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

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 non-cumulative 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