A test for spatial relationships between neighbouring plants in plots of heterogeneous plant density

Maps of plant individuals in (x, y) coordinates (i.e. point patterns) are currently analysed through statistical meth- ods 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 partition- ing 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 spa- tial randomness (CSR) through a classical Monte-Carlo ap- proach 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 co- variates. Another possibility uses the frequency distribution of p-values to test the whole point pattern against the null hypoth- esis of an inhomogeneous Poisson process. The method was demonstrated by considering computer-generated inhomoge- neous point patterns as well as maps of woody individuals in banded vegetation (tiger bush) in semi-arid West Africa. Lo- cal 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 inter- action between density and spatial pattern in the presence of resource gradients.

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