Modular Interdependency in Complex Dynamical Systems

Abstract

Simon’s characterisation of modularity in dynamical systems describes subsystems as having dynamics that are approximately independent of those of other subsystems (in the short term). This fits with the general intuition that modules must, by definition, be approximately independent. In the evolution of complex systems, such modularity may enable subsystems to be modified and adapted independently of other subsystems whereas in a non-modular system, modifications to one part of the system may result in deleterious side-effects elsewhere in the system. But this notion of modularity and its effect on evolvability is not well-quantified and is rather simplistic. In particular, modularity need not imply that inter-module dependencies are weak or unimportant. In dynamical systems this is acknowledged by Simon’s suggestion that, in the long term, the dynamical behaviours of subsystems do interact with one another, albeit in an ‘aggregate’ manner – but this kind of inter-module interaction is omitted in models of modularity for evolvability. In this brief discussion paper we seek to unify notions of modularity in dynamical systems with notions of how modularity affects evolvability. This leads to a quantifiable measure of modularity and a different understanding of its impact on evolvability.

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ORCID for Richard A. Watson: orcid.org/0000-0002-2521-8255

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