2.4. Data analysis
Differences in reproductive success between supplemental hand-pollination and natural pollination at community and species levels were tested for both seed production and seed weight. Because the data contained many zero values and even after transformation did not meet the normality assumption, we applied non-parametric tests. At community level we used permutational MANOVA with permutation of residuals under a reduced model, where treatment served as fixed and plant species as random factor. At species level we used a one-sided test in non-parametric permutational ANOVA. Both tests were done within the PERMANOVA package in Primer 6 software (Anderson et al. 2008).
We calculated the Pollen Limitation index (PL) as PL = (Ps −Po)/Pmax[Ps or Po] (Baskin and Baskin 2018), where Ps is the number of seeds from pollen-supplemented flowers, Po is the number of seeds from open-pollinated flowers and Pmax is the larger of the two values (Ps or Po). For all subsequent analyses, similarly to Larson and Barrett (2000), we established zero as the lower boundary of the PL, because any negative indices likely resulted from a potential experimental error (Young and Young 1992), and therefore are not meaningful in the context of our study.
Although most studies assumed a linear relationship between possible plant seed set and traits, some studies predicted numerous relationships between plant and visitors to be non-linear (Morris et al. 2010, Thomson 2019). Thus, all correlations of PL with plant characteristics were tested using both simple and multiple linear as well as unimodal regressions. Because of right-skewed distribution, the values for nectar production and number of flowers were log-transformed prior to analysis. For selection of the best model we used AIC stepwise selection. All analyses, unless otherwise specified, were conducted using R (R Core Team 2019).