Evolution of Boolean networks

Boolean networks are the simplest models for gene regulation networks and other cellular networks. These networks have a strong influence on the embryonic development and on the phenotype of an organism. There is good evidence that many important changes in evolutionary history are due to changes in the way genes are regulated. Studying the evolution of Boolean network models can give insights into the ways in which gene regulatory networks can evolve. The focus of this talk is on the fitness landscape of Boolean networks, and on its effect on the evolution of a population. We obtain the "fitness" of a network from its "phenotype", i.e., its dynamical behavior, for instance we select for dynamical robustness. The "genotype" is given by the network structure and update functions. "Mutations" are performed by changing connections and functions. We find that the fitness landscape has a plateau of very high fitness, which spans all of genotype space. This allows for ongoing evolutionary change of the networks, without a need to cross valleys of low fitness. While evolving on the plateau, a population can undergo long-term changes in the mean fitness and in the mutational robustness.

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