geoGraph: Connectivity modelling across geographic space with hexagonal discrete global grids

1. Estimating the movement and connectivity of organisms across landscapes is central to research in ecology and evolutionary biology. Although graph-based approaches representing geographic space as weighted networks provide a flexible and computationally efficient framework for such analyses, existing tools either perform their computations only on rectangular raster grids, thus introducing systematic directional and area distortions at global scales, or rely on bespoke pipelines that limit the general applicability of recent hexagonal-grid analyses. 2. To overcome these shortcomings, here we present geoGraph, an R package that brings graph-based spatial modelling to discrete global hexagonal grids. By representing landscapes on an equal-area hexagonal tessellation of the sphere, geoGraph enables global-scale analysis without projection distortion while retaining the flexibility of the graph framework and the performance of the graph and RBGL/Boost libraries. The package integrates both raster- and vector-based GIS data into a single cost surface, supports custom grids at various resolutions, and provides a complete pipeline from raw GIS layers to graph-algorithmic outputs, together with tools for visualising and interactively editing graphs. 3. We illustrate geoGraph by revisiting previous studies of isolation by distance among human populations in the Human Genome Diversity Project panel. At a global scale, restricting movement to land raised the correlation between geographic and genetic distance from r = 0.74 (great-circle) to r = 0.84. On a finer grid within Asia, accounting for terrain ruggedness improved the fit, with the best-fitting models implying reduced movement across the Himalaya and Tibetan Plateau. These analyses demonstrate that geoGraph can model movement and connectivity appropriate to the desired spatial scale and that the level of geographic realism required is itself scale-dependent. 4. By combining discrete global grids with the power of graph algorithms, geoGraph enables seamless connectivity analysis from landscape to global scales. It is broadly applicable across landscape genetics, phylogeography, conservation planning, and studies of human dispersal, and is particularly suited to large-scale problems that rectangular-raster tools cannot address without distortion.