Understanding what speeds of locomotion animals choose during interactions with conspecifics (i.e. social or reproductive behaviour), other species (i.e. predation or predator avoidance), and when moving through an often changing environment is paramount to better understanding their biology. Studies of terrestrial animal locomotion, however, are overwhelmingly conducted under laboratory conditions using treadmills [1]. Treadmill studies have facilitated great insight into the biomechanics of locomotion and using this approach the correlation between kinematic parameters like stride length (lstride), stride frequency (fstride) stance (tstance) and swing (tswing) time with speed (U) has been widely reported in the literature across a range of species. For example; treadmill kinematic data exists on a wide range of mammals including polar bears [2]; horses [3]; otters [4]; deer [5] cats [6], rodents [7, 8] and monkeys [9]. However, perhaps the most comprehensive research into animal locomotion has been conducted in birds [10-17]. The focus on avian biomechanics is likely due to birds evolutionary link to their theropod ancestors, being bipedal, easy to train, experimentally tractable and exibiting a wide range of adaptations. For example, the Svalbard rock ptarmigan (Lagopus muta hyperborea) has been extensively studied for locomotor adaptations related to energy savings upon gait change [18], sexual selection [19], efficient load carriage [20] and ontogeny [21].
Studying the locomotion of wild animals in their natural enviroment can be challenging, many animals are elusive and fieldwork can be protracted, expensive and prone to a wide range of factors that cannot be controlled. Trackways are one way to circumvent these issues and may provide insight into the biology of animals in the absence of the animal themselves. To this end tracks have been used to help understand aspects of extinct fauna such as their diversity, the description of new ichnotaxa, and to gain inference into morphological, behavioural, and ecological aspects of the trackmakers [e.g. 22, 23-26]. Trackways have also provided evidence of key evolutionary events such as the transition of tetrapods from water to land [27, see 28] and the first bipedal hominids [e.g. 29, 30, 31]. Outside of the evolutionary insights, perhaps the most common usage of the information gleaned from trackways relates to gait selection and speed [e.g. 23, 32-35]. An established concept for extracting speed (and gait) from trackways uses the Fr [10, 36], defined as:
