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The characteristic statistical response of superparamagnetic materials under magnetic stimuli provides quantitative insight into structure–function relationships, facilitating comparative data interpretation and paving the way for the design of superior functional materials. 

Impact statement One fundamental goal in microbial ecology is to predict how microbial diversity is changed across space and time. Although spatial patterns of microbial communities have been recently intensively examined, our understanding of microbial temporal dynamics is rudimentary, primarily due to the lack of appropriate experimental data and theoretical framework. By reconciling niche and neutral perspectives, this study developed a novel process model‐based framework to effectively encapsulate microbial species temporal dynamics, which is powerful for quantitatively assessing the assembly mechanisms underlying microbial community dynamics. This study represents a significant advance in explaining microbial temporal dynamics toward predictive microbial community ecology. 

Networks are vital tools for understanding and modeling interactions in complex systems in science and engineering, and direct and indirect interactions are pervasive in all types of networks. However, quantitatively disentangling direct and indirect relationships in networks remains a formidable task. Here, we present a framework, called iDIRECT (Inference of Direct and Indirect Relationships with Effective Copula-based Transitivity), for quantitatively inferring direct dependencies in association networks. Using copula-based transitivity, iDIRECT eliminates/ameliorates several challenging mathematical problems, including ill-conditioning, self-looping, and interaction strength overflow. With simulation data as benchmark examples, iDIRECT showed high prediction accuracies. Application of iDIRECT to reconstruct gene regulatory networks in Escherichia coli also revealed considerably higher prediction power than the best-performing approaches in the DREAM5 (Dialogue on Reverse Engineering Assessment and Methods project, #5) Network Inference Challenge. In addition, applying iDIRECT to highly diverse grassland soil microbial communities in response to climate warming showed that the iDIRECT-processed networks were significantly different from the original networks, with considerably fewer nodes, links, and connectivity, but higher relative modularity. Further analysis revealed that the iDIRECT-processed network was more complex under warming than the control and more robust to both random and target species removal ( P < 0.001). As a general approach, iDIRECT has great advantages for network inference, and it should be widely applicable to infer direct relationships in association networks across diverse disciplines in science and engineering.