How far is enough? Prediction of the scale of effect for wild bees

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 1) modelled bee categories with distinct foraging distances and identified the scale of effecton their simulated abundance 2) defined an index, noted lambda, that estimates the distance beyond which landscape composition has only negligible effects on simulated abundances. We validated our results by identifying the scale of effecton the abundances of 16 bee species collected in south-western France. We detected a significant positive relationship between the average foraging distance (alpha) of the modelled bees and their scale of effect. The lambda index was linearly related to the average foraging distances of bees (lambda = 5.4 alpha + 253) and was above the identified scale of effect for the modelled bees. The lambda was also found to be above the scale of effect for 93% of the observed bee species. Our results suggest that the lambda index is a good estimator of the upper limit of the scale of effect for wild bees. The lambda 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.

Automated summary

This study aimed to determine the upper limit of the scale of effect for wild bee species. The results showed a significant positive relationship between bee foraging distance and their scale of effect. An index lambda was introduced to estimate the distance beyond which landscape composition has negligible effects on bee abundances. The lambda index can be used to determine 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.