Many ungulates show a conspicuous nodding motion of the head when walking. Until now, the functional significance of this behaviour remained unclear. Combining in vivo kinematics of quadrupedal mammals with a computer model, we show that the timing of vertical displacements of the head and neck is consistent with minimizing energy expenditure for carrying these body parts in an inverted pendulum walking gait. Varying the timing of head movements in the model resulted in increased metabolic cost estimate for carrying the head and neck of up to 63%. Oscillations of the head-neck unit result in weight force oscillations transmitted to the forelimbs. Advantageous timing increases the load in single support phases, in which redirecting the trajectory of the centre of mass (COM) is thought to be energetically inexpensive. During double support, in which-according to collision mechanics-directional changes of the impulse of the COM are expensive, the observed timing decreases the load. Because the head and neck comprise approximately 10% of body mass, the effect shown here should also affect the animals' overall energy expenditure. This mechanism, working analogously in high-tech backpacks for energy-saving load carriage, is widespread in ungulates, and provides insight into how animals economize locomotion. BackgroundThe majority of larger mammals use the quadruped walking gait as the main form of locomotion for travelling large distances [1][2][3][4][5]. Running gaits are used in bursts and for high-speed locomotion, e.g. for hunting and escaping, so an animal's life depends largely on the effective outputs of this behaviour. Nevertheless, it is the walking gait in which on average the most energy in absolute terms is consumed over an entire day [4,6,7]. As locomotion is an important energy-consuming factor for most mammals [4,[6][7][8], the main selective pressure shaping the walking gait used in slow locomotion should be energy efficiency rather than high performance.Many large mammals, such as horses, exhibit a conspicuous nodding of the head when walking. The head and neck of mammals form a highly mobile cantilever on the trunk that constitutes a substantial part of the animal's whole body mass. To date, biomechanical studies on the locomotion of quadrupedal mammals have focused almost exclusively on movements of the limbs and the trunk. The potentially energy-consuming effects of head movements relative to the trunk remain for the most part unexplored in large mammals, but have been shown to be significant in birds [9]. The few existing studies on head movements that accompany the quadrupedal mammalian walking gait [10][11][12][13][14], confirm that the head's kinematics are decoupled from the movements

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