Reconciling emergences: An information-theoretic approach to identify causal emergence in multivariate data

PLoS Comput Biol. 2020 Dec 21;16(12):e1008289. doi: 10.1371/journal.pcbi.1008289. eCollection 2020 Dec.


The broad concept of emergence is instrumental in various of the most challenging open scientific questions-yet, few quantitative theories of what constitutes emergent phenomena have been proposed. This article introduces a formal theory of causal emergence in multivariate systems, which studies the relationship between the dynamics of parts of a system and macroscopic features of interest. Our theory provides a quantitative definition of downward causation, and introduces a complementary modality of emergent behaviour-which we refer to as causal decoupling. Moreover, the theory allows practical criteria that can be efficiently calculated in large systems, making our framework applicable in a range of scenarios of practical interest. We illustrate our findings in a number of case studies, including Conway's Game of Life, Reynolds' flocking model, and neural activity as measured by electrocorticography.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Animals
  • Behavior, Animal
  • Birds
  • Causality
  • Computational Biology
  • Computer Simulation*
  • Haplorhini
  • Humans
  • Information Theory*
  • Models, Biological*
  • Models, Statistical
  • Multivariate Analysis
  • Neurophysiology