Table 1 Three different measures of goodness of fit (r2 or percentage of variance explained in the cumulative distribution function, χ2 on log2 bins, and Akaike’s information criterion) are shown for six different species abundance models [see (40)].

All distributions shown have two parameters except the log-series and power distributions, which have one. Distributions were fitted for the number of observations per species across all species found (i) within ecological plots only and (ii) across all datasets within the BIEN database. Sampling species found only in plots standardizes for sampling influences, as all individuals within ecological plots are sampled and identified to species. Thus, the species abundance distribution from ecological plots is expected to more accurately describe the species abundance distribution. As predicted by the CLT, the Poisson lognormal distribution provides the best fit to both gSADs. Nonetheless, Pareto and truncated Pareto also all fit well. The log-series distribution, predicted by the k-niche model and neutral theory, falls behind these distributions across the different goodness-of-fit measures. AIC, Akaike’s information criterion; CDF, cumulative distribution function.

ModelPlot data onlyAll data
CDF r2χ2 log2AIC∆AICCDF r2χ2 log2AIC∆AIC
Zipf-Mandelbrot0.92954,188139,82225,8480.44773,884,9477,402,206330,9517
Weibull0.9991.6 × 1010127,11113,1370.9993.01 × 10104,269,287176,598
Log series0.9911.57 × 1013120,08261090.9995.08 × 10134,119,05726,368
Pareto0.9995.69 × 1013115,24412700.9991.46 × 10134,110,90018,211
Poisson lognormal0.999490113,97400.99929664,092,6890
Pareto with finite
sample
exponential
adjustment
0.999563114,0961220.998100,5584,203,550110,861