Biological processes involve movements across all measurable scales. Similarity measures can be applied to compare and analyze these movements but differ in how differences in movement are aggregated across space and time. The present study reviews frequently-used similarity measures, such as the Hausdorff distance, Fréchet distance, Dynamic Time Warping, and Longest Common Subsequence, jointly with several measures less used in biological applications (Wasserstein distance, weak Fréchet distance, and Kullback-Leibler divergence), and provides computational tools for each of them that may be used in computational biology. We illustrate the use of the selected similarity measures in diagnosing differences within two extremely contrasting sets of biological data, which, remarkably, may both be relevant for magnetic field perception by migratory birds. Specifically, we assess and discuss cryptochrome protein conformational dynamics and extreme migratory trajectories of songbirds between Alaska and Africa. We highlight how similarity measures contrast regarding computational complexity and discuss those which can be useful in noise elimination or, conversely, are sensitive to spatiotemporal scales.

Biological processes involve movements across all measurable scales. Similarity measures can be applied to compare and analyze these movements but differ in how differences in movement are aggregated across space and time. The present study reviews frequently-used similarity measures, such as the Hausdorff distance, Frechet distance, Dynamic Time Warping, and Longest Common Subsequence, jointly with several measures less used in biological applications (Wasserstein distance, weak Frechet distance, and Kullback-Leibler divergence), and provides computational tools for each of them that may be used in computational biology. We illustrate the use of the selected similarity measures in diagnosing differences within two extremely contrasting sets of biological data, which, remarkably, may both be relevant for magnetic field perception by migratory birds. Specifically, we assess and discuss cryptochrome protein conformational dynamics and extreme migratory trajectories of songbirds between Alaska and Africa. We highlight how similarity measures contrast regarding computational complexity and discuss those which can be useful in noise elimination or, conversely, are sensitive to spatiotemporal scales.

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