Comprehensive non-black box classification of highly correlated ecological time series pairs containing many zeros: the case of gut microbiome of mice

We developed a new data analysis method, named Coexistence–Exclusion–Synchronization– Antisynchronization (CESA), to reveal statistically significant correlations from a set of integer compositional abundance time series of Operational Taxonomic Unit (OTU) data of mouse gut microbiota. First, time series are transformed to 0 (absence) and 1 (presence), and statistical tests are applied to extract significant coexistence and mutual exclusion relationships. Subsequently, for all pairs, the difference time series are transformed to +1 (up), 0 (even), and −1 (down), and synchronized and antisynchronized pairs are classified based on statistical tests after carefully removing the effect of spurious correlation caused by changes in compositional shares. We performed a comprehensive classification of all pairs based on the p-values in terms of coexistence and synchronization, including time series data with many zeros, which are difficult to analyze using conventional methods. We found that almost all OTUs (419 out of 420) have significant correlations with at least one OTU in one of the four characteristics: coexisting, exclusive, synchronizing, or antisynchronizing. Considering OTU pairs, about 25% of all possible pairs (22,356 out of 87,990) show a high correlation with the p-values less than 10-5, which is less than the inverse of the total number of pairs. Interaction among phyla are summarized as a network diagram. Author summary The gut microbiota ecosystem is often thought to be stable. However, when observed over a long period, there are turnovers in the microbiota, each OTU time series is highly non-stationary, and even species with high overall abundance are often observed to have zero values in some periods. In this study, we developed a comprehensive data analysis method for extracting significant correlations between any pair of OTUs, including OTUs whose observed values contain many zeros or exhibit clear non-stationarity, for which processing methods have not yet been established. We focused on pairwise correlations in terms of coexistence, exclusivity, synchrony, and antisynchrony of increase/decrease, and all combinations of pairs were checked by statistical tests based on the p-values. In order to remove spurious correlations in compositional time series, a new method was introduced to correct the sample sizes for the remaining OTUs, hypothetically assuming a situation in which one OTU was not present. Low abundance OTUs are often overlooked in traditional analyses. However, it becomes evident that all OTUs, including those with low abundance, interact strongly with each other. Additionally, our findings suggest that coexistence and synchrony can be summarized as cooperative relationships, while exclusion and antisynchrony can be summarized as antagonistic relationships. Cooperative interactions are more likely to occur between pairs of OTUs in the same phyla, and antagonistic interactions are more likely to appear between OTUs in different phyla. The time series data analysis method developed in this paper includes no black-box, making it broadly applicable to compositional time series data with integer values. ### Competing Interest Statement The authors have declared no competing interest.