Diversity in metacommunities is traditionally viewed to consist of the diversity within communities (\(\alpha\)) that is complemented by the differences between communities (\(\beta\)) so as to result in the total diversity (\(\gamma\)) of the metacommunity. This perception of the partitioning of diversity, where \(\beta\) is a function of \(\gamma\) and \(\alpha\) (usually \(\beta =\gamma /\alpha\) with all components specified as effective numbers), has several drawbacks, among which are (1) \(\alpha\) is an average that can be taken over communities in many ways, (2) complete differentiation among communities cannot always be uniquely inferred from \(\alpha\) and \(\gamma\), (3) different interpretations of \(\beta\) as effective number of communities (e.g., distinct or monomorphic) are possible, depending on the choice of ideal situations to which the respective effective numbers refer, and (4) associations between types (species, genotypes, etc.) and community affiliations of individuals are not explicitly covered by \(\alpha\) and \(\gamma\). Item (4) deserves special regard when quantifying metacommunity diversity. It is argued that this requires consideration of the joint distribution of type-community combinations together with its diversity (joint diversity) and its constituent components: type and community affiliation. The quantification of both components can be affected by their association as realized in the joint distribution. It is shown that under this perception, the joint diversity can be factorized into a leading and an associated component, where the first characterizes the minimum number of communities required to obtain the observed joint diversity given the observed type distribution, and the second specifies the effective number of types represented in the minimally required number of communities. Multiplication of the two yields the joint diversity. Interchanging the roles of community and type, one arrives at the dual factorization with leading minimum number of types and associated effective number of communities. The two dual factorizations are unambiguously defined for all measures of diversity and can be used, for example, to indicate structural characteristics of metacommunities, such as type differentiation among communities and associated type polymorphism. The information gain of the factorization approach is pointed out in comparison with the classical and more recent modified approaches to partitioning total type diversity into diversity within and between communities. The use of factorization in analyses of latent community subdivision is indicated.

中文翻译：

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将联合元社区多样性分解为其边缘成分：特征多样性划分的替代方案。

元社区中的多样性传统上被视为由社区内的多样性（\(\alpha\)）组成，该多样性由社区之间的差异（\(\beta\)）补充，从而导致总多样性（\(\gamma \) ) 的元社区。这种对多样性划分的感知，其中\(\beta\)是\(\gamma\)和\(\alpha\)的函数（通常是\(\beta =\gamma /\alpha\)，所有组件都指定作为有效数），有几个缺点，其中有（1）  \(\alpha\)是可以通过多种方式对社区采取的平均值，（2）社区之间的完全分化不能总是从\(\alpha\)和\(\gamma\) 中唯一推断出来，（3）对\(\beta \)作为可能的群落有效数量（例如，不同的或单一的），取决于各自有效数量所指的理想情况的选择，以及（4）类型（物种、基因型等）和群落从属关系之间的关联的个体没有被\(\alpha\)和\(\gamma\)明确覆盖. 在量化元社区多样性时，项目 (4) 值得特别关注。有人认为，这需要考虑类型-社区组合的联合分布及其多样性（联合多样性）及其组成部分：类型和社区从属关系。如联合分布中所实现的那样，这两个分量的量化会受到它们的关联的影响。结果表明，在这种感知下，联合多样性可以被分解为一个领先的和一个相关的组成部分，其中第一个表征了在给定观察类型分布的情况下获得观察到的联合多样性所需的最少社区数量，第二个指定了有效的在最低要求的社区数量中表示的类型数量。两者相乘产生联合多样性。将社区和类型的角色互换，可以得到具有领先最小类型数和相关有效社区数的二元分解。这两个二元分解对于所有多样性度量都被明确定义，并且可以用于，例如，指示元社区的结构特征，例如社区之间的类型分化和相关的类型多态性。与将总类型多样性划分为社区内部和社区之间的多样性的经典方法和最近的修改方法相比，分解方法的信息增益被指出。指出了在潜在社区细分分析中分解的使用。一个到达双因子分解，具有领先的最小类型数量和相关的有效社区数量。这两个二元分解对于所有多样性度量都被明确定义，并且可以用于，例如，指示元社区的结构特征，例如社区之间的类型分化和相关的类型多态性。与将总类型多样性划分为社区内部和社区之间的多样性的经典方法和最近的修改方法相比，分解方法的信息增益被指出。指出了在潜在社区细分分析中分解的使用。一个到达双因子分解，具有领先的最小类型数量和相关的有效社区数量。这两个二元分解对于所有多样性度量都被明确定义，并且可以用于，例如，指示元社区的结构特征，例如社区之间的类型分化和相关的类型多态性。与将总类型多样性划分为社区内部和社区之间的多样性的经典方法和最近的修改方法相比，分解方法的信息增益被指出。指出了在潜在社区细分分析中分解的使用。指示元群落的结构特征，例如群落之间的类型分化和相关的类型多态性。与将总类型多样性划分为社区内部和社区之间的多样性的经典方法和最近的修改方法相比，分解方法的信息增益被指出。指出了在潜在社区细分分析中分解的使用。指示元群落的结构特征，例如群落之间的类型分化和相关的类型多态性。与将总类型多样性划分为社区内部和社区之间的多样性的经典方法和最近的修改方法相比，分解方法的信息增益被指出。指出了在潜在社区细分分析中分解的使用。