We develop a statistical method to infer the parameters of Hubbell's neutral model of biodiversity using data on local species abundances and their phylogenetic relatedness. This method uses the approximate Bayesian computation (ABC) approach, where the data are summarized into a small number of informative summary statistics. We used three statistics: the number of species in the sample, Shannon H index of evenness and Shao and Sokal's B(1) index of phylogenetic tree imbalance. Our approach was found to outperform previous methods, illustrating the potential of ABC methods in ecology. Applying it to four large tropical forest tree data sets, the best-fit immigration rates m were found to be two orders of magnitude smaller and regional diversities theta larger than previously reported for the same data. This implies that neutral-compatible regional pools of tropical trees should extend over continental scales, and that m measures, in this context, mostly the frequency of long-distance dispersal events.