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+LlUl2vqJfLVHs755gTgezuI8V/7Mgok0sitw2iQIoKyX+xBh2l0DXFsDois8zkRlJPU7vJXT3cIldjCOzchtQGVsINXTRr/Yp9jc/ybyr5ijJjTKOhGwHvWb/TB3BYv/MID07/vUeHyfc7+vh59Xvv4kfyIHew8Ja/xQtR8EI2Q76Y+R9cor2JobqqEkKxRT9aguxitpVjnJwW7LWP0Urn1NNgC0GmlilOrbYv/hf744/u8enAcGUp8Ek8SXJKMv8jB0je5ClmhLqxBhkZLJGBZlRR+ps5Iwm4lRmBMlfV9GQUCeaSu1ijaI/s3HDepykODfR6GX+oymK//WY+MseblgUyCwjBLBs043GxFvW8KwTPUGDIvcH7W5CRGQOC0IPRFOu3Ldp4JG/iv5i/+J//kMuwYIgsbaElByakSlt+6myoFK+LMIUFJE49NL4i4mvnmhyMzUNl7dzuI2djawXzz4dQPJOo8+pd6sl2qI/WaBp47ydw25I1G5bIxf760pWzYFj8b/kI+42vSz+kPgWwxM8UmQNprfbEgqm8dBRK+VJ0mLLzFevWmgNhDbrSGnVUUV/sT8sEC/Ca1cDLa6SuWALrYHQZh0prTqq+F8P9L8u5D36lGU8ek2a9Xq6Iwm05tKYXay08DtBapfrdeykeTeiI9AwN/iL/mL/4n+1qMobJf7yn8fcMoQ9r2jdJy724lPVtNRLv7EqhBubawUyKCaW7O0LxWdUp0nNKbLiIov+hkH4e+DGUVKxf90edKLoRzSR+xhBMVlGdVrxP7FOtIybtJfFn2xnUSPAAgCiQXLHEaQuDAWdcandTIIbEUwCurOxkxtWCPWQtt5FPwyhtlArx5Ygi/2TeyUrKU7b+e9y8T/4UIk/D6SW/IPElwUUkpM7Eq8qLX2Z/ZLbEe9kczlRoHAMV+9uytMT4IwDNNdJdQ5jRegKyCGqi34zJA1V7E9jwCWK/5khUJX4oy2SHSyZKdJjxjjwylpKKAkGLqENdLOqHCEDlbEBNjeUKuMHyJbTcyjpJI9LQ+2g9KPOTJ7jgMrYonxdXGb8ANkq+t0myRLJ5sX+yRbF//LA0hhz32EsWtwB1anxZ9tZNC3IiBz0WpB6yFF+I1VwOSHjX3IwE+Cg15mQHFX0M0w1gUmizz0ws9mSgZllHfQ6E5Cjiv2L/TvZ/+RSV37p6NUoelmJhi6bZKlkJM3ueg0qQUd+ibc86JyZsshg/ASlOF2JQGkI+YKu6KeVYJxif3EXmsJdRtys+J/Yxe+Sl/iDOZYi/8QNzOJgCDY3qHpddqT3NRV4u0arNURAKyaT6yCYunudrK2QXGgOS5j4ianwGtn1Neuiv9i/+H+vif8++c+pJj2mCSv5ag25xClSs+2IWp7RBtdxWphMHXbBTkHtJHQr+mk7NwjBDAbJW1Kz7Qh2i0Ubxf5unOJ/Jf7cF2KQBOzjc6TV9ghcWtwf4GT0kZBCtMU4cyDjcdGSxFSI96zJIp+oLvrNZGbEYn+xh7pO8b8SfxYezBcEl1P+kUtdOpnnMMpOxe6/AeH0yMvlRr5xSmbIuIRJOXlk8f6a/bSlHDlGedOx6PefGbef20yWe8X+yVWK/6UoEydRT+GRxf0njzb3Ja+VMz/23PiTDcy66HIT5QPXi89otCzb6lsE6YKKvURCtKL24pFL7SjdVjTkdrlFf7QegawU+6v/mEmK/8WYKfFHz8jyirTsIIlFs4v6T8Zn+UcSn1pTGc3F4v2jrIuTXIW02UsTngapygKGK0IWqYzGBrOc4ZQBR1Fd9Ed70GxiI5rKgJyY4Yr9zZ3g0MmN6GPRgOJg6l3AFf8zg2XxlgwXvSyZr2f6Xxe+UQCX4eD8GMcOQPGOYRCqeyXIabGud+kW7Wy5ZsfFTkU/TJEcNFk9QclWBrUaUQhNtLe1zo+5ROdSXNKaoJy7rSJjqEtKnpVrbvIkrqKfFkhWT5CZN1WtRhRaE+1trfNjEtWT7d+HYcXUx5Ke/tAQLELV8VtL0Jb+FI5kaZooI3GCtIgGbwAlutAu+ov9i/+V+GOWeEvzDxZ8SD/MSJbkpOZpJKy28qP/4rAr+tW6uqycn3B3