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Fitness landscapes for coupled map lattices

Abstract

Our goal is to match some dynamical aspects of biological systems with that of networks of coupled logistic maps. With these networks we generate sequences of iterates, convert them to symbol sequences by coarse-graining, and count the number of times combinations of symbols occur. Comparison of this with the number of times these combinations occur in experimental data—a sequence of interbeat intervals for example—is a measure of the fitness of each network to describe the target data. The most fit networks provide a cartoon that suggests a decomposition of the experimental data into a component that may be produced by a simple dynamical subsystem, and a residual component, the result of detailed, particular characteristics of the system that generated the target data. In the space of all network parameters, each point corresponds to a particular network. We construct a fitness landscape when we assign a fitness to each point. Because the parameters are distributed continuously over their ranges, and because fitnesses are estimated numerically, any plot of the landscape involves a finite sample of parameter values. We’ll investigate how the local landscape geometry changes when the array of sample parameters is refined, and use the landscape geometry to explore complex relations between local fitness maxima.

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Acknowledgements

This paper is an elaboration of the work in the first author’s Applied Mathematics Yale senior thesis [36]. In early stages of this project we benefitted from many thoughtful and energetic discussions with Rachel Lawrence and Hannah Otis. Comments by a very thoughtful anonymous referee led to improvements in the readability of this paper.

Funding

This research was supported by grant funding for the first author from the Science and Technology Research Scholars (STARS) II program at Yale University.

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Correspondence to Michael Frame.

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This article belongs to the Topical Collection: The Revolutionary Impact of Landscapes in Biology

Guest Editors: Robert Austin, Shyamsunder Erramilli, Sonya Bahar

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Driver, N., Frame, M. Fitness landscapes for coupled map lattices. J Biol Phys 47, 215–235 (2021). https://doi.org/10.1007/s10867-021-09577-6

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Keywords

  • Coupled logistic maps
  • Fractals
  • Chaotic dynamics
  • Fitness landscape