Estimating inter-group interaction radius for point processes with nested spatial structures

A statistical procedure is proposed in order to estimate the interaction radius between points of a non-stationary point process when the process can present local aggregated and regular patterns. The model under consideration is a hierarchical process with two levels, points and clusters of points. Points will represent individuals, clusters will represent groups of individuals. Points or clusters do not interact as soon as they are located beyond a given interaction radius, and are assumed to interact if their distance is less than this interaction radius. Interaction radius estimation is performed in the following way. For a given distance, observations are split into several clusters whose in-between distances are larger than this distance. For each cluster, a neighbourhood and an area in which this cluster is randomly located is defined under the assumption that the distance between the cluster and its neighbourhood is larger than the interaction radius. The pp-value of a test of this assumption is then computed for each cluster. Modelling the expectation of this pp-value as a function of the distance leads to an estimate of the interaction radius by a least-square method. This approach is shown to be robust against non-stationarity. Unlike most classical approaches, this method makes no assumption on the point spatial distribution inside the clusters. Two applications are presented in animal and plant ecology.