Topology in spatial sampling and modeling is often overlooked, yet it can have significant effects on outcomes. A 2008 study by White and Kiester shows how the arrangement of cells in a spatial network, such as hexagonal versus square grids, can influence ecological model results. This invites deeper reflection on the frameworks we adopt in geospatial analysis.
Topology and Its Role in Spatial Models
In this context, topology refers to the structure of spatial samples and how they are connected to each other. In ecology, this arrangement can influence patterns such as species dispersal and the stability of modeled populations. White and Kiester (2008) compared three types of spatial configurations: hexagonal grids, square grids with von Neumann neighborhoods which consider only adjacent sides, and square grids with Moore neighborhoods which include diagonal connections. Their study used neutral ecology models to assess whether these arrangements affect model behavior. As the probability of dispersal increased, the differences between topologies also became more apparent. More connected configurations led to broader and more uniform species distributions.
Hexagonal tessellations often outperform square grids because each cell is connected to six equally distant neighbors. This balanced structure supports more isotropic relationships and avoids geometric biases that occur in square grids. The study found that hexagons can support larger, more evenly spread populations. This suggests that the choice of tessellation is not just a background technical detail but a key factor in how spatial models perform.
Reflection on My Own Work
This study reminded me of my Master’s project where I used square sampling at 2 km intervals for a spatial autoregressive model. I chose that setup without questioning its limitations. It simply followed conventional practice. Yet, this paper made me think: what if I had used a hexagonal sampling grid instead? That change might have altered how spatial relationships were modeled, possibly leading to different outcomes. It also makes me wonder how established geostatistical tools like Moran’s I or Getis-Ord G* would behave if they were applied on hexagonal structures.
If spatial relationships are sensitive to topology, then it may be time to update how spatial statistics and spatial regression models are built. Many models rely on adjacency matrices and neighborhood definitions. These often assume square grids and Cartesian logic. By introducing hexagonal sampling as an option, we could improve spatial continuity and reduce edge effects. This could be particularly helpful in modeling natural phenomena where uniform neighborhood relationships are important.
This paper is a powerful reminder that core design choices, like grid structure, can meaningfully shape analytical results. Revisiting our spatial assumptions could lead to more consistent and realistic models across geospatial disciplines.