To represent species turnover in tropical rain forest, we use a neutral model where a tree’s fate is not affected by what species it belongs to, seeds disperse a limited distance from their parents, and speciation is in equilibrium with random extinction. We calculate the similarity function, the probability F(r) that two trees separated by a distance r belong to the same species, assuming that the dispersal kernel P(r), the distribution of seeds about their parents and the prospects of mortality and reproduction, are the same for all trees regardless of their species. If P(r) is radially symmetric Gaussian with mean-square dispersal distance r; FðrÞ can be expressed in closed form. If P(r) is a radially symmetric Cauchy distribution, then, in two-dimensional space, F(r) is proportional to 1=r for large r: Analytical results are compared with individual-based simulations, and the relevance to field observations is discussed.