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).