•A novel method to assess the distance of influence of agroforestry trees on crops.•Combining maps of spectral indices (Unmanned Aerial Vehicle) and geostatistics.•Geostatistical distance of influence of Faidherbia on millet was 17 m.•Crop-partial Land Equivalent Ratio computed (1.16), without need of true sole crops.•Yield (0.73 t ha−1) upscaled from sample plots to whole plot (error <20 %). The trees in agroforestry plots create spatial heterogeneity of high interest for adaptation, mitigation, and the provision of ecosystem services. But to what distance, exactly, from the tree? We tested a novel approach, based upon geostatistics and Unmanned Aerial Vehicle (UAV) sensing, to infer the distance at which a single agroforestry tree affects the surrounding under-crop, to map yield, litter (i.e. stover) and compute crop-partial Land Equivalent Ratio (LERcp) at the whole-plot level. In an agro-silvo-pastoral parkland of semi-arid western Africa dominated by the multi-purpose tree Faidherbia albida, we harvested the pearl-millet under-crop at the whole-plot scale (ca. 1 ha) and also in subplot transects, at three distances from the trunks. We observed that the yield was three times higher below the tree crown (135.6 g m−2) than at a distance of five tree-crown radii from the trunk (47.7 g m−2). Through geostatistical analysis of multi-spectral, centimetric-resolution images obtained from an UAV overflight of the entire plot, we determined that the ‘Range’ parameter of the semi-variogram (assumed to be the distance of influence of the trees on the Normalized difference vegetation index (NDVI)) was 17 m. We correlated the yield (r2 = 0.41; RRMSE = 48 %) and litter production (r2 = 0.46; RRMSE = 35 %) in subplots with NDVI, and generated yield and litter maps at the whole-plot scale. The measured whole-plot yield (0.73 t ha-1) differed from the one estimated via the UAV mapping by only 20 %, thereby validating the overall approach. The litter was estimated similarly at 1.05 tC ha-1 yr-1 and mapped. Using a geostatistical proxy for the sole crop, LERcp was estimated 1.16, despite the low tree density. This new method to handle heterogeneity in agroforestry systems is a first application. We also propose strategies for extension to the landscape level.