Limb phase flexibility in walking: a test case in the squirrel monkey (Saimiri sciureus)

Abstract

Background: Previous analyses of factors influencing footfall timings and gait selection in quadrupeds have focused on the implications for energetic cost or gait mechanics separately. Here we present a model for symmetrical walking gaits in quadrupedal mammals that combines both factors, and aims to predict the substrate contexts in which animals will select certain ranges of footfall timings that (1) minimize energetic cost, (2) minimize rolling and pitching moments, or (3) balance the two. We hypothesize that energy recovery will be a priority on all surfaces, and will be the dominant factor determining footfall timings on flat, ground-like surfaces. The ability to resist pitch and roll, however, will play a larger role in determining footfall choice on narrower and more complex branch-like substrates. As a preliminary test of the expectations of the model, we collected sample data on footfall timings in a primate with relatively high flexibility in footfall timings - the squirrel monkey (Saimiri sciureus) - walking on a flat surface, straight pole, and a pole with laterally-projecting branches to simulate simplified ground and branch substrates. We compare limb phase values on these supports to the expectations of the model.

Results: As predicted, walking steps on the flat surface tended towards limb phase values that promote energy exchange. Both pole substrates induced limb phase values predicted to favor reduced pitching and rolling moments.

Conclusions: These data provide novel insight into the ways in which animals may choose to adjust their behavior in response to movement on flat versus complex substrates and the competing selective factors that influence footfall timing in mammals. These data further suggest a pathway for future investigations using this perspective.

Keywords: Arboreality; Biomechanics; Duty factor; Gait; Locomotion; Primates; Speed.

Fig. 1

The phase wheel. Limb phase values from 0 to 100% (where 0% = 100%) can be represented as a circular continuum (a circular representation of the y-axis of a classic Hildebrand diagram). The circle can be segmented into four quadrants, each running between a simultaneous footfall pattern—a pace or a trot (black circle), and an evenly spaced footfall pattern—what Hildebrand [13] called the singlefoot (gray circle). The circle can be divided into halves vertically and horizontally by sequence and couplets respectively in which LS: lateral sequence, DS: diagonal sequence, LC: lateral couplet, DC: diagonal couplet; the shaded gray area is that of the DSLC gaits which appear to be uncommon in nature, see text for details

Fig. 2

The limb phase constraint model. The wheel is split into quadrants as described in Fig. 1. Gray arrows represent increases, black arrows directions of constraints and tradeoffs in locomotor mechanics. a) Energetics. Arrow a represents the incentive to move away from the singlefoot gait to avoid limb interference, while point b indicates an approximation of the predicted value of greatest energetic exchange derived from the models and empirical data of Griffin et al. [14], and Usherwood et al. [17], based on pendular and collisional mechanics respectively (see text for details). Point c represents an extrapolation of this into the diagonal sequence, diagonal couplet (DSDC) footfall pattern. b) Roll. Following Cartmill et al. [5], limb phase values can be split into a ‘zone of minimal bipedality’ (where, in walking, tripods and quadrupods predominate, helping to reduce roll), and two zones dominated by unilateral bipods around the pace (0, 100%) and bilateral bipods around the trot (50%). Bilateral bipedality is thought to generate less roll than unilateral bipedality. The gray arrow represents the continuum of maximal to minimal proportions of unilateral bipods, and minimal to maximal proportions of bilateral bipods contained within strides at a given limb phase value. At the edge and outside of the ‘zone of minimal bipedality’ (open circles) a DSDC gait will contain a greater proportion of bilateral bipods (point b) than the equivalent lateral sequence, lateral couplet (LSLC) gait (point a). c) Pitch. Pitching (both fore and aft) moments are minimized in a zone at the simultaneous gaits, increasing as limb phase values approach those of the singlefoot gaits

Fig. 3

The three substrate types a) ground, b) straight pole, c) side-branched pole

Fig. 4

Limb phase data from walking steps on each substrate type in our sample of Saimiri sciureus. Box plots indicate maximum, minimum, median and quartile values for each substrate. LS: lateral sequence, DS: diagonal sequence, LC: lateral couplet, DC: diagonal couplet. No gaits were observed within the limb phase range of LSDC gaits in these animals, no animal has yet been recorded using a DSLC gait. On the footfall diagrams arrows indicate the direction of weight transfer. The direction of the arrow moving from the right hind foot ‘RH’ indicates sequence (LS or DS), direction of the short arrow indicates couplet type (LC or DC). Arrow length indicates whether the delay between touchdowns is short (less than 25% of a stride) or long (greater than 25% of a stride)