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.

Dual Phase Evolution (DPE) is a widespread natural process in which complex systems adapt and self-organise by switching alternately between two phases: a phase of global interactions and a phase of local interactions. We show that in evolving networks of agents, DPE can give rise to a wide variety of topologies. In particular, it can lead to the spontaneous emergence of stabilising modular structure.

Analytical models show that high-dimensional fitness landscapes form “holey” rather than “rugged” topographies, but the implications of this finding for biological and artificial life systems remain largely unexplored. One of the reasons for this gap can be attributed to serious difficulties in the implementation of individual-based holey fitness landscape (HFL) models. Here, we introduce a method for simulating HFLs in spatially explicit individual-based models that overcomes these difficulties. We examine how the HFL changes predictions for the maintenance of genetic diversity in the face of migration. Previous models suggest that ecologically-based reproductive isolation will rapidly collapse under migration. Our results indicate that an underlying HFL can often maintain diversity in this situation. Hybrid species emerge frequently when HFL genetics are simulated, but are usually doomed to extinction because of small population sizes. However, hybridisation can also lead to novel adaptations and potentially the exploitation of new ecological niches. More generally, the results imply that HFL genetics should not be neglected in studies of adaptation and diversity.

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.

We describe a process, Dual Phase Evolution (DPE), which is a widespread mechanism by which systems evolve. The process occurs in systems that switch between two phases: a balance phase and a variation phase. In DPE, processes drive systems to settle in a “balance” phase, but external stimuli can flip the system into a temporary “variation” phase, in which rapid change occurs on all scales. The system gradually returns to a new balance phase, often with different structure than formerly. We argue that the system occurs in many natural systems and show how it results from landscape connectivity in both evolution and long-term forest change. We describe how it underlies certain optimization algorithms, and can be implemented to improve the performance of existing optimization methods. Finally, we present simulation experiments that show how DPE may play a role in creating cliques, clusters, modules and other kinds of order within social networks.

We provide a brief overview of the use of FLs in evolutionary biology and introduce an FL model suitable for individual-based models of species evolution. Our model combines different features of several analytic FL models used in evolutionary biology. Our new model overcomes several difficulties encountered with previous FL models, particularly arbitrary divergence thresholds. We discuss the difficulties encountered during the implementation of our model and how we have overcome these. We present a detailed numerical analysis of the proposed family of FLs that will inform future work based on our FL model.