+JxW56m3cnlFv669YaFi/+J/Jf6y9NJd1qjj5c0N9Rz2hQVJt0J7sp2hDPZ7duAQJvA5M4AWfkE4owlX0XZUWtEPO2TGc5NmqGJ/cZ/ifxoxOCpQ4s+DZQnzT3pzI+WjBsSwM+tG0IB6Jf24fvTtf/K01iemIVUjvFtixh2VZl3qijMOuadd9JupcsNkFlXwNYkZd8YXQQPqlfQp81/8vxPiT/9BcThwuhuX+byAvoIDE/IUfZ0Aa75iJi1/BESK5TKp5KA8whgPxCmjUHEo+tvZiQYr9lfL4AiXUbj4H+1Q4s+8YSnyT/r0PGMsKxSpqQlAbEQg42wPOqeck2whwOVJFJjJdMaGmBo6NiLQ4G5tOmfRD9sU+zNLFP8r8RcTRfr0PDIFk4UUAL7OkHY0WAScTflrR5Xi/ZnseEfGk548SyE/glE4XSQa2hM0AN5fRDsPsHmJ/DnSpHj/or/Yv/hfib9m/qm/ssZMIpev9QSjKYk4TzUGtzxRTJyai0Sg9WvKVA4enUuB2EoMkaPoV6MU+4vXFP/jr1oWQDUwI7SLqRRekSpAbCWGHhh/+sqaDBEDltyEtRLHzhJrS1p0tLgWA2xo1soqz2W9IbwUk/poS48u3MWgLfKK/mJ/8xN3EfE74Ir/wQjxWsYDR+oSf/SZJc8/+sqa9PEsBjvKqk9sLEnM/S4mOvKjuLEJaxfLgEkUSVJ8uqIvtwhLnYp+sxJNArDYPzqRAVoV/6Md1Aol/miLJc8/2XYWGpAdce8NF8QpDVGgFS5FhNCWKlPQQjGxNj8qqIWJ6KK/2B+OUfyvxN9bkH90O4ukI8tGuVLmIhbUAsodQuPz6zGnga1tPnN21vbnYsXJKV+KMRb9yY5uKLdxsT88xR3KjOO2SRR1Jz86u/keu7tZi//lm8jMUL0k/nTF555gY1fX0IvTts864FTsYhzuYu1rZWyh1dBFv9qn2N/8JPOumqMkN8o4ErId9Jr9M3UEi/0zg/Ts+E+fpfL7ekhpdotQ/UCcgd7Dwlr/FK2e4lRhIYcgmlilOpbq4u8NxRT9Zr5i/+J/GldylINHDWv9U7TyOdUcqMSfGKRpFbWOY+M9PkXQ5dSYYl9b7pEW85KR3cipFq7UBBSVEGuN7v5BISUX/cX+xf8kiCSc5JBCkYQSf2Ke1oPaKsdrTjGTWcPzT0x8sYP150bjLrmnREpNhDazpEgOnw/tbkJI0GkTqHYQkThEHUa1rkV/sX/xvzyqGB/tfxQyikVbib9oq27yT0x89URjSUiq3IhE5O0ctj45ymC9ePM7gkByf4bPqXerJVpDSpULJCJv57D1yVEGF/26klZz4FjsX/yvl8cfEt9iREKyggSHRohlEk022UUo7iGk1UgLa61XLhmEBrM260hp1VHSseiPF8HF/sX/4tVYS6iU+IsWaLFNhkgfKYjICCBP5emG+Qe05qVpVMO81uDPaCnrJflC9qbXkOHpskVe0V/sX/yvFlV5oyVecmKMqxRfQvam15GvTTz3oPhLHylo8/QirTHUgvovO2XWhLFor1jiKwaOz6hOk5pTZMUXm0V/wyBM/24cJRX71+1BJ4p+RBO5jxEUk2VUpxX/E+tEy7hJe1n8yT0+GkHGD4B+4bZQ90FLGCKXuZXj6WE5jW0rNXSt4RxSRwqAnqZ/3qvzwp133hWmTJkUNtjgnWGPPfcIffv07TXjT84UZ7k2djYipQfOfxm/T3ecZUfEOlLewvmXT8/HRIesrzBWZDwbbwkycgneyVI7nw1FcbG7YfXhhjYiB5quk/wO9wz9c+e9EtZee+3w7W+fF555ZlI4ePToMPoTo2XMagcefcwAe9j4U9BznL1v/sv4Oe9eVqz578ew85SWYGAcifNWkMkqIQUCKr/l4s9tZdWsBx01+HQl5zKcU8PepXaS/kULF4ZFCxeJAVZaqV/o06dPWLxoYVhIHAa78sp9w0orrRy+8pWvhM997nOh/4AB4dmpU8Jvfvs7saNbIo05twUs4kaJVvceatLebv8yfvgBXKK3xt+yzr/885JiQQ8wxhdhq7UlGLkk8bbcpYN2YYu8cjoWtAZrV4vjhHNIaxUgsMla0fVfcNEFYdXVVg3rrb9euOP2O8QsV101Jqy++uphnXXXDrfednvo169fOPXUU8MAJL1X580LN938p3DQQQcJb6ePv7fPfxk/AhVOLOFqMWuB3xnxz+0ssurgydtA0qJUEbX7bq/zZEcsYVEtIpv8pkf51GKdqH/mzJlhjTXWCKeddlo455xzJJnxsOE7NwwHfeSg8L3vfc+GWIX5CxaEUcBxbX3Vlb8Oq6y6inqMZfdOHH8ccBPw+QW+