Morphology and the gradient of a symmetric potential predicts gait transitions of dogs

Gaits and gait transitions play a central role in the movement of animals. Symmetry is thought to govern the structure of the nervous system, and constrain the limb motions of quadrupeds. We quantify the symmetry of dog gaits with respect to combinations of bilateral, fore-aft, and spatio-temporal symmetry groups. We tested the ability of symmetries to model motion capture data of dogs walking, trotting and transitioning between those gaits. Fully symmetric models performed comparably to asymmetric with only a 22% increase in the residual sum of squares and only one-quarter of the parameters. This required adding a spatio-temporal shift representing a lag between fore and hind limbs. Without this shift, the symmetric model residual sum of squares was 1700% larger. This shift is related to (linear regression, n = 5, p = 0.0328) dog morphology. That this symmetry is respected throughout the gaits and transitions indicates that it generalizes outside a single gait. We propose that relative phasing of limb motions can be described by an interaction potential with a symmetric structure. This approach can be extended to the study of interaction of neurodynamic and kinematic variables, providing a system-level model that couples neuronal central pattern generator networks and mechanical models

Biomechanics of predator–prey arms race in lion, zebra, cheetah and impala

The fastest and most manoeuvrable terrestrial animals are found in savannah habitats, where predators chase and capture running prey. Hunt outcome and success rate are critical to survival, so both predator and prey should evolve to be faster and/or more manoeuvrable. Here we compare locomotor characteristics in two pursuit predator–prey pairs, lion–zebra and cheetah–impala, in their natural savannah habitat in Botswana. We show that although cheetahs and impalas were universally more athletic than lions and zebras in terms of speed, acceleration and turning, within each predator–prey pair, the predators had 20% higher muscle fibre power than prey, 37% greater acceleration and 72% greater deceleration capacity than their prey. We simulated hunt dynamics with these data and showed that hunts at lower speeds enable prey to use their maximum manoeuvring capacity and favour prey survival, and that the predator needs to be more athletic than its prey to sustain a viable success rate

Selfish-herd behaviour of sheep under threat

Flocking is a striking example of collective behaviour that is found in insect swarms, fish schools and mammal herds [1]. A major factor in the evolution of flocking behaviour is thought to be predation, whereby larger and/or more cohesive groups are better at detecting predators (as, for example, in the ‘many eyes theory’), and diluting the effects of predators (as in the ‘selfish-herd theory’) than are individuals in smaller and/or dispersed groups [2]. The former theory assumes that information (passively or actively transferred) can be disseminated more effectively in larger/cohesive groups, while the latter assumes that there are spatial benefits to individuals in a large group, since individuals can alter their spatial position relative to their group-mates and any potential predator, thus reducing their predation risk [3]. We used global positioning system (GPS) data to characterise the response of a group of ‘prey’ animals (a flock of sheep) to an approaching ‘predator’ (a herding dog). Analyses of relative sheep movement trajectories showed that sheep exhibit a strong attraction towards the centre of the flock under threat, a pattern that we could re-create using a simple model. These results support the long-standing assertion that individuals can respond to potential danger by moving towards the centre of a fleeing group [2]

Charged boundary states in a Z(3) extended minimal string

In this poster, we study the boundary states of the three-state Potts model coupled to two dimensional gravity, which we call Z(3) extended minimal string. We find that two different boundary states of this model can be identified with a shift of the boundary cosmological constant. We also point out that the boundary states are classified with respect to the symmetry of the theory. This presentation is based on Ref. 1 to appear soon