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Boolean Threshold Networks as Models of Genotype-Phenotype Maps

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Complex Networks XI

Part of the book series: Springer Proceedings in Complexity ((SPCOM))

Abstract

Boolean threshold networks (BTNs) are a class of mathematical models used to describe complex dynamics on networks. They have been used to study gene regulation, but also to model the brain, and are similar to artificial neural networks used in machine learning applications. In this paper we study BTNs from the perspective of genotype-phenotype maps, by treating the network’s set of nodes and connections as its genotype, and dynamic behaviour of the model as its phenotype. We show that these systems exhibit (1) Redundancy, that is many genotypes map to the same phenotypes; (2) Bias, the number of genotypes per phenotypes varies over many orders of magnitude; (3) Simplicity bias, simpler phenotypes are exponentially more likely to occur than complex ones; (4) Large robustness, many phenotypes are surprisingly robust to random perturbations in the parameters, and (5) this robustness correlates positively with the evolvability, the ability of the system to find other phenotypes by point mutations of the parameters. These properties should be relevant for the wide range of systems that can be modelled by BTNs.

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Author information

Authors and Affiliations

  1. Oxford Internet Institute, University of Oxford, Oxford, UK

    Chico Q. Camargo

  2. Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, UK

    Ard A. Louis

Authors
  1. Chico Q. Camargo
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  2. Ard A. Louis
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Corresponding author

Correspondence to Chico Q. Camargo .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Exeter, Exeter, UK

    Hugo Barbosa

  2. Dept de Fisica de la Materia Condensada, Univ de Zaragoza, Fac de Ciencias, Zaragoza, Zaragoza, Spain

    Jesus Gomez-Gardenes

  3. Center for Data Science, Inc., New York, NY, USA

    Bruno Gonçalves

  4. University of Catania, Catania, Catania, Italy

    Giuseppe Mangioni

  5. Department of Computer Science, University of Exeter, Exeter, UK

    Ronaldo Menezes

  6. Leibniz Institute for the Social Sciences, Cologne, Germany

    Marcos Oliveira

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Camargo, C.Q., Louis, A.A. (2020). Boolean Threshold Networks as Models of Genotype-Phenotype Maps. In: Barbosa, H., Gomez-Gardenes, J., Gonçalves, B., Mangioni, G., Menezes, R., Oliveira, M. (eds) Complex Networks XI. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-40943-2_13

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