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 the functions of such systems it is important to analyze if and how the subsystems interact and to describe the effect of these interactions. In this work we investigate the extent to which the cause-and-effect framework is applicable to such interacting subsystems. We base our work on a standard notion of causal effects and define a new concept called natural causal effect. This new concept takes into account that when studying interactions in biological systems, one is often not interested in the effect of perturbations that alter the dynamics. The interest is instead in how the causal connections participate in the generation of the observed natural dynamics. We identify the constraints on the structure of the causal connections that determine the existence of natural causal effects. In particular, we show that the influence of the causal connections on the natural dynamics of the system often cannot be analyzed in terms of the causal effect of one subsystem on another. Only when the causing subsystem is autonomous with respect to the rest can this interpretation be made. We note that subsystems in the brain are often bidirectionally connected, which means that interactions rarely should be quantified in terms of cause-and-effect. We furthermore introduce a framework for how natural causal effects can be characterized when they exist. Our work also has important consequences for the interpretation of other approaches commonly applied to study causality in the brain. Specifically, we discuss how the notion of natural causal effects can be combined with Granger causality and Dynamic Causal Modeling (DCM). Our results are generic and the concept of natural causal effects is relevant in all areas where the effects of interactions between subsystems are of interest.