Support polygons and symmetrical gaits in mammals

1. What they did

When a four-legged mammal walks or trots, two numbers describe its gait: the duty factor (how much of each stride a foot spends on the ground) and the diagonality (how far behind the hind foot the forefoot on the same side comes down). The authors built a mathematical model, the “support-polygon model”, to work out which footfall timing keeps an animal on three or four feet for as much of the stride as possible, and so least often balanced on only two. They then tested the model against real animals.

• The model. They treated a four-legged animal as two people walking in a horse costume, and calculated how much of each stride the animal stands on two feet on the same side or two diagonally opposite feet, for any combination of fore and hind duty factors and diagonality.
• The animals. They filmed 51 captive and farm animals of 45 mammal species, from mouse lemurs and opossums to elephants, rhinoceros, giraffes and tigers. Horses, a llama and one dog were led or lunged on a slack line; all the others moved under their own control, on the ground or, for many primates and the woolly opossum, on horizontal poles.
• The measurements. For each stride, they noted the frame where every foot touched down and lifted off, and kept 346 symmetrical gait cycles. For one long-legged dog (a Great Pyrenees) they recorded 41 symmetrical cycles at different speeds, to see how much one individual varies.

2. What they found

The model’s predictions

• For a lateral-sequence walk (hind foot followed by the forefoot on the same side, as in most mammals), the best timing depends only on the forefoot’s duty factor.
• For a diagonal-sequence walk (hind foot followed by the opposite forefoot, as in most primates), the best timing depends only on the hind foot’s duty factor.
• At the run, animals should choose the trot over the pace.

The animals

• Fore and hind duty factors often differed: the hind duty factor, as a percentage of the fore, was on average 7.2 points away from equal, and five points or more away in 55% of the cycles. Lateral-sequence walks came closest to equal.
• Primates’ hind feet often stayed down longer than their forefeet, and this was linked to more diagonal walks (P < 0.001). But it was not the whole explanation: primate walks with equal fore and hind duty factors still had a diagonality above 50.
• Only 17 of the 346 cycles were true runs, with all four feet off the ground at times, and they clustered around the trot, as predicted.
• 26 cycles were “half-runs”: one pair of legs was running very slowly while the other pair was walking very fast. Most were close to a trot.
• Primate diagonal-sequence walks fitted the predicted line well. Most lateral-sequence walks did not: they fell below it, especially at duty factors of 60 to 70.

A revised model: three rules

The authors linked the misfit to long-legged animals avoiding hitting their front legs with their hind legs. Earlier work had shown that long-legged dogs, camels, giraffes and others pace at the run and walk with the two feet on one side landing close together (lateral couplets). Adding this to the model gave three rules:

• “Monkey rule” (diagonal-sequence, diagonal-couplets walk): diagonality equals the hind duty factor at the walk; trot at the run.
• “Horse rule” (lateral-sequence, diagonal-couplets walk): diagonality equals 100 minus the fore duty factor at the walk; trot at the run.
• “Camel rule” (lateral-sequence, lateral-couplets walk): diagonality equals the hind duty factor minus 50 at the walk; pace at the run.

The single Great Pyrenees used both the horse rule and the camel rule: of its fast walks, two were near-paces and the rest near-trots. One dog could choose to walk “like a horse or like a camel”.

The only diagonal-sequence walks they recorded in a non-primate came from the woolly opossum, an animal that lives in trees, and they matched the primate data. Its more ground-living relative, the gray short-tailed opossum, used lateral-sequence walks or walking trots. The common marmoset, which climbs with claws on large branches and trunks, had largely gone back to lateral-sequence walks.

3. What they concluded

• Mammal walking gaits come close to the theoretical best for support. Once you know which of three diagonality ranges a walk falls into (above 50, below 25, or between), you can predict its diagonality from its duty factors.
• Animals presumably follow these rules by timing certain foot events together, for example lifting each hind foot as the forefoot on the same side touches down (the monkey rule). An animal that switches rules must have nerve control that can use either timing.
• An individual having two rules suggests one way a new gait could evolve: a new rule is added, and the old one later fades.
• Leg length alone does not decide which lateral-sequence rule an animal uses, since one dog switched between them, and some short-legged animals such as raccoons and coatimundis use only lateral-couplets gaits.
• Their working hypothesis is that primates walk with a diagonal sequence so that a grasping hind foot is forward, under the body, on a tested branch at the moment the opposite forefoot lands on an untested one. If the new support breaks or bends, the animal can pull back or regain its balance. They see diagonal-sequence walks as part of primates’ tree-living, grasping-foot adaptations, reached independently by tree-living marsupials.
• Their data are a preliminary sample, and do not cover some unusual gaits reported for elephants and muntjacs.

6. Other technologies, skills or innovations

• Video at 60 fields per second with industrial-quality Panasonic camcorders or cameras.
• Frame-by-frame gait analysis with a Motus 2000 system (Peak Performance Technologies), with touchdown and liftoff times entered in a spreadsheet.
• A “modified Hildebrand diagram” that plots diagonality against the duty factor that matters for each gait type (fore or hind), and a “duty-factor index” comparing hind and fore duty factors.