Current research on human and animal microbiomes is largely focused on monitoring and reshaping individual microbes or global microbial communities to diagnose, treat, and prevent diseases, as well as track and improve population health. These fine-scaled and coarse-scaled analyses likely miss an important intermediate ecological scale---functional groups of microbes, which may serve as potent biomarkers of host or ecosystem health as well as targets for medical therapies. This project aims to identify functional groups of microbes by learning their temporal dynamics through longitudinal microbiome studies. However, longitudinal microbiome data possess unique characteristics, such as compositionality, high dimensionality, sparsity, and temporal dependence, and their cluster analysis thus presents distinct challenges. The investigators will develop flexible and scalable functional cluster analysis methods to generate biologically meaningful microbial groups. The investigators will develop, distribute, document, and maintain R software packages for their developed methods, will provide tutorials with example datasets, and will test the software in real-world settings. The investigators will train high-school, undergraduate, and graduate students at the intersection of statistics, ecology, and genomics. The project aims to expand the traditional toolbox of functional cluster analysis by introducing broader similarity measures of functional curves, incorporating the effects of