1. Measuring biodiversity quantitatively is a key component to its investigation, but many methods are known to be biased by undersampling (i.e. incomplete inventories), a common situation in ecological field studies.
2. Following a long tradition of comparing measures of alpha diversity to judge their usefulness, we used simulated data to assess bias of nine diversity measures – some of them proposed fairly recently, such as estimating true species richness depending on the completeness of inventories (Brose, U. & Martinez, N.D. Oikos (2004) 105, 292), bias-corrected Shannon diversity (Chao, A. & Shen, T.-J. Environmental and Ecological Statistics (2003) 10, 429), while others are commonly applied (e.g. Shannon’s entropy, Fisher’s α) or long known but rarely used (estimating Shannon’s entropy from Fisher’s α).
3. We conclude that the ‘effective number of species’ based on bias-corrected Shannon’s entropy is an unbiased estimator of diversity at sample completeness c. >0·5, while below that it is still less biased than, e.g., estimated species richness (Brose, U. & Martinez, N.D. Oikos (2004) 105, 292).
4. Fisher’s α cannot be tested with the same rigour because it cannot measure the diversity of completely inventoried communities, and we present simulations illustrating this effect when sample completeness approaches high values. However, we can show that Fisher’s α produces relatively stable values at low sample completeness (an effect previously shown only in empirical data), and we tentatively conclude that it may still be considered a good (possibly superior) measure of diversity if completeness is very low.