Generalized linear models
To assess the relative importance of biotic variables (flower and host
specialization and distribution of the interacting species) and bee body
size (which relates to foraging range) for explaining wild bee
occurrence in the Netherlands, we developed a series of Generalized
Linear Models (GLMs) (fig. 1). For the flower visiting bees, we used the
plant observation data, and we calculated the amount of grid cells
occupied by each visited plant species. Secondly, we computed a measure
of flower specialization, calculated as the diversity of genera visited
in the interaction database for every flower visiting bee, using the
Shannon-Wiener index (Shannon 1948). Thirdly, we used the information on
body size from the bee trait database. The body size was measured using
the intertegular distance (ITD, in mm) as a proxy, which is the distance
between the wing insertion points (Greenleaf et al., 2007). The
cleptoparasitic bees were modelled in a similar way, except that the
distribution of the interacting species was calculated from observation
data from potential host bees (table S2 in supporting information) and
the host specialization was the number of potential hosts in the
literature (Peeters & Nieuwenhuijsen 2012). In both cases, the
explanatory variables were standardized, centred, and a gamma
distribution with an inverse link function was used. The gamma
distribution is applicable for situations in which we want to speculate
about the response variable without certainty about its distribution
(Faraway 2016) and for ecological data with non-zero values (Foster &
Bravington 2013). Model performance was quantified with the AICc and the
R2, which represents the proportion of the variance in
the dependent variable that the model explains. Modelled species that
did not find a contribution (e.g. no features of the respective variable
present in the model) of their interacting species to their distribution
were left out of the analysis. The three explanatory variables resulted
in eight possible combinations of variables and we evaluated the models
using the AICc as described in Hurvich & Tsai 1989. The GLMs were
developed in the stats package in base R version 4.0.3 (R Core Team
2020).