A central question in complexity theory is how large-scale phenomena, such as such as self-organisation, perpetual novelty, and sustained diversity, emerge. Complex systems can be understood as networks of interacting components. The focus of this research is the role that the properties of such networks play in self-organisation and emergence in complex systems.
Based on the previously known concept of Dual Phase Evolution (DPE), I propose a theoretical framework, within which recurrent phase transitions in network connectivity underlie emergent phenomena in many systems. This DPE framework extends and refines the original concept.
Networks can exist in two general connectivity phases: well connected and poorly connected. DPE relates each of the two connectivity phases and the transition events between them to typical system dynamics. I analyse empirical and experimental evidence from published studies in areas as diverse as physics, biology, socio-economics, mathematics and computer science. The analysis implies that DPE is widespread and operates in many kinds of complex systems, where it drives emergence and self-organisation. What is more, the analysis uncovers hitherto unstudied deep similarities and common underlying processes between different complex systems.
To further understand the theoretical concepts of the DPE framework, I apply DPE in studies of mechanisms behind particular emergent properties in several types of complex systems:
Seeking to better understand the emergence of novelty and diversity in ecosystems, I develop and study an individual-based simulation model of adaptive radiation (speciation) in landscapes. Simulation results imply that recurrent external disturbances facilitate perpetual novelty and diversity in landscape populations through two complementary mechanisms: One mechanism constitutes recurrent DPE phase changes in landscape connectivity on several levels. The other mechanism is alteration of the environment in disturbed areas leading to modified selection regimes.
As a result of the simulation studies of landscape evolution, I develop a new genetic model that combines the advantages of two existing genetic models. The new model allows individual-based simulation studies of genetics on holey fineness landscapes (HFLs). Such fitness landscapes result from biochemical constraints to genetic viability and have previously only been studied analytically. Simulation studies of reproductive isolation uncover that when HFLs are considered, common predictions about maintenance of reproductive isolation in migrating populations change. Results also show that HFL-genetics can facilitate the emergence of stable hybrid populations, and the evolution of social selection though reinforcement.
Continuing to study and apply DPE, I investigate how DPE processes can lead to the emergence of important network topologies. Using simulations models, I demonstrate two possible mechanisms behind emergent connectivity phase transitions without facilitation by external stimuli. A study of social network models reveals simple mechanisms that lead to structures typical of some real social networks and points towards general principles for emergence of important topologies such as modularity. A study of a network model of co-operations in markets reveals further mechanisms behind the emergence of complex and hierarchical modularity.
Generative models for scale-free networks, that are ubiquitous in many natural systems, are well known, however, such models apply to growing networks. I propose and examine a generative model for scale-free topologies that can account for some scale-free networks of constant size found in nature.
A wider context for DPE as a framework for reasoning about complexity is provided by examining the relationship between DPE and other established concepts such as Self-Organised Criticality and the Adaptive Cycle. In conclusion, DPE complements other established theories.
In general, network-theoretical approaches, such as DPE, are powerful paradigms in understanding complexity. This thesis shows that recurrent changes in connectivity of component interaction networks constitute a broad mechanism for emergence and self-organisation in complex systems, and demonstrates this mechanism in several specific biological and socio-economic systems.