J89/c9ixXcYf89+KPP+4x5df6jIEWXi07IVKII6CxdfW3iYuh7OlmvQDf052sVqTozP1P/jAgzKE3YfvHsc/bdr0MAWXs3uN3ItWEfrixYvl3t5KffuFq8eM0aTnROHozPHXJjWf4F4y/2X84uJ66MD57xMnUBIcE1E2Cn3CoYMDySlSs+0IdotFG3IpIDgmU2eMTEZB5SR00xTgCNIymPqsu9RsO0JVGlUbb7b+u++9G+fTFXbdZVfNcNB+5513yBh2e/9uoOnJnXraqeHJsU+E888/P0yeNCkccMABYcGC+XKuwpGNoZPGj4G+rfYv+ov9lyX+++nNPCYLRiC9GX+s2OLqztCMVLTQRrj7qk8QxDmRDFokiFWIo1r4ZHGgB/CYkA7Rfxe2qGzzrm3kctdP/c477wxbbLlFWHPNNWXM454cHy684KKwaPGisPnmW8gYV111NXnoQYZOHr8MsBfPfxk/HVisEEPXWmYaEFfg+JdLXZ5fHIUNRiusW+z8hQWHuImWCdCRAqgUQQmIg/WNlAYfZZNJ6dJonMaKq/+xRx8Nu73//WoBG9cdd9yBFeAuOuEY1eZbDAsL8KSXd1FxLxV/VZg792Xtg2Mnj19+AH0kjXnVCe3Z81/G39nxL9/j09syMT25O6PWiy9LSYjUNFhNgH5Bp11EAg/SQXvxyNQWpWu0A5tkdZr+V199NUyaMiVsvfVWcVzPP/98eODBB8O++36ox4+fs92b59/HP2/e3PASHnJ56S3+7+NnDMe4BnJ5j3/RosXhBcTVm5F/+smkZYkqTiJGoVe6TFBRtZE5RMXxKC0kNLkCFjQwgkTDauVGQzrgYJfLc+fODV/+8pddbayRY+WSugqL5U2H7373u9lZiFDhFXGAupZSfxSSSSdO9fP0W8e/yiorh6222io8hERH/VzRnXnGV8OGG74z7P/h/dk7jvv1xk9dqpqSUnkt/SZcmN+O8Rf98ApM8U477himz3guzHjuubfU/5a3/Z96ekIYOHBgWHeddaIDrgj+d/nlV4RDDz0k/OQnPwlHHnlkPLflMX77NzeYSFScS9e8VA/6uFhzJksWErIetyIKDUtsnk9UA5lIS7r6rbQSDL52uOiii8JFF38PG39XDquuumpYDXvknnpqXLj4oovDNddco0mQ3WtFEXJ02hvUn49cYVXweuP/xje+Ee6+576w2Wab4f7dsPDgQw+E32Fz8oD+AyAAJ7OE419a/XaWUr0d4+/t+v/whz+Ev/7t8bD//vuri7/F/re87H87bs9sDh8eudde8hutct193/z4v/yKK8ImQzeW++Kvzl/g6iV89tlnpOyF/fGPfyz45Zl/8MuFu09YsmhxwGtiAcdmBIy/3su4M9ri1LWFmOTefPMtiP+uCpeO1lf1LFy4oBo06B3VEYcfUcNbI1b5WeUwT7zWbjasvSzjnzhxYjVz1qy25/JW6KfifFg5XPS/efOPjej8zapuvPHGjrD/Qw89VK27zrrVGWecYb4KT8H/f/nrX6vVVx9UjRp1UOZJuRcpn3bK8SYm60VMnaN7+0+e9Ey1/377I7PyRpf+zX3lFROapOyzz95i57FPjG2Rbsw1naknqd3r13t8epMtZluciGZYOXL14iQH/Noe58TTJpmnh+KPKrzlPRKjUqSXER9/4m8y/l34YECKEvpg79tRRx0TPvbxj9XwlKXqlo/++O/4mhYfsOrAucRBOJD0b7zRxuEdeFtjWca/LPqpV85KT3ap7F/0m/GWcP5ffnlOuP6GG/Ee9lrhX/f8146w/5w5s8OM52eEGbg016J+ve273hVmzXoxjBlzVRy9O/yS+P/S+t/wEXuEG3//+3DySSeFwYMHWf7zU9A4o/5PyLvtAZe7XPW1xt/S6kfio3hXhDrzAcGinaEM9rt+4NCuVqusFn5BOKMPzuVW4f5775N7JjtzT1zWmT0uvOCC8KH99gv8ygn3wo3CK19jxlwtaqdPnxEu/t7F4cMf/nA466z/A252rqdeESeH7vX7ILiwb+pnW7rbaSu8fMdf9OvcdIr9b731tjAP96b/7d8OCP3wnrYUGUIV/vznR/F+9lfDRz/60XDSySeF3/4O72a38b8brr8+/MfnPx8+gjd6Ljj/Ajztnxu++KVTw69/daWIe+GFF8IXTj45/PIXv6z537PTpoWTT/5CGIPXI8VvoHfChAnh3HPPCaNHHxwOPHBUOPkLXwhPPvmkyKHq//l//xP+679+JOdx3333hjPPPCN85cwz5cHMnNmzwxdP+WL46U9/Cj3J/xctWhR+/rOfhRM+f0L4CMZy+pdPD3/605/sXNT/GYenfOmUMH/+/