A crucial issue for landscape ecologists is identifying the spatial extents at which a landscape affects species occurrence. Multi-scale analyses are usually conducted to identify the “scale of effect”, that is, the spatial extent associated with the best relationship between landscape variables and species occurrence, which is assumed to be related to species traits. However, few guidelines exist to determine the range of distances to be investigated.

Based on the foraging distances of wild bee species, our main goal was to estimate the maximum distance of effect, that is, the distance beyond which the scale of effect for wild bee species is unlikely to be detected.

Using the InVEST pollination model, we (i) modelled bee categories with distinct foraging distances and identified the scale of effect on their simulated abundance (ii) defined an index, noted λ, that estimates the distance beyond which landscape composition has only negligible effects on simulated abundances. We validated our results by identifying the scale of effect on the abundances of 16 bee species collected in south-western France.

We detected a significant positive relationship between the average foraging distance (α) of the modelled bees and their scale of effect. The λ index was linearly related to the average foraging distances of bees (λ=5.4 α+253) and was above the identified scale of effect for the modelled bees. The λ was also found to be above the scale of effect for 93% of the observed bee species.

Our results suggest that the λ index is a good estimator of the upper limit of the scale of effect for wild bees. The λ index could be used to identify the minimum distance between sampling sites before setting up an experiment and the maximum buffer size required in multi-scale analysis to detect the scale of effect.

Using the InVEST pollination model, we simulated the visitation rate of 16 modelled bees that only differed in their average foraging distance (α-index), in 50 target sunflower fields located in south-western France in the Vallées et Coteaux de Gascogne site in 2016. The α-index ranged from 50 to 800 m with a 50-m increment. To assess the distance-weighted effects of landscape composition on the visitation rate of modelled bees we cropped the Land Use/Land Cover (LULC) input map around the centres of the 50 sunflower fields according to 108 different buffer radii (from 10 to 90 m with 10-m increment and from 100 to 5 000 m with 50-m increment).

In April 2016, we sampled bee species in 30 sites (situated in the Vallées et Coteaux de Gascogne) with three coloured pan traps per sampling site. The traps were set up and left for four days and wild bee individuals were counted and identified to the species level.

To identify the scale of effect for the 16 modelled bees and the 16 observed bee species, we performed multi-scale analyses with two landscape variables. The two landscape variables were (i) the mean availability of floral resources (in July for modelled bees, and in April for observed bee species), and (ii) the mean availability of belowground nests. These two variables were weighted means obtained by summing the indices of floral resource or nesting resource availability in each LULC category occurring around sampling sites within the 108 buffer radii.

Excel data files with (i) the visitation rates of 16 modelled bees in the 50 target fields and the mean availability of floral resources and mean availability of belowground nests according to 108 buffer radii, and (ii) the abundance of the 16 bee species collected in the 30 sampling sites (pan traps) and the mean availability of floral resources and mean availability of belowground nests according to 108 buffer radii.