A traveling wave of lateral movement coordinates both turning and forward walking in the ferret

Relative phase was recently suggested as a key variable for the dynamical modeling of coordination in both quadruped locomotion and undulation swimming in fish. Relative phase analysis has not yet been applied, however, to the behavior of intact, freely moving animals, but only to simplified situations involving restrained animals and humans. In order to investigate relative phase under free movement conditions, we filmed free locomotion of ferrets (Mustella putorius) from below (through a glass floor) and measured the lateral bending along the head, torso, and tail, and the location of the four paws. We introduced an algorithm which extracts the phase (and thus also the relative phase) even when the movements were neither periodic nor symmetric. Our results show that relative phases between segments have preferred values, which are relatively independent of the amplitude, duration, and asymmetry of the movement. In particular, both walking and turning can be explained as modulations of a single pattern: a cephalo-caudal, traveling wave of lateral movement with a wavelength of approximately one length of the body. The relative phase between movements of adjacent segments is similar when the body is in S shape (i.e., when walking forward), or C shape (i.e., when turning). The movements of the paws in the horizontal plane can also be considered as part of this traveling wave. Our findings suggest that the concept of traveling waves of lateral bending, as found in the locomotion of undulating fish, can be generalized in two ways: (i) by considering the axis around which the movement is centered, it applies not only to forward locomotion, but also to turning: (ii) by incorporating the position of the paws, it applies also to the movement of quadrupeds. Our findings suggest that the relative phase, once it is generalized to asymmetric and quasi-periodic movement, is suitable for modeling coordination patterns under free movement conditions.