Effects of topology on network evolution

Abstract

T he ubiquity of scale-free topology in nature raises the question of whether this particular network design confers an evolutionary advantage 1 . A series of studies has identified key principles controlling the growth and the dynamics of scale-free networks 2-4 . Here, we use neuron-based networks of boolean components as a framework for modelling a large class of dynamical behaviours in both natural and artificial systems [5][6][7] . Applying a training algorithm, we characterize how networks with distinct topologies evolve towards a preestablished target function through a process of random mutations and selection [8][9][10] . We find that homogeneous random networks and scale-free networks exhibit drastically different evolutionary paths. Whereas homogeneous random networks accumulate neutral mutations and evolve by sparse punctuated steps 11,12 , scale-free networks evolve rapidly and continuously. Remarkably, this latter property is robust to variations of the degree exponent. In contrast, homogeneous random networks require a specific tuning of their connectivity to optimize their ability to evolve. These results highlight an organizing principle that governs the evolution of complex networks and that can improve the design of engineered systems.In recent years, studies of the architecture of large complex networks have unveiled a topology, known as scale-free, in which the connectivity between elements is power-law distributed 3 . In biology, the intricate interactions of genes and proteins can be viewed as neuron-based networks that control biological signals 13 . It is also common to model large technological and social systems using similar neuronal networks. For example, electronic devices that carry out computational tasks are built using large networks of interconnected logic gates, whereas collective social behaviours emerge from a complex structure of social relations and the dynamics of personal influences 14,15 . In such real-world networks, the topology is important because it mediates the effect of modifications in local interaction that can sometimes affect the networks dynamical behaviour. Topology could thus be a determining factor to modify or evolve the function of networks 16 . In this picture, new dynamical behaviours emerge from 'tinkering' the local interactions from old systems. In living organisms, genetic and protein networks have evolved through a process of mutations and selection to carry out specific functions under specific environmental conditions. This process has inspired physical scientists to apply a similar evolutionary approach to explore solutions to difficult optimization problems and to search for novel designs of artificial systems 17 . For example, evolutionary algorithms have been used to train software and even reconfigurable electronic chips to carry out pre-determined tasks 18 . Also known as 'evolvable hardware' , these electronic devices are composed of large numbers of neuron-like elements whose interactions are programmable 19 . To exploit the power of th...

Evolution of regulatory networks towards adaptability and stability in a changing environment

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Intrinsic properties of Boolean dynamics in complex networks

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Lateral genetic transfer: open issues

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