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A topological approach to selecting models of biological experiments

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  • M Ulmer
  • Lori Ziegelmeier
  • Chad M Topaz

Abstract

We use topological data analysis as a tool to analyze the fit of mathematical models to experimental data. This study is built on data obtained from motion tracking groups of aphids in [Nilsen et al., PLOS One, 2013] and two random walk models that were proposed to describe the data. One model incorporates social interactions between the insects via a functional dependence on an aphid’s distance to its nearest neighbor. The second model is a control model that ignores this dependence. We compare data from each model to data from experiment by performing statistical tests based on three different sets of measures. First, we use time series of order parameters commonly used in collective motion studies. These order parameters measure the overall polarization and angular momentum of the group, and do not rely on a priori knowledge of the models that produced the data. Second, we use order parameter time series that do rely on a priori knowledge, namely average distance to nearest neighbor and percentage of aphids moving. Third, we use computational persistent homology to calculate topological signatures of the data. Analysis of the a priori order parameters indicates that the interactive model better describes the experimental data than the control model does. The topological approach performs as well as these a priori order parameters and better than the other order parameters, suggesting the utility of the topological approach in the absence of specific knowledge of mechanisms underlying the data.

Suggested Citation

  • M Ulmer & Lori Ziegelmeier & Chad M Topaz, 2019. "A topological approach to selecting models of biological experiments," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-18, March.
  • Handle: RePEc:plo:pone00:0213679
    DOI: 10.1371/journal.pone.0213679
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    References listed on IDEAS

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    1. Huepe, Cristián & Aldana, Maximino, 2008. "New tools for characterizing swarming systems: A comparison of minimal models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2809-2822.
    2. Dane Taylor & Florian Klimm & Heather A. Harrington & Miroslav Kramár & Konstantin Mischaikow & Mason A. Porter & Peter J. Mucha, 2015. "Erratum: Topological data analysis of contagion maps for examining spreading processes on networks," Nature Communications, Nature, vol. 6(1), pages 1-1, December.
    3. Chad M Topaz & Lori Ziegelmeier & Tom Halverson, 2015. "Topological Data Analysis of Biological Aggregation Models," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-26, May.
    4. Dane Taylor & Florian Klimm & Heather A. Harrington & Miroslav Kramár & Konstantin Mischaikow & Mason A. Porter & Peter J. Mucha, 2015. "Topological data analysis of contagion maps for examining spreading processes on networks," Nature Communications, Nature, vol. 6(1), pages 1-11, November.
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