Table 3.
A summary of the developments in the history of the zero-sum multinomial distribution (ZSM) of the spatially implicit neutral model (SINM), and the SAD of the spatially explicit neutral model (SENM), and the attempts to fit both to the Barro Colorado Island 50 ha tree dataset
| Study Authors | Best Model/Main Finding | Subsequent Criticisms |
|---|---|---|
| Hubbell (2001) | ZSM | Goodness of fit only determined by graphical observation. |
| McGill (2003) | ZSM does not fit the data better than the lognormal | Used simulations to fit the ZSM |
| Volkov et al. (2003) | Derived an analytical solution for the ZSM and found the ZSM provided the best fit | Analytical equations did not represent the full solution as they applied solely to the mean number of species in a given class (Etienne and Olff 2004) |
| Vallade and Houchmandzadeh (2003) | Published a full analytical solution for the ZSM | Equations were later determined to be flawed (i.e., they applied the mean number of species in a given class) and were corrected by Etienne and Alonso (2005) |
| Alonso and McKane (2004) | Developed a different analytic solution | Rigorous fitting of the ZSM required likelihood methods |
| Etienne and Olff (2004) | Found slightly better support for the lognormal using a Bayesian approach | |
| Etienne (2005) | Published the correct analytical solution and sampling formula. Two forms of the likelihood equations exist: (a) Ewens’ (1972) sampling formula of neutral alleles is used in the case of no dispersal limitation and (b) Etienne's (2005) formula in cases of dispersal limitation | |
| Etienne and Alonso (2005) | Unified two different approaches to arrive at the full analytical solution: the genealogical approach (Etienne 2005) and master equation-based approach (e.g., Alonso and McKane 2004) | |
| McGill et al. (2006) | Compared nine goodness-of-fit measures with the BCI data and found that for eight out of the nine measures the lognormal outperformed the ZSM | |
| Jabot and Chave (2011) | Built on Etienne's (2005) maximum likelihood framework to develop a more robust test of neutrality incorporating the SAD of Hubbell's SINM and Shannon's index. The SAD of the BCI 50-ha plot did not significantly differ from neutrality; however, the SADs of smaller scale subplots from within the BCI plot were significantly non-neutral | |
| Rosindell and Cornell (2013) | (a) The gamma and negative binomial distributions provided a better fit than the ZSM (b) The SENM predicts SADs which are more realistic than those from the SINM |