Shannon diversity index: a call to replace the original Shannon’s formula with unbiased estimator in the population genetics studies

Abstract

Background The Shannon diversity index has been widely used in population genetics studies. Recently, it was proposed as a unifying measure of diversity at different levels—from genes and populations to whole species and ecosystems. The index, however, was proven to be negatively biased at small sample sizes. Modifications to the original Shannon’s formula have been proposed to obtain an unbiased estimator. Methods In this study, the performance of four different estimators of Shannon index—the original Shannon’s formula and those of Zahl, Chao and Shen and Chao et al.—was tested on simulated microsatellite data. Both the simulation and analysis of the results were performed in the R language environment. A new R function was created for the calculation of all four indices from the genind data format. Results Sample size dependence was detected in all the estimators analysed; however, the deviation from parametric values was substantially smaller in the derived measures than in the original Shannon’s formula. Error rate was negatively associated with population heterozygosity. Comparisons among loci showed that fast-mutating loci were less affected by the error, except for the original Shannon’s estimator which, in the smallest sample, was more strongly affected by loci with a higher number of alleles. The Zahl and Chao et al. estimators performed notably better than the original Shannon’s formula. Conclusion The results of this study show that the original Shannon index should no longer be used as a measure of genetic diversity and should be replaced by Zahl’s unbiased estimator.