On the correlation structure between point patterns and linear networks

During the last few decades, it has become increasingly popular the study of events that occur on a network of lines. Examples include, for instance, wildlife–vehicle collisions, street crimes, traffic accidents or invasive trees in agricultural areas. For all these examples, as points are related to a linear network, the analysis of such spatial configurations is focused on the description of the spatial configuration of points assuming that the whole point pattern is placed over the linear network. However, in some cases, the dependence between a point pattern and a linear network is not evident. In cases where the points do not occur directly over the linear network, but within an area of influence, the spatial dependence between points and line segments is not immediately obvious. In this work, we defined a new second order characteristic, based on the Ripley's K function, to analyse the spatial structure between point patterns and linear networks. An edge-corrected estimator is defined and illustrated through a simulation study. We applied the resulting estimator to analyse the spatial interaction between human-caused fires (HCFs) and a road network in a square area of 30 × 30 km2 in Asturias (North of Spain). Our results suggest that HCFs depend on the underlying road network, where fires tend to be placed within a buffer area of around 0.5 km away from the roads.