We measured the direction of body axis in 4,144 cattle of 122 “usable” herds from the sample of pastures, the coordinates of which were provided by Hert et al. (2011). The discrepancy to the above-stated numbers of usable data (n = 104 herds; 3,830 individuals) is based on the fact that some of the coordinates did not lead to a single pasture but contained several neighboring pastures. We evaluated all these separate pastures individually and included all of them in the analysis.
First, we have analyzed axial orientation of cattle following the methods described by Begall et al. (2008), except for the fact that we now measured the direction of the body axis directly on the screen using the digital ruler of the Google Earth tools. Briefly, we calculated one mean vector/herd to obtain statistically independent data and subsequently used second-order Rayleigh test to assess clustering of the mean axis bearings. This procedure clearly rejected random distribution, the mean herd axes were significantly clustered along the North–South axis (Fig. 2
a, left column, and Table 1). Subsequently, we ran the same test but with exclusion of those herds, in which body orientation of individual cattle did not reach level of significance (i.e., we considered only pastures where the Rayleigh test resulted in p < 0.05). To illustrate the effect of this procedure, we plotted all mean axis bearings and only significant mean axis bearings in circular diagrams for the same samples (Fig. 3). Clustering of the significant mean herd axes along the North–South axis was even more pronounced (grand mean axis = 178°/358°, r = 0.385, Z = 10.39, p = 3 × 10−5, n = 70). These results are not significantly different from the results provided by Begall et al. (2008) and control data provided by Burda et al. (2009). Indeed, according to the Mardia-Watson-Wheeler test the distributions of the control data from Burda et al. (2009) and the “usable” data based on Hert et al.’s sampling did not deviate significantly (W = 4,437, p = 0.109; cf. Fig. 2a, b). Also, the mean vectors of both samples were not significantly different (Watson-Williams F-test: F = 1.008; p = 0.317).
Second, for the sake of comparability with the data published by Hert et al. (2011), we have also analyzed axial orientation of individual cattle (i.e. pooled data, neglecting the herds). The analysis of 4,144 individual cows resulted in even lower p-values and confirmed that individual cattle tend to align along approximately North–South axis (see Fig. 2
a, right column, and Table 1).
Finally, we measured the orientation of the head direction in 887 cattle of 53 herds from images of good resolution enabling us to distinguish between head and rear and between lying (n = 459) and standing (n = 428) animals. Of the examined herds, 11 herds contained only lying, 5 herds only standing and 37 herds both lying and standing animals. We considered grazing animals also as standing, yet only in cases when vector direction of all the animals on the pasture could be determined (see above for reasoning). Here again, for the sake of comparability with the data published by Hert et al. (2011), we have analyzed orientation of individual cattle. The Rayleigh test was used to determine whether cattle are directionally oriented. Doubling the angles and double-doubling the angles techniques (Batschelet 1981) were used to test for bimodal and quadrimodal distribution, respectively. The total data set as well as subsets of lying and standing/grazing animals exhibited bimodal distribution––cattle preferentially point their heads in either approximately northern or southern directions (see Fig. 4). Notably, the analyses of both angular (Fig. 4) and axial data (Fig. 2c, Table 1) show that alignment is more pronounced in lying than in standing/grazing cows. This finding is in line with the expectation that magnetic alignment should be displayed particularly by relaxing animals, when other factors influencing postural orientation are of less importance.