We found that a lognormal model was a better fit for all three data sets (Table 3). In the ATDN data set, this model is based on the truncated negative binomial with lognormal error (i.e., t 0, t 1 and b), which predicts a skewed distribution with a long left tail and to the right of the mean and a lognormal distribution (underlying distribution) that has positive skewness and a fairly narrow distribution. We compared estimates of the model parameters to those of the logseries model to assess whether that more complex model might yield better estimates of species richness. The lognormal model generally gave better fits to the observed species abundances (Table 3), implying that the relative abundance (or species count) distribution is more skewed in the Amazonian tree flora than a logseries model would predict.
All three models with 4 FSPs as predictors of SADs from the samples of the three datasets had substantial support from the data (AIC differences of 0.5 to 1, Table 3, Supplementary Figs. 2-4). The models had very similar posterior probabilities (Table 3), and were all very good at predicting the species abundances of the samples (Fig. 2).
Visually, the best fit was provided by the truncated negative binomial (TNB) model (Fig. 2). The logseries and TNB distributions provided comparable fits (Supplementary Figs. 2, 3). We found that the different versions of the data, the number of individuals in the different ATDN datasets, and the number of species in the data had little effect on the fit of the models to the data (Table 3, Supplementary Figs. 2-4, data not shown).
Our results indicated that the (TNB) sampling model of the data could be explained by a simple stochastic process, presumably with infinite rates of speciation and extinction (Table 3, Supplementary Fig. 5).
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