Abteilung Forstgenetik und Forstpflanzenzüchtung, Universität Göttingen, Büsgenweg 2, 37077, Göttingen, Germany.
Institut für Populations- und ökologische Genetik, Am Pfingstanger 58, 37075, Göttingen, Germany.
Theory Biosci. 2020 Sep;139(3):253-263. doi: 10.1007/s12064-020-00316-4. Epub 2020 Jun 1.
Diversity in metacommunities is traditionally viewed to consist of the diversity within communities ([Formula: see text]) that is complemented by the differences between communities ([Formula: see text]) so as to result in the total diversity ([Formula: see text]) of the metacommunity. This perception of the partitioning of diversity, where [Formula: see text] is a function of [Formula: see text] and [Formula: see text] (usually [Formula: see text] with all components specified as effective numbers), has several drawbacks, among which are (1) [Formula: see text] is an average that can be taken over communities in many ways, (2) complete differentiation among communities cannot always be uniquely inferred from [Formula: see text] and [Formula: see text], (3) different interpretations of [Formula: see text] 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 [Formula: see text] and [Formula: see text]. 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.
传统上，后生群落的多样性被认为由群落内的多样性组成（[公式：见正文]），再加上群落间的差异（[公式：见正文]），从而导致后生群落的总多样性（[公式：见正文]）。这种对多样性的划分方式存在一些缺点，其中包括：（1）[公式：见正文]是一个平均值，可以通过多种方式在群落之间进行计算；（2）群落间的完全分化并不总是可以从[公式：见正文]和[公式：见正文]中唯一推断出来；（3）[公式：见正文]作为有效群落数的不同解释（例如，独特或同形）是可能的，这取决于对各自有效数所指的理想情况的选择；（4）个体的类型（物种、基因型等）和群落归属之间的关联并没有被[公式：见正文]和[公式：见正文]明确涵盖。在量化后生群落多样性时，第（4）项值得特别关注。有人认为，这需要考虑类型-群落组合的联合分布及其多样性（联合多样性）及其组成部分：类型和群落归属。这两个组成部分的量化都可能受到它们在联合分布中的关联的影响。结果表明，在这种认识下，联合多样性可以分解为一个主导成分和一个关联成分，其中第一个成分特征是给定观察到的类型分布时获得观察到的联合多样性所需的最少群落数量，第二个成分指定在所需最少群落数量中表示的有效类型数量。两者的乘积就是联合多样性。互换群落和类型的角色，就可以得到具有主导最小类型数量和相关有效群落数量的对偶分解。对于所有多样性度量，这两种对偶分解都是明确定义的，可以用于指示后生群落的结构特征，例如群落间的类型分化和相关的类型多态性。与传统和最近的修改方法将总类型多样性划分为群落内和群落间多样性相比，指出了分解方法的信息增益。还指出了在潜在群落细分分析中使用分解的方法。
