1. Clark et al. (2019) sought to extend the Loreau–Hector partitioning scheme by showing how to estimate selection and complementarity effects from an incomplete sample of species. We demonstrate that their approach suffers from serious conceptual and mathematical errors. Instead of finding unbiased estimators for a finite population, they inserted ad hoc correction factors into unbiased parameter estimators for an infinite population without any mathematical justification in order to force the sample estimators of an infinite population to converge to the true finite population parameter values as sample size n approached population size N. In doing so, they confused the unbiasedness of a sample estimator with its equivalence to the true population parameter value when .
2. Additionally, we show that their estimators of complementarity, selection and the net biodiversity effect are incorrect. We then derive the correct unbiased estimators but caution that, contrary to what Clark et al. claim, these quantities will not approximate the corresponding population parameters without significant repeated random sampling, something that would likely be unfeasible in most if not all biodiversity experiments.
3. Clark et al. also state that their method can be used to compare distinct experiments characterized by different species and diversity levels, or extrapolate from biodiversity experiments to natural systems. This is incorrect because relative yields are not a property of individual species like monoculture yields but an emergent and specific feature of an experimental community. As such, two experimental communities, even when overlapping significantly in species, are incommensurable for the purpose of predicting relative yields. In other words, different experimental communities are not equivalent to different samples taken from the same statistical population.
4. Finally, Clark et al. incorrectly claim that both the original Loreau–Hector partitioning scheme and their extension work for any baseline despite the fact that recent research has shown that a nonlinear relationship between monoculture density and ecosystem functioning will likely inflate the net biodiversity effect in plant systems, and will always lead to spurious measurements of complementarity and selection.

中文翻译：

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关于无偏估计量在生物多样性研究中的正确数学推导和生态学应用

1. 克拉克等。（2019）试图通过展示如何从不完整的物种样本中评估选择和互补效应来扩展Loreau-Hector划分方案。我们证明他们的方法遭受严重的概念和数学错误。他们没有找到有限总体的无偏估计量，而是在没有任何数学依据的情况下将临时校正因子插入无限群体的无偏参数估计量中，以迫使无限总体的样本估计量收敛为真实的有限总体参数值作为样本大小ñ走近种群大小ñ。通过这样做，他们将样本估计量的无偏及其等价于真实人口参数值混淆了。
2. 此外，我们表明，他们对互补性，选择和净生物多样性影响的估计是不正确的。然后，我们得出正确的无偏估计量，但请注意，与Clark等人相反。他们声称，如果不进行大量重复的随机抽样，这些数量将不会接近相应的种群参数，这在大多数（如果不是全部）生物多样性实验中可能是不可行的。
3. 克拉克等。还指出，他们的方法可用于比较以不同物种和多样性水平为特征的不同实验，或从生物多样性实验推算到自然系统。这是不正确的，因为相对产量不是单个物种的属性，例如单一养殖产量，而是实验社区的新兴特征。因此，两个实验群落即使在物种上明显重叠时，也无法预测相对产量。换句话说，不同的实验社区并不等同于从同一统计人群中获取的不同样本。
4. 最后，克拉克等。错误地声称，尽管最近的研究表明，单一种植密度与生态系统功能之间的非线性关系可能会夸大植物系统中的净生物多样性影响，但原始的Loreau-Hector划分方案及其在任何基准上的扩展工作均不正确。导致对互补性和选择的虚假测量。