Multivariate point processes and spatial variation of species diversity

Multivariate point processes were applied to introducing two functions indicating spatial variation of species diversity when mapped data are given. They are extensions of the Simpson index of species diversity. The one function, alpha (r), is defined as the probability that a randomly selected pair of individuals within distance r belong to different species. The other function, beta (r), is the conditional probability that the two individuals belong to different species given that their distance is r. The functions were applied to examining the effects of thinning favoring desirable species in mixed hardwood forest on multispecies spatial patterns and biodiversity. Low alpha (r) and beta (r) for small r and high beta (r) for intermediate r in the thinned plots mean that the thinning involved forming single-species dominant patches. In contrast, almost constant alpha (r) and alpha (r) show that every species is uniformly distributed over the unthinned plots. However, if the largest 50% trees in DBH were selected, the thinned plots have higher diversity at the almost all distances and higher overall diversity. (C) 2001 Elsevier Science B.V. All rights reserved.