Direct self-pollination rate ( S
) versus mean inflorescence size in Apis mellifera (A) and Bombus spp. (B). We estimated S
for each maternal genotype (i.e., inflorescences with the same genotype), and calculated mean inflorescence size as the average number of open flowers on all inflorescences with the same maternal genotype. For both plots, we based the best-fit lines on coefficients (β) estimated using a quasi-binomial mixed model (GLMM) with a logit-link function. We calculated χ2s and Ps using likelihood ratio tests to determine if the βs were significantly different from zero. Many of the S
values were 0 or 1 because of one or any combination of the following reasons: most inflorescences had a single pollinium inserted (the mode value for insertion rate was one pollinium), the multiple pollinia inserted into a single inflorescence were either all self- or all outcrossed pollinia, and we successfully genotype only one of the pollinia inserted into an inflorescence due to the extremely small amount of genetic material in each pollinium. The mean inflorescence sizes in A. mellifera and Bombus spp. were markedly different, but the range of inflorescence sizes (A. mellifera = 29–173; Bombus spp. = 15–151) overlapped.