Damage per plant and their interaction term as explanatory variables. The random structure in all models included cage identity (N=28) nested within block (N=7), except for yield (kg.ha-1) per cage where only block was included. If significant interactions were found, post-hoc tests using the “emmeans” package were carried out to investigate the direction of the effect.
To test the effects of herbivory on observed pollinator behaviour (proportion of legitimate , robbing and EFN visits) and on pollinator visitation rate (visits per flower per time unit) we used a generalized mixed‐effects model with a binomial and a normal distribution respectively. The explanatory variables included H+/H- treatment and the number of open flowers per m2 and their interaction term. To account for addition of sugar-water to the pollinators on the 7th of July a binary factor (sugar-water: yes/no) was included as well as its interaction with number of open flowers per m2 and herbivory treatment. The interaction between herbivory treatment and sugar-water was never significant and did not improve the models as determined by the Akaike Information Criterion (AIC), indicating that the effect of herbivory on pollinator behaviour did not change after the addition of the sugar-water. This interaction was therefore excluded. To investigate the effect of herbivores on number of open flowers per m2 in cages with pollinators, we used a generalized mixed‐effects model with H+/H- treatment as explanatory variable. The random structure for all models incorporated the sampling round (N=15) nested within cage identity and block.
The residuals of all models were visually inspected to validate the model assumptions and additionally, generalized linear models were checked for overdispersion using “DHARMa” (Hartig & Lohse, 2020). Multicollinearity was checked for all models (variation inflation factor <2). All analyses were conducted in R version 3.6.3, using packages “nlme” (Pinheiro & Bates, 2020), “lme4” (Bates et al., 2020), “emmeans” (Lenth et al., 2021) and “ggplot2” (Wickham et al., 2020) to plot data.