The calculation of β-diversity for different sample sizes

Aims: Measuring differences in species composition between plots, i.e., β-diversity, is a common approach in ecological studies. In empirical studies, sample sizes between plots are often inconsistent. While species rarefaction curves can be used to calculate α-diversity for different sample sizes, commonly-used β-diversity indices do not take sample sizes into account. To overcome the limitation, this study introduced the species rarefaction-extended β-diversity index—the expected species shared (ESS) and its normalized format, with particular emphasis on the chord-normalized expected species shared (CNESS) index. Methods: Based on empirical data, this study demonstrated the application of CNESS using principal coordinates analysis (PCoA) under different sample size parameter (m), and compared results between the CNESS and a commonly used abundance-based index, the Chao-Jaccard index. Results: Simulation results showed that the PCoA results of the CNESS index and the Chao-Jaccard index were generally positively correlated and that the correlation was largely independent of m. By adjusting m, results of the CNESS can be tuned to focus on the species composition of both dominant and rare species, whereas the Chao-Jaccard cannot represent the relevant information. The CNESS index was not sensitive to the sample size, which offers advantages compared to the Chao-Jaccard index. Conclusions: ESS-based dissimilarity indices are abundance-based and are suitable for the calculation of β-diversity Biodiversity Science when sample sizes vary among plots, which is especially important when studying insects and other invertebrates that commonly have vast differences in the number of samples among plots. In order to comprehensively understand species composition differences between plots, calculation of CNESS results under different m values is recommended. As plots with a sample size smaller than m will be excluded in the calculation, in practice, a sufficient number of individuals are required for each plot to ensure the integrity of plot information under a large m.