HDFr67AIuXIcOyxx4UrrviV6OZBht5m/Id88pPhkT8/gpj+LhYO75D4z/WzL0066sADAXSF317Dd9w9FpdD/Plysfs6WzxG0IB6JSL8slFIkb+d9ETcZuutYZquCoYQxtmzZ1UbbrhhhclAe3EFJ6g+8IEPVNu+a9sK9/+wZF+7wsRWG6y/QbXeeuvRrNWnP/3pbvVPmzatOuqoo7K/owEfqe2jj6qOFhpwgOUPbbySZiedzjOtqQ1Xr7rVb4IaVSa3Qak3M74I1hVHNDoujf3r+pqtTHoEe7f+r33tLPG5c885V4zlZvnvSy6p8GGKCh+sqIbANyVO8Tv8mc9+tmbUs876mtLgt119+FguVNtv/8+M++rQww4V3r/85S/Cc9CoA1NfKLr33nuF/9BDwYf2I488UuE+ufCug7hYc821BF5p5VWqxx59TPoOHz486tPcIZd4EkNPT3xa5O09cp+ox+ONvDy3/v37x/6nnHIK+HTERx5xpOD32XdfqZGfIt/Z3/yWs0W5dcCtVlVDN94Y/bqqufPm1lmktbgaMmSIxP3iRd7H6nql3DnO2dtI5RNJOcHG1XCNVfvnRx1T7OPRVuvljXbaE+6Ff/wDxtWJ+OEPf1j94Pvfr0aMGCEG/CvuP7DwPsRnPvPpasGCBdWOO71XnGXTzYZVl19xeTVnzpwKT9eqq6++2hU26sXVuHHjqiFIkEyS6w1hva7CaK9L3LqsFed806dPj3LykfuZs14e4xd5OERZUWsCVGd+XH72L/plIt+Q/T/6sY9KoF72s8t0kuD/kydPrvoP6I+EN6Ryv73r7ruqzYdtJr58/333Ce+EpydU/fr1rfDhiuqPf/xjNRv++8Mf/LDq2w8fSkKSOYwJDcUTH65wLM3o/N9z732SIA8BH30G+0lxD/zw6uGHH5Z+eEWyYnKirM9+jgl3cYXtV9UNN9wguCOOPKKaNWumxA07THj6acGP3Huk9OfhhBNOENyHPvSh6rnnn6sWQeZNN/1vtcYag4Hvqu6+525IrSrKYmLsi0SPd9NlLGOuHiN9Bw0aVC3APXr1VErNi46FGEK4XSR9sOrNmSK84047CX3KlCnCTwL7xZhZivwToqSoRoF0aqZF0DVso0e96Zw8J55gy7kZw43X64Ssv/761Yf3378aOXJktdpqq1WD11wTfYzJKrwBgYcdg8QI3/j61+sKGy3rInpfS//bPf6ivzFx1vT5k2ZsRKB9pwzrnK/nf0tjf/4wM+BvueWWqPG8884Tv8Stmdopn3balwV/9tnfFPy5554r7VNO5soJxU700ksvFZmykgP6MVvxjRo1KvIQ4IovT5Aio3F4Ag8CuHpk4vLx4/Jc+h133HHKbXonTtDEt/feewuei4tVVlmlWgVXVs8991yN9+yzvyEy8Jk1wWOLiej5PhYredlxRyQq6J80aVLU76Ec+eIEIfHJii9U8+b6w41syOhw4AEHim1uv/222P31gCgeQLv4xytrMCMLhkTp0gSsN7yN6DyROXZpYEwQsLrqRS19cTAZOGHg2OYDgq5w1z13o1NXOPzwI8I5uE9BtsMOPQz3H/6hfBRpff/+t7+HmTNn4UvGG4TTTj+dp+wkcllR7JLq1/ND1yUcf1cXnwdRR7vCE23QoACfuRZm2tfJmA6Abh/Fvx32f6Pjl4HYgaOyqcnQin2z7J8pElO+Hfr5ZR6OElcL8XTGjh0LuCtc+uNL8eDjBsBqh2fwfjbPEU8xhXcC7sexDB/xL8phA9h22+3QRoMTgq64AgaXEa3StjZIdY5XXnk5/O5314RHH30sTJs2Nbz44ktC5L03nd8uyFNxjD8pFn/ik9BDNCkTn5kYuEF/1113lo/oKq92GYEHEjyH8ePHC0Ik4bDDDjsog2E33nij8OCDD4QX//Ei9rZuKH18KM349/Nj18WBsYUCmXn+GbLBEKC6wtSpzyrdjtQfTRMpin09/5M7s8IKCWpr0doQ6SpYs1AdTsUj1cmKtZNRHuf1U4zv+YKLHPfcc4/0+sBu74/6sURPN41B1Snpko8AEOaNY1wuODrVwqlyc73PPTcj4BdXJLU78PTpGMhF6KaDOfubZ4fVB+JprRQfIGv+tSnozwSnVGkoa8ShT62rn6ei6QBvh/05Ep5W0b/k9scVCc0WXkJgS4EB//Eifqhhyf4DBuL7iwNVGOYe96/xt1XAfTBhffFF7bMa9ntiyr27JibOBJ0QBEmCMjNkkRmymk7KwvgLYdr0aWH47iPC2HFPhHXXXidsOmxYYs/6UwKbzfgjmoQ+yDmUxzclWAZE32eLvflx3ZUExqpQavFXQFGNYmXvnQyuxqCjbadflkDi/9QjJ4narRPCi3jQQ3zfvr7oIG3Z8o8kPlWRFDL7SybmeYgOHLJa0YYDC2mK43TFhnVWBhfFlha8k7G4Cli6S3PnXXZWHei/8867tNV/1513U3oYsceeOC65/pdemhl+dMklKpPaeDJ2xoS0pDOskND5NsnqA5D4qDAmeP4yanIjOi8+/swYOblFW65fZUGCGF1/fd8K++vg/Fj0L6n9B60xWNxi0uRJYVf8x8bGGw+VOT7xxBP0nxdoOAj9gwX3AKWeOPFpqXkg60K80+2F8bcyvt7NMnMWXonL/Q8xwx4SZ+h44YUXhrFPPhFOOPHEcP53v4Pk0C88O+XZsMGGGwgfZZBf9IMfl32KanikrARBx2Wn8D81/qnkoqZ/wlNPy7kO3WRT4ZEGIJL1rDT+9XEN1YAgRfV7S3HagzDxHLOyt/r/pElTyBbWGDRYmJQVvVwg6lx/GlpiiOJFEhY6VuvZW0OXmaJDJHJgUry2JoWpSpyDNOIZGEeqzPRyTtqrKzz22GNy6crl8DprrxuZu9N/5113yWB3YZJEWVL9W2yxRZiLy4FXXn4lvIy/V15B/cpcqQnL38upPXfunIAHIWpYKHmzxh8HLINJxu1u/HGireOSjp/s7exvYrSKgwSv/1LzlMr4W+Z/2LDNxPcmTZ6sBsLxPe/Wy71LL7k0Sy5mWkS123/77beXafzpZT/DDz/+mQIUPOAIp37pdBoeLaQ02B9PMoX28IMPhznwXZaXZs0KJ550IiC+yKn+PxafPGMSHLH7cEl6PDF+Mq1ZBvRfVTqMHevbXNzfrK40FQwZsn7Y4J1D8NbUU+G666+L88+P6f7f//xPnl7Yc889RLz6H5MIzkAaIIq/OCWdhY/fKbRIvZBDcU3/mzSFdg5h2Oab17qoLD3m+ltEo1dTv6z4RJr05IljRYMJiKcFIMJMy9JWTH4knqcgc5efniCBsMCSPjiw5oc52Usm+XX0z5gxI4wb92TYZJOhYX1zCpHlZ4fGG9Wfn6bOHIW8deMv+jMLvM78C+dy9r9MOxzSHHUJ5t+T3DNPPw0R6oWHHPLJ8C3co77p5pvC7rvvjv10B4bV+vcPf374kYAnneG6a6/DlczO4eCPjw5f+uKXwq233Br23Wff8D7gLr/88jBu/Dh1YOqHTP4TBniIEm659ZYwYvhw+bvqqqsCV5ks1Mq/97xnx/Cb3/wWVyinhyfHPxmemfhM+MEPfkAWLTasTYZuFlbqt1K4G1dNRx99NP5tmIXh2+edBx4yoHTZShD6v/rVs8K/f+rf5ZYSntwGbBsL1+K10fsfeCDstNOOWNEeLF181cQz5smIKjWH0EWyINFsxP/5ePd+IuxHMvcs0v4nYbXcr2/f8AHY7+BPfEJk4Mkw/q2aqWHNwYPl1TZq8eykqkxhG/3xJMjS0K/bWbDObVvio5H6Uxbh9cc08tSkbe8a0kURSfiSS/67wiA5Co69Ov7442v80vBOqK+59lrhO/jgg5VvGfWrfD7veY3iRNQORu6iX03RzjbRSAnI7Rdh2DDCiTVBTkTtYCS+jfZ/avx48cVhw4bJifm5TZkyFa9+jcJePt1Xx2gm/MEPfrCaNiNtj3ro4YeqLbfcSmTQ/7fccssKl6zSPvQQ3c7CcT459kns79te+RAj2223XXX77bdXfbAk4hYWFlzFVAcceKDxdMk2mTPPOFP2we69d9qbx3PEP5EgewwZbytjnx8+jFs9M3mS9N1vv/1Enh8u+dGP5BU38vJvwMCBsu81vp4J+x977LFCu+/++72b1KMPHi34v/3t7xHvNiKC8D/9k43L4t/1sD7mmGO0Hxivu+46kcUx1soyzj/vWemZ5GdmbiaoGj6pVnQ3xMTWxmOVWOvJRgvCUDV8EqzoboiJrSE3EWo92WhBLLv+G7F36tvnfVv2OCXNCrWoa0Esu37RVJObzqKGZqMFUfSLSWp2SfZ79w47cA2B/XMPJaRB3BKCp7zVeOwfnTd3XgudCIqdOnWqbCLGRrnq3nuwPw/ydDuLKnX93IDPPWxeXsY7rQsWLjQpisVDk+rxxx/HXtf5guCeuAXzATfOf/bs2dU4bP6fhdrLy7PnVPPnU56XpH/as9NkH2zcWmYs5OC79HgVzjvFmuPn/lopDf3OVEOz0YJQFN/Tp531ZQbv7ey1TomYQ92waOITRudo9yucaKrS2vUqqtNk3J7okjjQuian1LEqNNE6ST83lQ7Gpk/up/LiI+kN45cxxwHXZ7LTx3/xxRdLosI/NsWh1MrS+P+9994jVz+HHXpIizwP8+T7prFexXNYGv25juZ4clo6B6h7k/W/isTNfbuD1ngHNl3zQyBU6H/Lpt8v0+XKWa7V/Qqa0yqrXB7tAlquk3nBzL9mJR0ULWRbwxqrLphJNj7g/VpdseQnzbAdpP9l3Jye9uxU2Ykg2xps/Ftvs43cmOY9nwXzF4bp+MeIeuL4dYp71/wffcwxYa011wpXXnmlRcOyj5/uH+9gdZD/v1nz/8c//h4PP2eG44//tG4tW475Jz7c0JPHkQaXKk4BmkAKg3IpjzLK/KR0Zd2VptwKm3egymSIXG3Ho7HrLV7HAimgtlcU/bNnzQnHHn9cuPnmm+UjpNyw+Sz2Vb2Em7Xcp/XwQw+FhdhEyn9pbdNhm4Qpk6eEo/BBxR/jw4oyhg4fPyeF08Xi86rTp0edLYV92p2v08c/cED/cO1112LD7zMyFB/X0o5/06FDwxfx0OP9u+oXijrB/9/s+d92m23DZZddhm8e7gdV5kd0NgGTpZfG/7Dnlo/KIAtV2lxIjJdMoaDydg4bf44y2CdRmzgyc1sOi1o6UP9ee30QO+Wnh9vwtY7Baw4O3DbDD5HyqxMsF15wYfgCvpTxnp3eE6769VXha1//Ouorw8yXZvWI8ZsH+hRq3Yvmv4w/n2xzgxxl8IoY/7jU5dkhDm0firQUZSNhhuKpe8GvvOZKINIvvlPzhCYrU+HSLCdJmwyW9FSmHjtN//XYnvC/N92EL0dfLEmP4+enhXbBqz5e+DreAKwMmPSG4hd9FjZSb7TRRj1i/DrG3jv/Zfy0QOfOfx/f3+KZTYYSE5OnO1vIW8LzJKVDVxfgMU+PTZokWJHrMi3+PTsaulP0j/nN1WHttdbGZs4RHGrAl5gDnrzJvixB4HAvXsfjt8yY9HBTNtx6221ht912c7Lm/w4dvw/CXEWavWn+y/jVAp06/9x0bSPwhOQIJqYEkyn+05LWhcnSewnKg5i8inBOdlZY6ixEXIUuB8HjiBVbPxPdJnhNKchHC0L4zne+I+f+3p3eK+OcjCQ4GZtN99hjD2k//vcnwvMvPB92/5fhaHf++GVQmGSdZ2mlOZYREpdRe9j8y4jL+PMZ7qj5l6e66p5IOM2J9GEJgzzblfnOHVrTlElIOUvTlzs7e3liE556Su1E/fyHw/mViunPTpevyP7yF7/AZe1q4V34R8ZZuNrjAvl973uftB9/4u8wWxWGbjo0HHfc8XhahS9oWOnE8fu599b5L+NXC3Tq/Ms9vpivkJx8IHpVay2pIhdGbNf2QMWgBVbhVGeLt9RH7OWcbLhOsjiMFZGwrJj6uTVl9OhPhtUG9peXwcfjhe499twzvPd9O8v7kjz1++67X1474j9DybL11tsEfOMsjPzgyLDddtvihes1BN+J4+/t81/G3/nx38XtgJ7SGLDtYI3QnBpjNnUQlPFIlfEDpBI1lyUz05VxSeJc0fVjI6Ws4vCV23D4YYeHufPm4b3HBQGfzw7f/NY3wwkn4CXybsY/G6u8PnhfcuCAAXGsnTZ+m3mt8pPvJfNfxp9ZoIPnX75PqJFqOYyDQfErU20JRoLV23KXCllK2K1PzIKSvTyFUZhTEs4hrVWAwCu4fm6o5P29qfjgI7+FNmHihPDxj308bITEd/TRx6h5ZCA+wjT+d2CVx6TH4lStO2f8cvI49Nb5L+NXC3T8/MsrIAhDSXSIQoagLWQFIkJXazblvAZt+QSL0VipAEEI2OR3uhKNr7P0X3vd9eHnP/9ZeB4fbRyMr0a8e4d3h08d/6mw1lpr9Yrx9/b5L+P3n20J3/rB4xvYFTn+4wZmTXC8x9bNoLIBWbZKy5YardZoYa1bKWuhWyX3+Ir+zCoJbJo1b+dw/stjvWvkJLEOganYv/h/b4l/7OMz/0e+0UE7Anh9wqAMoDtFarYdUctV2pClsPSkMzmj6bJKsE5Ct6KftnODEMxgkLwlNduOYLdYtFHs78Yp/lfiz30hBgk/nupIq+1Rh7R4Setk9JGQQrTFOHMg43HRksRUiPesySKfXl57Z6uLfjGhmq7Yv/ifuIMcSvzBDMsp/8ilLoPMc1gyMyGuG5Ti9MjL5UbtXl+kaIKzm4bEsnh/IwrOe3gtyNqh6C/2L/7HkPD4ibFS4m+Z8o9sYNZFn6eoPPPoxacbPc+2+hZHuqBiL5EQZyY5LJfaUbqt6Mjtcov+aL3c+ICL/ekj7ifF/1LMlPijV2R5RVp2EIdRr+GxXf6RxKeepYzgk8IfFJa6aMVZipMGe2nC0yBVWcAkAeAwGjmZ5aRDpk/ArE2ZwkNWA0SbHxKu6Ddz4gclmRH2SQYs9i/+p75R4i/mH9vAzESit0Ab6UfwKd3wF0dTjUNOi7WKik0Hmmhv55od5300pNMZMQkW/cX