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A Test for Spatial Relationships between Neighbouring Plants in Plots of Heterogeneous Plant Density

Pierre Couteron, Josiane Seghieri and Joël Chadœuf
Journal of Vegetation Science
Vol. 14, No. 2 (Apr., 2003), pp. 163-172
Published by: Wiley
Stable URL: http://www.jstor.org/stable/3236691
Page Count: 10
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A Test for Spatial Relationships between Neighbouring Plants in Plots of Heterogeneous Plant Density
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Abstract

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.

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