1. β‐diversity is a primary biodiversity pattern for inferring community assembly. A randomized null model that generates a standardized β‐deviation has been widely used for this purpose. However, the null model has been much debated and its application is limited to abundance data.
2. Here we derive analytical models for β‐diversity to address the debate, clarify the interpretation and extend the application to occurrence data.
3. The analytical analyses show unambiguously that the standardized β‐deviation is a quantification of the effect size of non‐random spatial distribution of species on β‐diversity for a given species abundance distribution. It robustly scales with sampling effort following a power law with exponent of 0.5. This scaling relationship offers a simple method for comparing β‐diversity of communities of different sizes.
4. Assuming log‐series distribution for the metacommunity species abundance distribution, our model allows for calculation of the standardized β‐deviation using occurrence data plus a datum on the total abundance.
5. Our theoretical model justifies and generalizes the use of the β null model for inferring community assembly rules.

中文翻译：

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β多样性的分析模型和β偏差的幂律定标

1. β多样性是推断社区聚集的主要生物多样性模式。为此，广泛使用了生成标准化β偏差的随机零模型。但是，空模型已经引起了很多争论，其应用仅限于丰度数据。
2. 在这里，我们推导了β多样性的分析模型，以解决辩论，阐明解释并将其扩展到发生数据。
3. 分析分析清楚地表明，对于给定的物种丰富度分布，标准化的β偏差是对物种非随机空间分布对β多样性的影响大小的量化。它遵循幂指数为0.5的幂定律，可以随着采样工作而稳健地扩展。这种比例关系为比较不同规模的社区的β多样性提供了一种简单的方法。
4. 假设元社区物种丰度分布的对数序列分布，我们的模型允许使用出现数据加上总丰度数据来计算标准化的β偏差。
5. 我们的理论模型证明和推广使用的β空模型推断社区组装规则。