The synthesis of information deriving from complex networks is a topic receiving increasing relevance in ecology and environmental sciences. In particular, the aggregation of multilayer networks, i.e. network structures formed by multiple interacting networks (the layers), constitutes a fast-growing field. In several environmental applications, the layers of a multilayer network are modelled as a collection of similarity matrices describing how similar pairs of biological entities are, based on different types of features (e.g. biological traits). The present paper first discusses two main techniques for combining the multi-layered information into a single network (the so-called monoplex), i.e. Similarity Network Fusion (SNF) and Similarity Matrix Average (SMA). Then, the effectiveness of the two methods is tested on a real-world dataset of the relative abundance of microbial species in the ecosystems of nine glaciers (four glaciers in the Alps and five in the Andes). A preliminary clustering analysis on the monoplexes obtained with different methods shows the emergence of a tightly connected community formed by species that are typical of cryoconite holes worldwide. Moreover, the weights assigned to different layers by the SMA algorithm suggest that two large South American glaciers (Exploradores and Perito Moreno) are structurally different from the smaller glaciers in both Europe and South America. Overall, these results highlight the importance of integration methods in the discovery of the underlying organizational structure of biological entities in multilayer ecological networks.

翻译：综合来自复杂网络的信息是生态学与环境科学领域中日益受关注的主题。特别是多层网络的聚合（即由多个相互作用的网络（层）构成的网络结构）构成了一个快速发展的研究领域。在多种环境应用中，多层网络的各层被建模为相似性矩阵的集合，这些矩阵描述了基于不同特征类型（如生物性状）的生物实体对之间的相似程度。本文首先讨论将多层信息组合成单一网络（即单层网络）的两种主要技术：相似性网络融合（SNF）与相似性矩阵平均（SMA）。随后，基于九个冰川（四个位于阿尔卑斯山，五个位于安第斯山脉）生态系统中微生物物种相对丰度的真实数据集，测试了两种方法的有效性。对通过不同方法获得的单层网络进行的初步聚类分析显示，形成了一个由全球冰尘穴典型物种构成的紧密连接群落。此外，SMA算法分配给不同层的权重表明，南美洲的两个大型冰川（Exploradores冰川和Perito Moreno冰川）在结构上与欧洲及南美洲的小型冰川存在差异。总体而言，这些结果凸显了整合方法在揭示多层生态网络中生物实体潜在组织结构方面的重要性。