Identification of significant biological relationships or patterns is central to many metagenomic studies.Methods that estimate association networks have been proposed for this pur-pose;however,they assume that associations are static,neglecting the fact that relationships in a microbial ecosystem may vary with changes in environmental factors(EFs),which can result in inaccurate estimations.Therefore,in this study,we propose a computational model,called the k-Lognormal-Dirichlet-Multinomial(kLDM)model,which estimates multiple association networks that correspond to specific environmental conditions,and simultaneously infers microbe-microbe and EF-microbe associations for each network.The effectiveness of the kLDM model was demonstrated on synthetic data,a colorectal cancer(CRC)dataset,the Tara Oceans dataset,and the American Gut Project dataset.The results revealed that the widely-used Spearman's rank correlation coefficient method performed much worse than the other methods,indicating the importance of separating samples by environmental conditions.Cancer fecal samples were then compared with cancer-free samples,and the estimation achieved by kLDM exhibited fewer associations among microbes but stronger associations between specific bacteria,especially five CRC-associated operational taxonomic units,indicating gut microbe translocation in cancer patients.Some EF-dependent associations were then found within a marine eukaryotic community.Finally,the gut microbial heterogeneity of inflammatory bowel disease patients was detected.These results demonstrate that kLDM can elucidate the complex associations within microbial ecosys-tems.The kLDM program,R,and Python scripts,together with all experimental datasets,are accessible at https://github.com/tinglab/kLDM.git.

The recent advancement of single-cell RNA sequencing (scRNA-seq) technologies facilitates the study of cell lineages in developmental processes and cancer.In this study,we developed a computational method,called redPATH,to reconstruct the pseudo developmental time of cell lineages using a consensus asymmetric Hamiltonian path algorithm.Besides,we developed a novel approach to visualize the trajectory development and implemented visualization methods to provide biological insights.We validated the performance of redPATH by segmenting different stages of cell development on multiple neural stem cell and cancer datasets,as well as other single-cell transcriptome data.In particular,we identified a stem cell-like subpopulation in malig-nant glioma cells.These cells express known proliferative markers,such as GFAP,ATP1A2,IGFBPL1,and ALDOC,and remain silenced for quiescent markers such as ID3.Furthermore,we identified MCL1 as a significant gene that regulates cell apoptosis and CSF1R for reprogram-ming macrophages to control tumor growth.In conclusion,redPATH is a comprehensive tool for analyzing scRNA-seq datasets along the pseudo developmental time.redPATH is available at https://github.com/tinglabs/redPATH.