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

In a recent paper, I presented a sampling formula for species abundances from multiple samples according to the prevailing neutral model of biodiversity, but practical implementation for parameter estimation was only possible when these samples were from local communities that were assumed to be equally dispersal limited. Here I show how the same sampling formula can also be used to estimate model parameters using maximum likelihood when the samples have different degrees of dispersal limitation. Moreover, it performs better than other, approximate, parameter estimation approaches. I also show how to calculate errors in the parameter estimates, which has so far been largely ignored in the development of and debate on neutral theory.