Linking Specialisation and Stability of Plant ... - OPUS Würzburg

5.3 methods 91
lated for all 56 insect species that were found at two or more
sites with at least five individuals per site.
In order to test whether a value of S as high or higher than the
observed value could have occurred by chance, we performed
randomization tests. For this purpose, we drew random samples
from all plant species available to the focal insect at each
site. In a first step, samples were taken separately for each date
at which the insect species was observed. The sample size was
equal to the number of flower visits of the insect species observed
at that date, while the probability of choosing a certain
plant species equalled the proportion of visits of all insects to
this plant species at that date and site. In a second step, all plant
visitation samples of the separate days were summed to obtain
an overall sample of flower visits as large as the total number
of visits of the focal insect observed at the site. The similarity
of these overall plant visitation samples of the two sites was
assessed in the same way as for the real visitation data. The
procedure was repeated 1000 times. A p-value was then calculated
as the proportion of all similarity values as high or higher
than the observed value (i.e., the value obtained from real visitation
data). Following (Manly, 2007), the observed value of
S was included in both the numerator and the denominator of
the proportion. Significance was assessed at the 5% level in all
randomization tests.
As in the case of floral tube lengths, due to an excess of zero
values the statistical analysis relating visitation consistency to
local specialisation (d’) and taxonomic group was divided into
two stages. First, consistency was analysed as a binary variable
(zero / non-zero consistency). In addition to d’ and order, we
included the mean consistency of random plant samples (mean
of 1000 replicates) and sample size (minimum number of observations
at the two sites) as covariates in the model. We then
built a second model including only non-zero consistency values,
this time treating consistency as a continuous variable. In
both cases, we first compared the fit of a mixed-effects model
with species as a random factor to a (G)LM with only fixed
effects. Since for the continuous data the mixed model did
not perform significantly better in a likelihood ratio test, we
proceeded with a linear model, whereas for the binary data a
GLMM was used. The GLMM was fitted using the function
“lmer” included in the R package “lme4” (Bates et al., 2012).
5.3.2.5 Phenological synchrony
For flower visitors that depend on particular sets of plant species
for survival and/or reproduction, we expected that the WMD