Neutral models in ecology have attracted much attention in recent literature. They can provide considerable insight into the roles of non-species-specific factors (e.g. stochasticity, dispersal, speciation) on community dynamics but often require intensive simulations, particularly in spatial settings. Here, we clearly explain existing techniques for modelling spatially explicit neutral processes in ecology using coalescence. Furthermore, we present several novel extensions to these methods including procedures for dealing with system boundaries which enable improved investigation of the effects of dispersal. We also present a semi-analytical algorithm that calculates the expected species richness in a sample, for any speciation rate. By eliminating the effect of stochasticity in the speciation process, we reduce the variance in estimates of species richness. our benchmarks show that the combination of existing coalescence theory and our extensions produces higher quality results in vastly shorter time scales than previously possible: years of simulation time are reduced to minutes. As an example application, we find parameters for a spatially explicit neutral model to approximate the species richness of a tropical forest dataset. (C) 2008 Elsevier B.V. All rights reserved.