Assessing biological models using topological data analysis

TL;DR

This paper applies topological data analysis to evaluate how well mathematical models fit experimental aphid movement data, demonstrating that topological signatures can effectively distinguish models without prior mechanistic knowledge.

Contribution

It introduces the use of topological data analysis as a model assessment tool in biological collective motion studies, showing its effectiveness compared to traditional order parameters.

Findings

Topological signatures match the performance of known order parameters in model evaluation.

Topological data analysis outperforms non-a priori order parameters in model assessment.

Topological approach is useful when mechanistic knowledge of data is limited.

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, and the second model is a control model that excludes these interactions. 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.