The IIASA gridded population downscaling methodology is one of only a few existing models for constructing spatially explicit global population scenarios. Furthermore, this methodology is unique in that it does not employ proportional scaling techniques or extrapolated rates of change. Instead, the IIASA methodology applies a gravity-type spatial allocation model to distribute projected national-level change. In this technical note we present and analyze the IIASA methodology within the context of a hypothetical population situated in one-dimensional space. Our results indicate that border effects exert significant influence over spatial population outcomes. Furthermore, over a reasonable time horizon (100-150 years), we find that in most cases the IIASA methodology will have a smoothing effect on existing population distributions. This paper is the first in a series related to the construction of spatial population scenarios organized around the IIASA methodology, and the results presented within not only help to explain the IIASA scenarios, but inform feature research and refinements to the methodology.