Publications

Understanding the origins of complexity is a key challenge in many sciences. Although networks are known to underlie most systems, showing how they contribute to well-known phenomena remains an issue. Here, we show that recurrent phase transitions in network connectivity underlie emergent phenomena in many systems. We identify properties that are typical of systems in different connectivity phases, as well as characteristics commonly associated with the phase transitions. We synthesize these common features into a common framework, which we term dual-phase evolution (DPE). Using this framework, we review the literature from several disciplines to show that recurrent connectivity phase transitions underlie the complex properties of many biological, physical and human systems. We argue that the DPE framework helps to explain many complex phenomena, including perpetual novelty, modularity, scale-free networks and criticality. Our review concludes with a discussion of the way DPE relates to other frameworks, in particular, self-organized criticality and the adaptive cycle.

This is a republication of this 2009 paper.

Evidence from several fields suggests that dual phase evolution (DPE) may account for distinctive features associated with complex adaptive systems. Here, we review empirical and theoretical evidence for DPE in natural systems and examine the relationship of DPE to self-organized criticality and adaptive cycles. A general model for DPE in networks is outlined, with preliminary data illustrating the emergence of phase changes.

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.

Evidence from several fields suggests that Dual Phase Evolution (DPE) may account for distinctive features associated with complex adaptive systems. We review empirical and theoretical evidence for DPE in natural systems and examine the relationship of DPE to other complexity theories such self-organised criticality and adaptive cycles.

Evidence from several fields suggests that dual phase evolution (DPE) may account for distinctive features associated with complex adaptive systems. Here, we review empirical and theoretical evidence for DPE in natural systems and examine the relationship of DPE to self-organized criticality and adaptive cycles. A general model for DPE in networks is outlined, with preliminary data illustrating the emergence of phase changes.

In this study, we describe an evolutionary mechanism – Dual Phase Evolution (DPE) – and argue that it plays a key role in the emergence of internal structure in complex adaptive systems (CAS). Our DPE theory proposes that CAS exhibit two well-defined phases – selection and variation – and that shifts from one phase to the other are triggered by external perturbations. We discuss empirical data which demonstrates that DPE processes play a prominent role in species evolution within landscapes and argue that processes governing a wide range of self-organising phenomena are similar in nature. In support, we present a simulation model of adaptive radiation in landscapes. In the model, organisms normally exist within a connected landscape in which selection maintains them in a stable state. Intermittent disturbances (such as fires, commentary impacts) flip the system into a disconnected phase, in which populations become fragmented, freeing up areas of empty space in which selection pressure lessens and genetic variation predominates. The simulation results show that the DPE mechanism may indeed facilitate the appearance of complex diversity in a landscape ecosystem.

Recent studies suggest that macro-evolutionary patterns such as punctuated equilibrium may be generated by a process termed Dual Phase Evolution (DPE). According to the DPE hypothesis, evolution in landscapes exhibits two phases – selection and variation. Disturbances such as mass extinctions can flip the landscape from selection to variation phases. Similar processes occur in a wide range of artificial, natural and social complex systems. Here, we show that mass extinctions induce DPE in a simulation model of adaptive radiation. The model is based on a previous model of adaptive radiation which did not incorporate Dual Phase Evolution. Results confirm that mass extinctions caused by external disturbances can trigger periods of rapid species turnover and adaptive radiation (variation phases), which are followed by long periods without innovation (selection phases). Our simulations also show that the spatial configuration of disasters leading to mass extinctions strongly influences whether and to what extent such disasters are capable of inducing evolutionary variation phases.