Improved estimation of neutral model parameters for multiple samples with different degrees of dispersal limitation

The standard neutral model of biodiversity, as introduced by S. P. Hubbell, is currently increasingly used as a null model for the structure of ecological communities. In such applications, estimation of the model parameters is essential. An exact maximum likelihood approach has been developed for data sets consisting of multiple, spatially separated, samples of species abundances. This approach is only computationally tractable when it is assumed that all these samples have the same amount of dispersal limitation. Recently, an approximate approach has been proposed that does not require this assumption. However, this approach cannot estimate the fundamental biodiversity number theta when there are only a few samples or many, very different, samples. In this note, I present a modification of this approximate approach that does not suffer from this shortcoming. I illustrate it with simulated and real data sets.