Connectivity and complex systems: learning from a multi-disciplinary perspective

Abstract

In recent years, parallel developments in disparate disciplines have focused on what has come to be termed connectivity; a concept used in understanding and describing complex systems. Conceptualisations and operationalisations of connectivity have evolved largely within their disciplinary boundaries, yet similarities in this concept and its application among disciplines are evident. However, any implementation of the concept of connectivity carries with it both ontological and epistemological constraints, which leads us to ask if there is one type or set of approach(es) to connectivity that might be applied to all disciplines. In this review we explore four ontological and epistemological challenges in using connectivity to understand complex systems from the standpoint of widely different disciplines. These are: (i) defining the fundamental unit for the study of connectivity; (ii) separating structural connectivity from functional connectivity; (iii) understanding emergent behaviour; and (iv) measuring connectivity. We draw upon discipline-specific insights from Computational Neuroscience, Ecology, Geomorphology, Neuroscience, Social Network Science and Systems Biology to explore the use of connectivity among these disciplines. We evaluate how a connectivity-based approach has generated new understanding of structural-functional relationships that characterise complex systems and propose a 'common toolbox' underpinned by network-based approaches that can advance connectivity studies by overcoming existing constraints.

Keywords: Connectivity Studies; Emergent Behaviour; Functional Connectivity; Fundamental Unit; Measuring Connectivity; Structural Connectivity.

Fig. 1

Network-based representation of structural and functional connectivity. Illustration of ways in which structural and functional connectivity within a multitude of systems can be conceptualised using a network-based approach across Systems Biology, Neuroscience/Computational Neuroscience, Geomorphology, Ecology, and Social Network Science

Fig. 2

Coincidence in spatial location and timing of activations in the brain. The demonstration of the coincidence in spatial location and timing of the earliest visually evoked (top) and spatial attention (bottom) related activations (responses to images presented in the left visual field). The green lines here indicate the V1/V2 borders (representation of vertical meridian) with the schematic views on the right showing how the activations look on a flat representation of the local cortex, showing clearly the early visual cortex and their boundaries

Fig. 3

Geomorphic feedbacks between structural and functional connectivity. Schematic diagram of feedbacks between structural and functional connectivity (source: Wainwright et al., 2011). The relative locations of values of different variables which control SC may initially (t = 1) be quite discrete, leading to functional disconnections which are only connected during events of specific types or magnitudes, which in turn can create structural feedbacks by reorganizing landscape elements (e.g. vegetation, soil types). Through time (t = 2, …, n), these feedbacks may be reinforced so that structural and functional connectivity follow similar patterns, and the system become difficult to reverse (see Turnbull et al., 2008)

Fig. 4

The relationship within the common resource pool motif subset display across effective-complexity space. This shows the various combinations of social interactions (white) that govern connected natural resources such as wetlands (grey). From Kininmonth et al. (2015)

Fig. 5

Network diagram of the interaction of fishers with people who buy fish. Black = single trade relationship, grey = multiple traders and white = traders. This network diagram highlights the emerging property of organised fishing businesses that are dependent on the access to capital. From Kininmonth et al. (2017)

Fig. 6

Network-centred common toolbox. Diagram showing how a network-centred common toolbox implicitly addresses the four (inextricably linked) key challenges: defining the fundamental unit, separating SC and FC, understanding emergent behaviour and measuring connectivity. A. Groups of nodes form fundamental units at higher levels of organization (denoted by grey dashed lines); B. Topological representation of system structure (spatially embedded depending in the system in question); C. Identifying parts of the network that are dynamic (functionally connected); D. Adaptive network where the evolution of topology depends on the dynamics of nodes (source: Gross and Blasius; 2008). Network adaptation at multiple (cross scale) levels of organization shapes emergent behaviour; E. FC may have an emergent aspect (self-organised, collective patterns on the structural network) that is independent of network adaptation; F. The fundamental unit should dictate the measurement approach; G. Measurements of SC and FC should be used to parameterise and test network-based representations; H. How we measure connectivity determines our ability to detect how connectivity leads to emergent behaviour