Many 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.

Digitization of video recordings often requires the laborious procedure of manually clicking points of interest on individual video frames. Here, we present progressive tracking, a procedure that facilitates manual digitization of markerless videos. In contrast to existing software, it allows the user to follow points of interest with a cursor in the progressing video, without the need to click. To compare the performance of progressive tracking with the conventional frame-wise tracking, we quantified speed and accuracy of both methods, testing two different input devices (mouse and stylus pen). We show that progressive tracking can be twice as fast as frame-wise tracking while maintaining accuracy, given that playback speed is controlled. Using a stylus pen can increase frame-wise tracking speed. The complementary application of the progressive and frame-wise mode is exemplified on a realistic video recording. This study reveals that progressive tracking can vastly facilitate video analysis in experimental research.

In in-vivo motion analyses, data from a limited number of subjects and trials is used as proxy for locomotion properties of entire populations, yet the inherent hierarchy of the individual and population level is usually not accounted for. Despite the increasing availability of hierarchical model frameworks for statistical analyses, they have not been applied extensively to comparative motion analysis. As a case study for the use of hierarchical models, we analyzed locomotor parameters of four Swinhoe's striped squirrels. The small-bodied arboreal mammals exhibit brief bouts of rapid asymmetric gaits. Spatio-temporal parameters on runways with experimentally varied dimensions of the setup enclosure were compared to test for their potentially confounding effects. We applied principal component analysis to evaluate changes to the overall locomotor pattern. A common, non-hierarchical, pooled statistical analysis of the data revealed significant differences in some of the parameters depending on enclosure dimensions. In contrast, we used a hierarchical Bayesian generalized linear model (GLM) that considers subject specific differences and population effects to compare the effect of enclosure dimensions on the measured parameters and the principal components. None of the population effects were confirmed by the hierarchical GLM. The confounding effect of a single subject that deviates in its locomotor behavior is potentially bigger than the influence of the experimental variation in enclosure dimensions. Our findings justify the common practice of researchers to intuitively select an enclosure with dimensions assumed as "non-constraining". Hierarchical models can easily be designed to cope with limited sample size and bias introduced by deviating behavior of individuals. When limited data is available-a typical restriction of in-vivo motion analyses of non-model organisms-density distributions of the Bayesian GLM used here remain reliable and the hierarchical structure of the model optimally exploits all available information. We provide code to be adjusted to other research questions.