The Chord-Normalized Expected Species Shared (CNESS)-distance represents a superior measure of species turnover patterns

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.

1. β多样性(β-diversity)是表征不同样本间物种组成差异的度量指标，在生态学研究中应用广泛。然而，常用的相异度指标通常要求样本完整性较高，或至少比较样本的样本量需相近。与之相对，弦标准化期望共有物种（Chord-Normalized Expected Species Shared, CNESS）相异度指标通过计算标准化规模的随机样本中采集到相同物种集合的概率，因此不受比较样本的完整性与样本量影响。迄今为止，由于计算难度较高且缺乏系统性对比该指标与其他指标的研究，CNESS的应用仍较为有限。
2. 本研究开发了一款全新的R语言函数，可用于计算期望共有物种（Expected Species Shared, ESS）相关的各类指标。本研究基于已知物种分布结构的模拟数据集对CNESS指标的性能进行评估，并在不同样本完整性与样本量条件下，将CNESS与主流相异度指标——如布莱-柯蒂斯指数（Bray-Curtis index）、查俄-瑟伦森指数（Chao-Sørensen index）以及基于比例的欧氏距离——进行了对比。
3. 模拟结果显示，当样本量（m）较小时，CNESS主要反映优势物种的组成相似性；而当样本量取值较大时，则更侧重整体物种集合的组成差异。置换检验结果表明，即便样本完整性发生变化，CNESS的变异系数（coefficient of variation, CV）始终维持在较低水平；而查俄-瑟伦森指数的变异系数则较高，尤其在采样完整性较低时表现明显。此外，在采样不足的场景下，CNESS距离相较于其他指标也具备更强的鲁棒性，尤其当两个物种集合主要共享稀有物种时这一优势更为突出。
4. 本研究结果证实，在样本完整性与样本量存在差异的样本对比中，CNESS具备显著优势，这一点对于采样完整性通常较低的高移动性、高物种丰富度类群的研究尤为关键。通过调整样本量参数m，CNESS不仅可以揭示共享物种的整体分布结构相似性，还可解析优势物种与稀有物种的组成差异，因此能够提供主流相异度指标无法实现的额外重要研究视角。