1.    Measures of β-diversity characterizing the difference in species composition between samples are commonly used in ecological studies. Nonetheless, commonly used dissimilarity measures require high sample completeness, or at least similar sample sizes between samples. In contrast, the Chord-Normalized Expected Species Shared (CNESS) dissimilarity measure calculates the probability of collecting the same set of species in random samples of a standardized size, and hence is not sensitive to completeness or size of compared samples. To date, this index has enjoyed limited use due to difficulties in its calculation and scarcity of studies systematically comparing it with other measures.

2.    Here, we developed a novel R function that enables users to calculate ESS (Expected Species Shared)-associated measures. We evaluate the performance of the CNESS index based on simulated datasets of known species distribution structure, and compared CNESS with more widespread dissimilarity measures (Bray-Curtis index, Chao-Sørensen index, and proportionality based Euclidean distances) for varying sample completeness and sample sizes.

3.    Simulation results indicated that for small sample size (m) values, CNESS chiefly reflects similarities in dominant species, while selecting large m values emphasizes differences in the overall species assemblages. Permutation tests revealed that CNESS has a consistently low CV (coefficient of variation) even where sample completeness varies, while the Chao-Sørensen index has a high CV particularly for low sampling completeness. CNESS distances are also more robust than other indices with regards to undersampling, particularly when chiefly rare species are shared between two assemblages.

4.    Our results emphasize the superiority of CNESS for comparisons of samples diverging in sample completeness and size, which is particularly important in studies of highly mobile and species-rich taxa where sample completeness is often low. Via changes in the sample size parameter m, CNESS furthermore cannot only provide insights into the similarity of the overall distribution structure of shared species, but also into the differences in dominant and rare species, hence allowing additional, valuable insights beyond the capability of more widespread measures.
 

ESS.R

R scripts to calculate the Expected Species Shared (ESS)-associated dissimilarity measures

Simulation.R

Simulation R scripts