Supplement 1. Program code for maximum likelihood estimation of neutral model parameters for multiple samples of species abundances using the two-stage approach described in the paper.

File List ML-TwoStage.zip -- (all files at once) logKDA1.gp loglikSAD1a.gp MLthetaISADstage2.gp MLthetaISADtwostage.gp Description ML-TwoStage.zip contains files to calculate the parameters that maximize the likelihood of a particular species-abundance data set in multiple samples where dispersal limitation may differ across samples. It runs under PARI/gp which can be downloaded for free from http://pari.math.u-bordeaux.fr/download.html Put all files in the PARI/examples folder. Then open “MLthetaISADtwostage.gp” in any editor and read the instructions (where the species-abundance data should be put) and start the program by typing read("MLthetaISADtwostage.gp") at the PARI/GP prompt, or by \r MLthetaISADtwostage.gp, depending on what version of PARI/GP you are using. The output will be, for each sample: the sample number, the sample size, the number of species in the sample, Fisher's alpha, the θ-value obtained by maximizing the likelihood given by the Ewens sampling formula, the Ewens maximum-likelihood itself, the θ-value obtained by the two-stage approach, the <i>m</i>-value obtained by the two-stage approach, the <i>I</i>-value obtained by the two-stage approach, and the Etienne (2005) likelihood for these parameter values if this sample was considered in isolation. <i>Note</i>: the total likelihood will not be the sum of the sample likelihoods, because the order of the species matters in the multple sample case.