Spatial Intensity Estimation of Fish Distribution in Colombian River Networks Using Hydrological Distance and Point Pattern Analysis on Linear Networks

Abstract

Colombia possesses one of the most extensive and biodiverse hydrographic networks in the world, creating the need for spatial methodologies capable of accurately representing the structure and connectivity of river systems. This study presents a methodological framework for analyzing the spatial distribution of fish populations in river networks using hydrological distance rather than traditional Euclidean distance. The proposed approach incorporates flow direction, network connectivity, and watershed topology, which are essential features for properly characterizing ecological processes in freshwater environments. The methodology was implemented in Python through the construction of a directed graph based on HydroRIVERS data for the department of Cundinamarca, Colombia. A total of 500 simulated points representing fish observations were generated and assigned to their nearest river segments through a snapping procedure. Subsequently, a hydrological distance matrix was computed among all points, and an intensity function was estimated using a Gaussian kernel adapted to linear networks. The bandwidth parameter was objectively selected through leave-one-out cross-validation to optimize the intensity estimation process. The results enabled the identification of areas with higher concentrations and intensities of fish occurrences across the river network, demonstrating that hydrological distance provides a more realistic representation of spatial relationships in aquatic ecosystems than conventional Euclidean metrics. Furthermore, the proposed implementation offers a reproducible and scalable framework for ecological, hydrological, and conservation studies. The findings highlight that incorporating network connectivity and flow direction into spatial modeling significantly improves the characterization of fish distribution patterns and other phenomena associated with hydrographic networks.