Maps of plant individuals in (x, y) coordinates (i.e. point patterns) are currently analysed through statistical methods assuming a homogeneous distribution of points, and thus a constant density within the study area. Such an assumption is seldom met at the scale of a field plot whilst delineating less heterogeneous subplots is not always easy or pertinent. In this paper we advocate local tests carried out in quadrats partitioning the plot and having a size objectively determined via a trade-off between squared bias and variance. In each quadrat, the observed pattern of points is tested against complete spatial randomness (CSR) through a classical Monte-Carlo approach and one of the usual statistics. Local tests yield maps of p-values that are amenable to diversified subsequent analyses, such as computation of a variogram or comparison with covariates. Another possibility uses the frequency distribution of p-values to test the whole point pattern against the null hypothesis of an inhomogeneous Poisson process. The method was demonstrated by considering computer-generated inhomogeneous point patterns as well as maps of woody individuals in banded vegetation (tiger bush) in semi-arid West Africa. Local tests proved able to properly depict spatial relationships between neighbours in spite of heterogeneity/clustering at larger scales. The method is also relevant to investigate interaction between density and spatial pattern in the presence of resource gradients.
Abbreviations: CSR = complete spatial randomness; IPP = inhomogeneous Poisson process.
Nomenclature: Hutchinson & Dalziel (1954–1972).