Quantifying intralimb coordination of terrestrial ungulates with Fourier coefficient affine superimposition

Abstract

AbstractMany phenomena related to motor behaviour in animals are spatially and temporally periodic, making them accessible for transformation to the frequency domain via Fourier Series. Although this has been applied previously, it had not been noticed that the characteristic arrangement of Fourier coefficients in their complex-valued representation resembles landmarks in geometric morphometrics. We define a superimposition procedure in the frequency domain, which removes affine differences (mean, amplitude, phase) to reveal and compare the shape of periodic kinematic measures. This procedure is conceptually linked to dynamic similarity, which can thereby be assessed on the level of individual limb elements. We demonstrate how to make intralimb coordination accessible for large-scale, quantitative analyses. By applying this to a dataset from terrestrial ungulates, dominant patterns in forelimb coordination during walking are identified. This analysis shows that typical strides of these animals differ mostly in how much the limbs are lifted in the presence or absence of obstructive substrate features. This is shown to be independent of morphological features. Besides revealing fundamental characteristics of ungulate locomotion, we argue that the suggested method is generally suitable for the large-scale quantitative assessment of coordination and dynamics in periodic locomotor phenomena.