Aggregation patterns in hierarchy/proximity spaces

The classical approaches for modelling spatial structures address aggregation through a set of distributional hypotheses. They require a large number of data and the definition of a spatial distance for the characterisation of spatial correlations. When only scarce abundance data and no Euclidean distance are available, we propose a method to explore the structuring patterns by the association of a hierarchical/proximity description of the space under study (units formed by subunits) and a multiple permutation test battery capturing the similarity between units (permutation being applied at subunits or units level). No Euclidean distances being available among the elements of a hierarchical level, proximity will be used instead of distance and will be defined by the structural relationships of units or subunits. The multiple test aims to assess different types of structuring, determined either by occupancy or by abundance or by both, at unit or subunit level. We address the relevancy of this approach with a simulation study where samples, formed by ordered subunits and units, are designed to exhibit the different types of structuring. The method is also illustrated with a case study (distribution of aphids on Citrus branches). It results from this application a decomposition of the complexity of pattern structuring and the evidence, for a single species in its natural environment, to develop diverse types of pattern structuring. Additionally to their direct implications, the results of the test battery may provide valuable preliminary hypotheses and could serve as a constraining context for the next step of modelling