Abstract
There generally exists a critical state or tipping point from a stable state to another in the development of colorectal cancer (CRC) beyond which a significant qualitative transition occurs. Gut microbiome sequencing data can be collected non-invasively from fecal samples, making it more convenient to obtain. Furthermore, intestinal microbiome sequencing data contain phylogenetic information at various levels, which can be used to reliably identify critical states, thereby providing early warning signals more accurately and effectively. Yet, pinpointing the critical states using gut microbiome data presents a formidable challenge due to the high dimension and strong noise of gut microbiome data. To address this challenge, we introduce a novel approach termed the specific network information gain (SNIG) method to detect CRC's critical states at various taxonomic levels via gut microbiome data. The numerical simulation indicates that the SNIG method is robust under different noise levels and that it is also superior to the existing methods on detecting the critical states. Moreover, utilizing SNIG on two real CRC datasets enabled us to discern the critical states preceding deterioration and to successfully identify their associated dynamic network biomarkers at different taxonomic levels. Notably, we discovered certain 'dark species' and pathways intimately linked to CRC progression. In addition, we accurately detected the tipping points on an individual dataset of type I diabetes.