Data analysis
We assessed whether honey bee abundance, measured as the total number of honey bees visiting flowering plants during morning and afternoon netting transects, was associated with native bee abundance in meadows and native bee visits to C. quamash using two separate linear mixed effects models (LMMs). The first model had honey bee abundance as a fixed effect and the second had the abundance of honey bees visiting C. quamash during netting transects as a fixed effect. In both models, site and sample round were included as separate random effects. We fit models using the lmer() function in the lme4 package (Bates et al. 2015) and tested for significance using likelihood ratio tests. All analyses were conducted in R (R Core Team 2022).
We determined the association between native bee and honey bee C. quamash visitation and three measures of pollination: pollen deposition, pollen tubes, and seed set. Because these measures were taken from the same plants, but not necessarily the same flowers, we performed separate analyses using generalized linear mixed effects models (GLMMs). Each model included as fixed effects (i) the abundance of honey bees visiting C. quamash and (ii) and the abundance of native bees visiting C. quamash . We also included random intercepts for site and sample round. Pollen deposition and pollen tube data were over-dispersed, so we modeled responses using negative binomial distributions. We modeled seed set as a binary response where fertilized ovules were successes and unfertilized ovules were failures and included plant as a random effect to account for non-independence of flowers on the same plant. For all models, we used the glmmTMB package (Brooks et al. 2015), and calculated p-values using likelihood ratio tests.
Using data from the controlled honey bee visit experiments described above, we assessed the direct relationship between increasing honey bee visits and C. quamash pollination by fitting a GLMM which included the number of honey bee visits as a fixed effect as well as date and plant ID as separate random effects to account for non-independence of flowers observed on the same plant and/or day. We modeled C. quamash pollination as a binomial response: successes were flowers that produced fertilized ovules and failures were flowers with no fertilized ovules. We tested for significance using likelihood ratio tests.
We evaluated how pollen and nectar availability responded to honey bee introductions by fitting two separate GLMMs which included as fixed effects (i) the abundance of honey bees in meadows, (ii) the abundance of native bees in meadows, and (iii), to control for baseline pollen and nectar resources, either the mean pollen availability (measured as the proportion of dehisced anthers with pollen) or the mean nectar availability in unvisited bagged flowers. Both models included site and sample round as separate random effects. Data collectors varied in their ability to extract nectar from flowers, so we also included data collector as a random effect in both models. Nectar and pollen data were zero-inflated, so we modeled nectar and pollen availability as presence/absence binary responses. We calculated p-values using likelihood ratio tests.
To assess whether native bees were more effective than honey bees as pollinators of C. quamash we first confirmed that pollinator taxon was an important predictor of effectiveness using generalized linear models. We modeled seed set as a binomial response where successes were flowers that produced fertilized ovules and failures were flowers that produced no fertilized ovules. Flies and large-bodiedAndrena spp. were infrequent visitors (Table S1), so we removed their visits from the analysis. Our maximal model used three predictors: (i) the pollinator taxon observed, (ii) whether the stigma was contacted, and (iii) the day of the observation. We tested for significance of predictors by stepwise model simplification and performed Chi-square tests to compare individual taxa.