Environmental and Ecological Statistics 1, 265-286 (1994) Diversity pattern and spatial scale: a study of a tropical rain forest of Malaysia FANGLIANG HE, PIERRE LEGENDRE and CLAUDE BELLEHUMEUR Ddpartement de sciences biologiques, Universitd de Montrdal, C, P. 6128 Suceursale Centre-ville, Montrial, Qudbec, Canada H3C 3J7 JAMES V. LaFRANKIE Smithsonian Tropical Research Institute, P.O. Box 2072, Balboa, Panama Received October 1994; revised January 1995 Scale is emerging as one of the critical problems in ecology because our perception of most ecological variables and processes depends upon the scale at which the variables are measured. A conclusion obtained at one scale may not be valid at another scale without sufficient knowledge of the sealing effect, which is also a source of misinterpretation for many ecological problems, such as the design of reserves in conservation biology. This paper attempts to study empirically how scaling may affect the spatial patterns of diversity (tree density, richness and Shannon diversity) that we may perceive in tropical forests, using as a test-case a 50 ha forest plot in Malaysia. The effect of scale on measurements of diversity patterns, the occurrence of rare species, the fractal dimension of diversity patterns, the spatial structure and the nearest-neighbour autocorrelation of diversity are addressed. The response of a variable to scale depends on the way it is measured and the way it is distributed in space. We conclude that, in general, the effect of scaling on measures of biological diversity is non-linear; hetero- geneity increases with the size of the sampling units, and fine-scale information is lost at a broad scale. Our results should lead to a better understanding of how ecological variables and processes change over scale. Keywords: fractal dimension, richness, scale, Shannon diversity, spatial structure, tree density, variogram 1. Introduction Ecology must deal with scale, because the objects it focuses on, the organisms and types of environ- ment, are rarely found to be homogeneously distributed through space or time. Environmental forcing, population and community dynamics, and chance events, are all sources of heterogeneity (Dutilleul and Legendre, 1993) and contribute to create spatial structures of various kinds, the most common of which are gradients and patches (Boreard and Legendre, 1994; Legendre and Fortin, 1989). Thus heterogeneity makes ecological variables and processes scale-dependent. An explo- ration of how diversity patterns change over scale is needed for extrapolation of fine-scale results to broader-scale phenomena, or the reverse. The concept of spatial scale refers to three main com- ponents of the sampling design: (i) Grain size, or size of the sampling unit, which is the surface or volume support of any parti- cular measurement. (ii) Extent of the total area being sampled, or field size. 1352-8505 © 1994 Chapman & Hall