Data-driven causal analysis of observational time series: a synthesis

Complex systems such as microbial communities play key roles in global processes and human life, yet are often challenging to understand. Although mechanistic knowledge in biology is generally rooted in manipulative experiments, perturbing these systems can encounter practical and ethical barriers. Thus, extensive attempts have been made to infer causal knowledge by analyzing observations of taxon abundance over time. When, and to what extent, does this strategy yield genuine insight? Unfortunately, the literature of causal inference can be formidable and controversial, as it draws from divergent fields such as philosophy, statistics, econometrics, and chaos theory. Most benchmarking papers focus on performance details of causal inference approaches, rather than fundamental issues such as the the underlying assumptions and their reasons, conceptual distinctions, and universal limitations. Here, we provide a synthesis of popular causal inference approaches including pairwise correlation and Reichenbach’s common cause principle, Granger causality, and state space reconstruction. We find that each of these requires that certain properties of the data do not change with time (e.g. “IID”, “stationarity”, “reverting dynamics”). We provide new ways of visualizing key concepts, point out important issues that have been under-emphasized, and in some cases describe novel pathologies of causal inference methods. Although our synthesis is motivated by microbial communities, all arguments apply to other types of dynamic systems. We strive to balance precision with accessibility, and hope that our synthesis will motivate future development on causal inference approaches. To facilitate communication to a broad audience, we have made an accompanying video walkthrough (https://youtu.be/TZvEk3jXQfY).