Spatial embedding as an enabling constraint: Introduction to a special issue of complexity on the topic of “Spatial Organization”

Abstract

We introduce and discuss the role of spatial embedding as an enabling constraint on complex system structure and function.Key words: complexity, space, spatial embedding, networks, Space as an Enabling ConstraintThe vast majority of real-world complex systems are extended in space. Some parts are close together, others are far apart. Moreover, the tendency for particular system parts to interact is partly determined by the distances that separate them. Consequently, there is considerable evidence that this spatial embedding has a significant impact on both the structural and functional organisation of complex systems. Spatial constraints are implicated in the way that populations of termites construct their impressive mounds [15,16], the way in which species of plants compete for light [8], and even the way in which genes are packed onto linear strands of DNA [18]. Moreover, we are beginning to understand that this influence is not neutral, but can sometimes be positive, with spatially embedded systems enjoying an improved ability to effectively organise in order to support useful functionality.Key examples are offered by [5] in their work modelling the tendency of molecules to organise into mutually self-reinforcing "hypercycles" [11], and by [9] in the context of trying to understand how biological populations of simple creatures might evolve to exhibit co-operative tendencies (see [6], this volume, for more details of both models). In each case, the system being Preprint submitted to Complexity April 22, 2010 modelled was unable to exhibit organised complex behaviour when its constituent parts were well-mixed. However, when each system was extended over a two-dimensional space such that its parts could only interact with their close spatial neighbours, the systems were able to spontaneously achieve and maintain functional organisation in the face of exploitative disturbance. Spatial embedding enabled each population (of modelled molecular species or simple simulated creatures) to structure itself in such a way as to maintain co-operative functional organisation through exploiting the "useful" asymmetries that space introduces into the ecology of interactions [7]. These results suggest an intriguing possibility: might understanding the role of spatial embedding help us to better deal with problems concerning a wide range of spatially embedded complex systems? For instance, how to organise the built environment such that community coherence is consolidated rather than fragmented [4]; how to arrange social care processes such that they are vital and integrated [17]; how to engineer accountability in virtual communities [12]; how to achieve bioremediation using bacterial biofilm communities [19]; and how to improve the resilience of the infrastructural systems upon which we rely [10], etc. Could the influence of spatial embedding in these contexts, when properly understood, allow and encourage individuals to organise in a way that makes good solutions easier to achieve?It is in this sense that space sh...