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).