Dual Phase Evolution
Dual Phase Evolution is a theory that aims to explain different behaviours of many complex systems in relation to properties of networks that can be used to describe those systems.
What are complex systems?
Complex systems are entities composed of many interacting components that as a whole exhibit emergent properties not easily understood from studying the individual components. Examples of complex systems include our planet as a whole, landscapes and ecosystems, insect colonies, organisms, cells, human economies and organisations, telecommunication networks and many others. In fact, a large proportion of "interesting" phenomena in our environment are complex systems. Complex adaptive systems have the ability to evolve by adapting to their environment.
Complex systems are difficult to understand and study. Their emergent properties are hard to describe mathematically, but modern computers allow us to simulate complex systems. While traditional natural sciences can resort to an established body of formal theories, the search for general theories of complexity continues to engage scientists across many disciplines.
Dual Phase Evolution (DPE)
Most complex systems can be represented in terms of networks that underlie such systems . Understanding properties of these networks helps understanding the systems they represent. An unexpected property of all networks is that adding or removing just a few edges can cause a connectivity phase transition - a sudden change from a phase in which a network consists of many separate components to a phase where most of the network nodes belong to a single connected super-component . Systems were underlying networks are in the "disconnected" phase exhibit typical properties that are different from systems in the "connected" phase.
Dual Phase Evolution (DPE) is a theory that explains a wide range of phenomena found in a variety of complex systems in terms of repeated connectivity phase transitions that occur in underlying networks.
DPE has been studied in a number of complex adaptive systems including landscape ecosystems [3, 4, 5, 6], social groups [7, 8] and complex networks [8, 9]. It was also shown that some complex phenomena that were previously attributed to other processes can also be explained in terms of DPE [3, 4, 8, 9, 10]. These results are an important step towards a unified understanding of our complex environment.
Dual Phase Evolution in landscape ecosystems
Fossil records show that evolution on earth occurred in fits and starts , a phenomenon known as punctuated equilibria. Charcoal record analysis shows that plant composition in forests also develops in fits and starts . The time scales of these two processes differ by several orders of magnitude. Might there be a common mechanism?
Simulation experiments [5, 6] have shown that changes in habitat connectivity induced by disturbances can cause bursts of adaptive radiation (speciation). Disasters lead to repeated connectivity phase changes in habitats by introducing natural barriers between established sub-populations and by clearing up areas for newcomers. Simulations  of this dual phase process show that patterns of stability intermitted by vivid evolutionary exploration match various natural ecosystems on different time scales. This is an important result for understanding and managing today's vulnerable ecosystems and climate.
Dual Phase Evolution in social groups
The routine is familiar to everyone: Most of the time we go about our daily business interacting with a small circle of colleagues, friends and family. We exercise only a few local connections. Once in a while, we attend a meeting, a conference or a party where we interact with a lot of people and make new friends. We exercise global connections and make new ones. Our interaction network flips between phases of low and high connectivity and our social network is subject to Dual Phase Evolution (DPE). What are the consequences of this realisation?
Studies [8, 13] of processes that lead to social networks of different kinds have demonstrated that many of these social structures can be a result of DPE processes. The connections between friends on a social networking site have a very different topology from romantic relationships in a high school, but all these networks can be created by the DPE mechanism. Understanding the forces that govern our social interaction networks is a key issue for sociologists, politicians and business people.
Dual Phase Evolution in complex networks
Networks are inherent in the structure and behaviour of complex systems . A thorough understanding of mechanisms responsible for important types of networks is crucial to understanding the systems represented by those networks. Some well understood key network types include small world networks  and scale-free networks . The mechanisms behind modular networks are less well understood.
All of the above network topologies can be a result of Dual Phase Evolution (DPE) acting on the systems represented by the networks. Traditionally it was thought that scale-free networks are formed through preferential attachment in growing networks. However, it has been demonstrated  how a scale free topology can arise in a fixed size network subjected to DPE. Simulations  also show that DPE can lead to modular networks. These results provide crucial hints on the mechanisms that occur within fixed size systems with scale-free dynamics, such as brain connectivity patterns. The results also suggest a common mechanism for the emergence of modular compositions that are ubiquitous in nature.
Dual Phase Evolution as a general framework for complex adaptive systems
Dual Phase Evolution (DPE) is ubiquitous in natural as well as in artificial complex systems. A few examples are outlined above and the amount of work investigating DPE in those and other areas is growing. One of the key objective of this research is to appropriately integrate the DPE theory with other frameworks for understanding complex systems, such as Self-Organised Criticality [16, 17], the Adaptive Cycle  and others. These frameworks may be described as observational formalisms: they provide rigorous descriptions of systems' behaviour, which is essential for understanding complex systems, however, they do not provide a causal explanation for the observed dynamics. On the other hand, DPE can provide a causal explanation for many properties of complex adaptive systems in terms of the underlying network dynamics. The results obtained from studying DPE contribute towards a better unified understanding of emergence and complexity.
- Overview paper:
Dual Phase Evolution in Complex Adaptive Systems.
- Thesis on DPE:
Mechanisms for Emergence and Self-Organisation in Complex Adaptive Systems: A Network-Theoretical Perspective.
- More publications on DPE.
- Even more publications on DPE.