Biological invasions represent one of the most significant threats to global biodiversity and agricultural systems, causing substantial ecological and economic damage worldwide. Among emerging invasive pests in East Asia, Aromia bungii, commonly known as the red-necked longhorn beetle, has become a serious threat in Japan. The species attacks several Prunus species, including ornamental cherry trees (Cerasus spp.), peach (Prunus persica), and plum (Prunus salicina). Because cherry trees play an important ecological and cultural role in Japan, the spread of this invasive beetle has raised growing concerns for landscape management and biodiversity conservation.
Since its first detection in Aichi Prefecture in 2012, A. bungii has expanded rapidly across urban and peri-urban areas. Understanding its spatial pattern is therefore essential for effective monitoring and early intervention. Spatial analysis can be applied to these processes. However, such analyses fundamentally depend on how spatial data are defined, including the geometry of the spatial grid, which can influence the results.
Thus, to examine how grid shape influences spatial analysis results, this study evaluates spatial autocorrelation measures using different tessellations of invasive species occurrence data and environmental variables. Specifically, we compared rectangular and hexagonal grids for analysing spatial patterns in A. bungii occurrence records and density of rivers in Saitama Prefecture, Japan.
Volunteer-based occurrence data for A. bungii were compiled from field surveys across Saitama Prefecture from 2017 to 2023, yielding 2,412 confirmed presence records. Records were classified as confirmed presences if either adult beetle observations (Adult-yes = 1) or evidence of tree damage (Tree_damage = 1) was recorded. All records were georeferenced using latitude–longitude coordinates (WGS84) and then reprojected to UTM Zone 54N (EPSG:32654) to ensure metric accuracy in spatial calculations. We assembled the occurrence data into predefined grid cells to explore spatial patterns across the study area and to enable consistent spatial aggregation and neighbourhood-based analyses.
We calculated density of rivers networks in Saitama, such original data were obtained by Digital Map (Basic Geospatial Information) of Geospatial Information Authority of Japan.
Two grid tessellation schemes were constructed over the study area. The rectangular grid consisted of 6,372 cells at a 1 km × 1 km resolution. Each rectangular cell contained pre-calculated directional river and road connectivity values (normalised lengths: 0–1) in four directions: top, bottom, left, and right. This configuration corresponds to rook contiguity, where only four directly adjacent neighbours are considered. To evaluate the effect of diagonal bias, the same rectangular grid was also analysed using queen contiguity, which includes eight neighbouring cells by incorporating both direct and diagonal neighbours. The hexagonal grid was generated using the H3 hierarchical spatial indexing system, producing hexagonal cells with an equivalent spatial resolution to the rectangular grid. To keep the overall grid coverage comparable to the rectangular representation, 6,392 hexagonal cells were generated to cover the study area. The rectangular grid had a side length of 1.0 km, whereas the hexagonal grid had a slightly larger side length of 1.074 km. H3 provides a discrete global grid system based on hexagonal indexing, enabling consistent spatial aggregation and neighbourhood relationships.
We found that grid type and spatial-weight configuration influenced the global Moran’s I results. For spatial autocorrelation, the rectangular grid produced Moran’s I values of 0.5373 (p = 0.001) under rook contiguity and 0.4636 (p = 0.001) under queen contiguity. Meanwhile, the hexagonal grid produced a lower value of 0.4144 (p = 0.001). The hexagonal grid yielded the lowest Moran’s I because all six shared edges are equidistant.
The higher value observed in the rectangular grid reflects inflated clustering due to diagonal adjacency, where diagonal neighbours are treated as equivalent to directly adjacent cells despite being farther apart. In contrast, the hexagonal grid provides a more geometrically balanced structure because all neighbouring cells are equidistant.
To further investigate the influence of weight configuration, we designed a distance-weighted queen scheme by assigning diagonal neighbors a weight of 1/√2. Moran’s I was 0.4732 (p = 0.001). Comparing Moran’s I across configurations in descending order (rook, queen, distance-weighted queen, and hexagonal), we found that the degree of spatial autocorrelation can be influenced by the choice of spatial grid, although all values were positive and statistically significant.

For river network density, all grid configurations produced high Moran’s I values (rectangular rook: 0.8365; rectangular queen standard eight: 0.8345; rectangular queen distance-weighted: 0.8349; and hexagonal: 0.5170), with p = 0.001 in all cases, indicating strong spatial clustering characteristics.
In both cases, the rectangular grid produced higher Moran’s I values under both rook and queen contiguity, indicating stronger spatial clustering. Theoretically, rook contiguity captures neighbourhood effects directly, but limits spatial association to four directions. Queen contiguity considers eight neighbours, but treats diagonal neighbours, which are farther away (1.414 km), as equivalent to direct neighbors at 1.0 km. Even when a distance-weighted scheme was applied to the queen configuration, the Moran’s I values changed little. In contrast, the hexagonal grid produced the lowest Moran’s I values in both experiments, suggesting greater stability because it uses six neighbors at equal distances.
In conclusion, we found that the choice of grid system is important for quantifying spatial autocorrelation. The rectangular grid tended to yield higher Moran’s I values, whereas the hexagonal grid tended to yield lower values. Further analyses should be conducted, specifically to investigate spatial clustering patterns using local Moran’s I under different spatial configurations.
Keywords: hexagonal grid, rectangular grid, tessellation, spatial autocorrelation, Moran's I, invasive species, Aromia bungii, Saitama, Cellular Automata