Microbes can affect processes from food production to human health. Such microbes are not isolated, but rather interact with each other and establish connections with their living environments. Understanding these interactions is essential to an understanding of the organization and complex interplay of microbial communities, as well as the structure and dynamics of various ecosystems. A common and essential approach toward this objective involves the inference of microbiome interaction networks. Although network inference methods in other fields have been studied before, applying these methods to estimate microbiome associations based on compositional data will not yield valid results. On the one hand, features of microbiome data such as compositionality, sparsity and high-dimensionality challenge the data normalization and the design of computational methods. On the other hand, several issues like microbial community heterogeneity, external environmental interference and biological concerns also make it more difficult to deal with the network inference. In this paper, we provide a comprehensive review of emerging microbiome interaction network inference methods. According to various assumptions and research targets, estimated networks are divided into four main categories: correlation networks, conditional correlation networks, mixture networks and differential networks. Their scope of applications, advantages and limitations are presented in this review. Since real microbial interactions can be complex and dynamic, no unifying method has captured all the aspects of interest to date. In addition, we discuss the challenges now confronting current microbial associations study and future prospects. Finally, we highlight that the research in microbial network inference requires the joint promotion of statistical computation methods and experimental techniques.
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