In a general sense, a metacommunity can be considered as a network of communities, the coherence of which is based on characteristics that are shared by members of different communities, whatever forces were responsible (dispersal, migration, local adaptation, etc.). The purpose is to show that by basing the assessment of coherence on the degree of nestedness of one community within another with respect to the shared characteristics, coherence components can be identified within the network. To assess coherence, a measure of nestedness is developed, and its application to complex (variable) object differences (including multiple traits or characters) is investigated. A community network is then viewed as a graph in which the nodes represent the communities and the edges connecting nodes are weighted by the reverse of the degrees of nestedness between the corresponding communities. Given this framework, it is argued that a minimum requirement for a set of communities to be coherent is the existence of a spanning tree known from graph theory, i.e. a subgraph that connects all nodes through a cycle-free sequence of edges with positive weights. Of all spanning trees, minimum spanning trees (MST, or spanning trees with the minimum sum of edge weights) are most indicative of coherence. By expressing the degree of coherence as one minus the average weight of the edges of an MST, it is uniquely determined which communities form a coherent set at any given level of community distinctness. By this method, community networks can be broken down into coherence components that are separated at a specified distinctness level. This is illustrated in a worked example showing how to apply graph theoretical methods to distinguish coherence components at various threshold levels of object difference (resolution) and community distinctness. These results provide a basis for discussion of coherence gradients and coherence at various levels of distinctness in terms of MST-characteristics. As intuitively expected and analytically confirmed, coherence is a non-decreasing function of the object difference threshold, and the number of coherence components is a non-increasing function of both the object difference and the community distinctness thresholds.

在一般意义上，元社区可以被认为是社区的网络，其一致性是基于不同社区成员共享的特征，而不论所负责任的力量是什么（分散，移民，本地适应等）。目的是表明，通过基于一个社区在另一个社区相对于共享特征的嵌套程度的一致性评估，可以在网络中识别一致性成分。为了评估一致性，开发了一种嵌套性度量，并研究了它在复杂（可变）对象差异（包括多个特征或字符）中的应用。然后，将社区网络视为一个图形，其中节点代表社区，而连接节点的边缘则通过相应社区之间嵌套度的倒数来加权。在这种框架下，有人认为，要使一组社区保持连贯性，最低要求就是存在图论所知的生成树，即，一个子图通过具有正权重的无周期边沿序列连接所有节点。在所有生成树中，最小生成树（MST或边缘权重总和最小的生成树）最能说明相干性。通过将一致性程度表示为一个MST边缘的平均权重减去其一致性，可以唯一确定在任何给定的社区清晰度水平下，哪个社区形成了一个连贯的集合。通过这种方法，社区网络可以分解为以指定的不同程度级别分离的一致性组件。在一个工作示例中对此进行了说明，该示例显示了如何应用图论方法来区分对象差异（分辨率）和社区区分度的各种阈值级别的相干成分。这些结果为讨论相干梯度和不同水平的MST特性下的相干提供了基础。正如直观地预期和分析确认的那样，相干性是对象差异阈值的不递减函数，而相干分量的数量是对象差异和社区差异性阈值的不递增函数。在一个工作示例中对此进行了说明，该示例显示了如何应用图论方法来区分对象差异（分辨率）和社区区分度的各种阈值级别的相干成分。这些结果为讨论相干梯度和不同水平的MST特性下的相干提供了基础。正如直观地预期和分析确认的那样，相干性是对象差异阈值的不递减函数，而相干分量的数量是对象差异和社区差异性阈值的不递增函数。在一个工作示例中对此进行了说明，该示例显示了如何应用图论方法来区分对象差异（分辨率）和社区区分度的各种阈值级别的相干成分。这些结果为讨论相干梯度和不同水平的MST特征下的相干提供了基础。正如直观地预期和分析确认的那样，相干性是对象差异阈值的不递减函数，而相干分量的数量是对象差异和社区差异性阈值的不递增函数。这些结果为讨论相干梯度和不同水平的MST特性下的相干提供了基础。正如直观地预期和分析确认的那样，相干性是对象差异阈值的不递减函数，而相干分量的数量是对象差异和社区差异性阈值的不递增函数。这些结果为讨论相干梯度和不同水平的MST特性下的相干提供了基础。正如直观地预期和分析确认的那样，相干性是对象差异阈值的不递减函数，而相干分量的数量是对象差异和社区差异性阈值的不递增函数。