Grid origin affects scaling of species across spatial scales

Aim Distribution maps of species based on a grid are useful for investigating relationships between scale and the number or area of occupied grid cells. A species is scaled up simply by merging occupied grid cells on the observation grid to successively coarser cells. Scale-occupancy relationships (SORs) obtained in this way can be used to extrapolate species down, in other words to compute occupancies at finer scales than the observation scale. In this paper we demonstrate that the SOR is not unique but depends on where one positions the origin of the grid map. Innovation The effect of grid origin on SORs was explored with the aid of the Dutch national data base FLORBASE, which contains the observation records of all 1410 wild vascular plants in the Netherlands on a 1-km square basis. For each species, we generated 2500 unique SORs by scaling up from 1 km, in steps of 1 km, to squares of 50 km. We computed the sensitivity of the SOR to the grid origin for each species, and subsequently analysed the factors that determined this sensitivity. The effect of grid origin on downscaling was demonstrated by means of a simple power function that we used to extrapolate down from both a 2-km and a 5-km grid, to the original 1-km grid. It appeared that the position of grid origin could have a substantial effect on SORs. The sensitivity of SORs to the position of the grid origin depended on three characteristics of a species' spatial distribution: rarity, degree of spatial clustering and the position of the distribution relative to the border of the investigated area. Rare species with a clustered distribution near the border were particularly highly sensitive. The dependence of SOR on grid origin caused unpredictable and non-random errors in downscaled occupancies. Main conclusions In future, the whole bandwidth of scaled occupancies should be considered when testing and interpreting mathematical relationships between scale and occupancy. Moreover, downscaled occupancies should be interpreted cautiously.