Statistical analysis
If pollen-supplemented plants have greater reproductive success than
control plants within our experimental pairs, this indicates that plant
reproduction is pollen-limited. We first tested for pollen limitation
within each site using linear mixed effects models (LMMs) and
generalized linear mixed effects models (GLMMs) using the lme4 (Bates et
al. 2015) and glmmTMB (Brooks et al. 2017) packages respectively with
treatment (pollen addition vs. control) as a predictor, measures of
reproductive success as response variables (fruit to flower ratio, seeds
per fruit, fruit size, and fruit mass), and experimental pair as a
random intercept term. Plant individual was also included as a random
intercept term for responses that were measured multiple times within
individuals (seeds per fruit, fruit size, and fruit mass). We used GLMMs
for fruit and seed set, with a binomial error distribution for fruit
set, or betabinomial when overdispersed, and a Poisson distribution for
seed set, or negative binomial when overdispersed. We used LMMs for
fruit size and mass. Because individuals produced varying numbers of
flowers, fruit set models were weighted by the number of flowers
produced by each individual. We used a Bonferroni correction to
determine our critical p-value for significance to account for multiple
tests. As we repeated each test for each of our six sites, our critical
p-value is 0.0083 (0.05/6).
Second, to investigate the relationship between impervious surface and
the magnitude of pollen limitation, we used linear models with
impervious surface as our predictor variable, and the differences in
reproductive success within pairs as response variables. To calculate
the difference, control reproductive responses were subtracted from
supplement responses for each plant pair within each site. Because
impervious surface at 500 m and 1000 m radii were highly correlated (r =
0.99, p < 0.001) and produced consistent results, we focus
only on impervious surface at 500 m for our analyses.
To assess how impervious surface related to pollinator visitation, we
used GLMMs with impervious surface as a predictor variable, visitation
rate per flower per minute as a response variable, and date as a random
intercept to account for repeated sampling of pollinator visitation
across multiple days. Because our visitation rates were based on
observations conducted across varying numbers of flowers, we also
weighted our model by the number of flowers observed. We used a
betabinomial error distribution because our visitation data were
overdispersed. For one observation period in C. pepo , the
visitation rate was slightly greater than 1 (1.044); we rounded this
value to 1 to fit the betabinomial model. To determine whether
visitation patterns were driven by the most frequently observed
pollinators or by the taxa expected to be the most effective, we also
ran the visitation rate models with only Bombus spp. and only
“other bees,” those too small to identify in the field, for tomato and
with only Peponapis pruinosa for squash (which was the
most frequent and expected visitor).