An equation-free method reveals the ecological interaction networks within complex microbial ecosystems

1. Mapping the network of ecological interactions is a key to understanding the composition, stability, function and dynamics of microbial communities. In recent years various approaches have been used to reveal microbial interaction networks from metagenomic sequencing data, such as time-series analysis, machine learning and statistical techniques. Despite these efforts it is still not possible to capture details of the ecological interactions behind complex microbial dynamics. 2. We developed the sparse S-map method (SSM), which generates a sparse interaction network from a multivariate ecological time series without presuming any mathematical formulation for the underlying microbial processes. The advantage of the SSM over alternative methodologies is that it fully utilizes the observed data using a framework of empirical dynamic modelling. This makes the SSM robust to non-equilibrium dynamics and underlying complexity (nonlinearity) in microbial processes. 3. We showed that an increase in dataset size or a decrease in observational error improved the accuracy of SSM However, the accuracy of a comparative equation-based method was almost unchanged for both cases and equivalent to the SSM at best. Hence, the SSM outperformed a comparative equation-based method when datasets were large and the magnitude of observational errors was small. The results were robust to the magnitude of process noise and the functional forms of interspecific interactions that we tested. We applied the method to a microbiome data of six mice and found that there were different microbial interaction regimes between young to middle age (4-40week-old) and middle to old age (36-72week-old) mice. 4. The complexity of microbial relationships impedes detailed equation-based modelling. Our method provides a powerful alternative framework to infer ecological interaction networks of microbial communities in various environments and will be improved by further developments in metagenomics sequencing technologies leading to increased dataset size and improved accuracy and precision.