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.