When two become one: the limits of causality analysis of brain dynamics

Biological systems often consist of multiple interacting subsystems, the brain being a prominent example. To understand/nthe functions of such systems it is important to analyze if and how the subsystems interact and to describe the effect of/nthese interactions. In this work we investigate the extent to which the cause-and-effect framework is applicable to such/ninteracting subsystems. We base our work on a standard notion of causal effects and define a new concept called natural/ncausal effect. This new concept takes into account that when studying interactions in biological systems, one is often not/ninterested in the effect of perturbations that alter the dynamics. The interest is instead in how the causal connections/nparticipate in the generation of the observed natural dynamics. We identify the constraints on the structure of the causal/nconnections that determine the existence of natural causal effects. In particular, we show that the influence of the causal/nconnections on the natural dynamics of the system often cannot be analyzed in terms of the causal effect of one subsystem/non another. Only when the causing subsystem is autonomous with respect to the rest can this interpretation be made. We/nnote that subsystems in the brain are often bidirectionally connected, which means that interactions rarely should be/nquantified in terms of cause-and-effect. We furthermore introduce a framework for how natural causal effects can be/ncharacterized when they exist. Our work also has important consequences for the interpretation of other approaches/ncommonly applied to study causality in the brain. Specifically, we discuss how the notion of natural causal effects can be/ncombined with Granger causality and Dynamic Causal Modeling (DCM). Our results are generic and the concept of natural/ncausal effects is relevant in all areas where the effects of interactions between subsystems are of interest.The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007- 2013) under grant agreement no. 269921 (BrainScaleS). AL is supported by the Ramon y Cajal program from the Spanish government. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript