A comparison of methods for the statistical analysis of spatial point patterns in plant ecology

Abstract

We describe a range of methods for the description and analysis of spatial point patterns in plant ecology. The conceptual basis of the methods is presented, and specific tests are compared, with the goal of providing guidelines concerning their appropriate selection and use. Simulated and real data sets are used to explore the ability of these methods to identify different components of spatial pattern (e.g. departure from randomness, regularity vs. aggregation, scale and strength of pattern). First-order tests suffer from their inability to characterise pattern at distances beyond those at which local interactions (i.e. nearest neighbours) occur. Nevertheless, the tests explored (first-order nearest neighbour, Diggle's G and F) are useful first steps in analysing spatial point patterns, and all seem capable of accurately describing patterns at these (shorter) distances. Among second-order tests, a density-corrected form of the neighbourhood density function (NDF), a noncumulative analogue of the commonly used Ripley's K-function, most informatively characterised spatial patterns at a range of distances for both univariate and bivariate analyses. Although Ripley's K is more commonly used, it can give very different results to the NDF because of its cumulative nature. A modified form of the K-function suitable for inhomogeneous point patterns is discussed. We also explore the use of local and spatially-explicit methods for point pattern analysis. Local methods are powerful in that they allow variations from global averages to be detected and potentially provide a link to recent spatial ecological theory by taking the 'plant's-eye view'. We conclude by discussing the problems of linking spatial pattern with ecological process using three case studies, and consider some ways that this issue might be addressed.

Estrutura demográfica e padrão espacial de uma população natural de Araucaria angustifolia (Bertol.) Kuntze (araucariaceae), na Reserva Genética Florestal de Caçador, Estado de Santa Catarina

“…Esse fato sugere distribuição uniforme dos agregados (de diâmetro aproximado de 50 m) pela área. É interessante ressaltar que a Função K de Ripley é de natureza cumulativa, e seu viés pode estar interferindo nos resultados (PERRY et al, 2006). Suas sementes pesadas e barocóricas à primeira vista sugerem baixa capacidade de dispersão para A. angustifolia, como também observado para A. araucana (BURNS, 1993).…”

“…A função K de Ripley (1981) é um método por medidas de distância (DIGGLE et al, 1976) e de natureza cumulativa (PERRY et al, 2006), contudo ele indica a escala de um padrão, o que é importante na análise espacial (MATTEUCCI e COLMA, 1982;WIENS, 1989;CAMPBELL, 1996;RAHBEK, 2005).…”

Species spatial distribution analysis using nearest neighbor methods: aggregation and self‐similarity

“…Diggle (1983) also used the probability distribution of the NND to test spatial randomness. Nearest neighbor methods are very useful in spatial analysis and were once referred to as distance sampling methods (Buckland et al 1993;Perry et al 2006). In our previous paper, the probability distribution model of the nth NND was presented (Gao 2013).…”

“…In spatial statistics, a spatial point pattern is considered a realization of a spatial point process that generates countable events in the plane (Gatrell et al 1996;Perry et al 2006). For quadrat sampling, the Poisson and NBD models are the most widely used probability distribution models for random and aggregated spatial distribution patterns, respectively (Pielou 1960;He and Gaston 2000).…”

Spatial Distribution and Composition of Trees in an Aging Coppice Forest in Japan

“…Conventional methodologies applied in ecological research require the mapping of the trees (Moeur, 1993) which is time consuming. Moreover, it is recognized that "all tests have their weaknesses" (Perry et al, 2006), but the information provided is usually a valuable indicator of ecological processes. Other methods are mostly designed to minimize field effort.…”