Fig. 1.

Causal emergence is diminished in the brain dynamics of DOC patients. (A) Relationship between emergence and supervenience. A macroscale feature Vt of a system is supervenient on the state of the system at time t, denoted by $X_t$, if $V_t$ is fully determined by $X_t$ (beyond the addition of noise), such that anything about $V_t$ that can be predicted from the system's previous state, $X_{t-1}$ can also be predicted from the system's current state, $X_t$. Then, a supervenient feature $V_t$  is said to be causally emergent if it has “unique” predictive power over the future evolution of the system $X_t$— in the sense of providing information about the dynamics of the system that cannot be found in any of the parts of the system when considered separately. The two components of emergence capacity are causal decoupling, the unique predictive power of $V_t$ on $V_{t+1}$corresponding to the system's macroscale influencing the macroscale's future;  and downward causation, the unique predictive power of  $V_t$ on $X_{t+1}$i.e. the macroscale influencing the microscale.  (B) The global emergence capacity of the human brain is obtained from Integrated Information Decomposition as the average emergence capacity (downward causation + causal decoupling) between each pair of discretised regional fMRI BOLD signals (Methods and Fig. S1). (C) Violin plots of each subject's emergence capacity by group. Data points represent subjects. White circle, median; centre line, mean; box limits, upper and lower quartiles; whiskers, 1.5x interquartile range. ** p < 0.01; *** p < 0.001, FDR-corrected. Here we used a time-step of 1 TR (2 s), the fastest available for our functional MRI data. No significant difference was observed when using a slower timescale of 4 TRs. We also show that analogous results are obtained using continuous (rather than discretised) signals (Fig. S3A), and using a different information-theoretic formalism (Methods and Fig. S3B), with UWS patients exhibiting significantly lower emergence capacity than healthy controls in both cases. We found that differences in emergence capacity can be attributed to downward causation (Fig. S4), rather than causal decoupling (all p > 0.05): that is, the overall difference in emergence capacity is primarily accounted for by the effects of the macroscale on the microscale.