RESULTS
Relative to a saturated model, the terrestrial species inventory data show split support for the three distributions (Fig. 2A). However, there is an interesting trend as more and more non-singleton species are picked up by the sampling process. When samples are poor (blue points in Fig. 2A), support is ambiguous but slightly shifted toward the axis connecting the log series and odds models. The reason is that small samples are often either flat at random (resembling the log series) or heavily dominated by a single species at random (resembling the odds distribution). The more heavily sampled and rich an inventory, the closer it moves toward the expe corner of the graph (red points in Fig. 2A). There are exceptions: some of these points are on edges of the triangle leading to the other distributions.
However, it seems fair to argue that although different communities follow different rules, a plurality of diverse ones most closely adhere to the expe population dynamics system. Thus, it may be common for turnover rates to vary among species but not through time. This fact is striking because the log series has been heralded as a key feature of tropical tree communities (Ulrich et al., 2015), but it makes little sense unless species instead behave almost identically.
There is clear variation in support across ecological groups (Figs. 2B – D). Tree inventories occupy much of the expecorner and the edge of the central arch on that side (Fig. 2B). Bird inventories also take up the outer edge of this arch, but mammal inventories cluster on the inner edge. Insect samples are widely scattered, but ant, butterfly, dung beetle, and mosquito communities are all routinely found in the expe area. Finally, frog and lizard samples are concentrated in the main arch. They tend to approach the odds corner when sampling is strong.
In principle, saturated models might be hard to beat because any extreme outlier count or suggestion of bimodality could challenge the one-parameter models. This is rarely true in practice: the saturated model is best in only 859 cases (27.8%). It is notable that expe cannot be rejected most of the time: it fits 1749 of 3095 SADs (56.6%) better than the saturated model, as opposed to 1231 cases and coincidentally also 1749 cases (39.8 and 56.6%) for the odds and log series. Regardless, support for saturated models should never be mistaken as potential support for multi-parameter distributions like the PLN because outliers, bimodal patterns, and the like aren’t naturally predicted by those distributions either.
The SADs best fitting the four models are all diverse (Fig. 3). Of particular note, the Barro Colorado Island tree counts (Fig. 2C: Condit et al., 1996) have been the subject of a high-profile dispute: Hubbell (2001) argued that they follow the zero-sum multinomial distribution generated by his neutral theory, McGill (2003b) that they are closer to the log normal, and Gray et al. (2006) that nothing could be concluded because of difficulties with the octave plotting method of Preston (1948) used by the other authors. So what may well be the most famous SAD in ecology is very closely matched by one of two models presented here (expe ).
The scaled odds and expe species richness estimators are highly consistent (Figs. 4B, C). The median estimates for half-samples are respectively 0.093 and 0.020 log units below the values for full samples. Fisher’s α is equally consistent (Fig. 4A: median 0.055), but Chao 1 is greatly biased (Fig. 4D: 0.204). It is meaningful that when assumptions are met, the estimates are almost exactly right: the median offset is 0.012 for samples best matching expe and 0.003 in the other direction for those best matching the odds distribution.