++nPoP6bJWwRqdaK2aGcr/pci322SLFrH9KT4kw3M/u5GevrDAbNokPmiK6WgutM5N3vEK1k20NFp0tcboIgutEWDdSr63UBeF/vLj5+Zo/ifBJVET7KFWMgJJf5yw7xW/sEba3ArepYFmdRqR8dGq0bAcz+7ol+ta3e9usNTqNO8VkX1VlQu/Lr2A0fRX+xf/C+FUIylPF4Idx9NiVbnqbdyeZ0f//KRAo0cDh8exNFaoT+xnaEM9hUfOIQJfM4MoIVfEM5owlW0HZVW9MMOmfHcpBmq2F/cp/ifRgyOCpT482BZwvyT3txI+agBMezMuhE0oF5JP64fffuf7WhpyPNmFOaIbuqML4IG1CvpX/QX+xf/09/PEn9ICf7D0MgufZg7uIxId+MaHDGDgglChN9wfMWJBdkzdvKtfaJPDokWmUSKnpFQcSj629lJrGs2B73Yv/ifBJFeVZX405hZmvzTxX+mkgHVLBQZ0bERgSZ7S9s5JSfKFhZcnkSBYI8MuaIkxsmCiY0IJMZuIOcs+mGgYn/4W/G/En8pWaRPzyNTMFlIAVC7UxcTVgSczTrklUrx/jQ278i40eM/VIRgFE4XiYb2hCwA3l8kOw+weYn8OdKkeP+iv9i/+F+Jv2b+qb+yxkwil6/1BKMpiThPNQa3PFFNnJqLRKD1a8pUDh6dS4HYSgyRo+hXoxT7i9cU/+OvWhZANTAjtIupFF6RKkBsJYYeGH/6ypoMEQOW3IS1EsfOEmtLWnS0uBYDbGjWympXzd4vY4goEZwLdzHgEHlFf7G/OYk7jfgdcMX/YIR4LeOBI7WaqsSfpBD3m9fIP/rKmuQhz2Kwo6z6xMaS0dzvohzyo7ixCWsXy4BJFElSfLr8nFpuLEYlRX+xv3kJ/QhgdI2GXxX/Y2ipFUr80RZLnn+y7Sw0IDvi3hsuiBs+RqlCU0JbqkxBC8XE2vyonBYmEY4DCEV/sX/xvxJ/minqR14KSe5om0DeUP7R7Swi3oTlTqc/JvKjIqDcITQ+vx4Dwdnano6zs7Y/55ckF4dmjEV/cno3lNu42N+cCFXxP40c941kGcX7scSfWMLukujairaSV9Y8wMxImsr04rTtsw50ZBfjEMHdHpSxhVxDF/1qn2J/85PMu2qOktwo40jIdtBr9s/UESz2zwzSs+M/fZbK7+shpfn9N/EDOdB7WFjrn6LVU5wqLOQQRBOrVMdSXdy0TDFFv5mv2L/4n8aVHOXgUcNa/xStfE41ByrxJwZpWkWt49h4j08RdDk1ptjXlnukxbxkZDdyqoUrNQFFJcRao7t/0EbJRX+xf/E/CSIJJzmkUCShxJ+Yp/WgtsrxmlPMZNbw/BMTX+xg/bnRuEvuKZFSE6HNLCmSw+dDu5sQEnTaBKodRCQOUYdRrWvRX+xf/C+PKsZH+x+FjGLRVuIv2qqb/BMTXz3RWBKSKjciEXk7h61PjjJYL978jiCQvNPoc+rdaonWkFLlAonI2zlsfXKUwUW/rqTVHDgW+xf/6+Xxh8S3GJGQrCDBoRFimUSTTXYRinsIaTXSwlrrlUsGocGszTpSWnWUdCz640VwsX/xv3g11hIqJf6iBVpskyHSRwoiMgLIU3m6Yf4BrXlpGtUwrzX4M1rKekm+kL3pNWR4umyRV/QX+xf/q0VV3miJl5wY4yrFl5C96XXkaxPPPSj+0kcK2jy9SGsMtaD+y06ZNWEs2iuWuMXe8RnVaVJziqz4YrPobxiE6d+No6Ri/7o96ETRj2gi9zGCYrKM6rTif2KdaBk3aS+LP9nOokaABQBEg+SOI0iu5rwkLsVpO/8xFrw7G7u5YYVQD2nrXfTDEMmyNJq1pCr2L/5Hn2BJXlLiL9njjeQfJL4soJCc3JBc1cZLTktWxGjRBxVk1inwXkqN06Loeh9pRQ60XCfAor/Y3/yj+B8NYXElVR5MJf48PS1t/sEra8mgCQYuod384pJ+EDK0ZmyA7TSkUlj4AbLl9BxKOvMUWPTnhlUbZ/YUW+IAVLG/eJgc3L/04iKzF0C2nJ5Dxf+SByVb9Pz4s+0s6hbiPQ56nfzKnEcRfiNV2NrwZt2WAMwEOOh11jtHFf10Uw1lCfTkv5nFlhTMLOug15mIHFXsX+zfyf4nl7qS6enVKHpbDg392ZSfSiPp6kKvQSToyC/xlgedM1MWGYyfoBSnKxEoDSFlRktkgVj0R3u5ydQ02vK7pMX+MFPxP/UVHt1ZHCzxl2yT2SduYKbB/HWOOqe1aNCmg3m7Rqs1pHMrpo0GMBX9uopoYx11aLc3GXKj5nCNoJJq5LbCVV6xf7G//6C2uEnTifJ2DneI//WR8+QoEVQ6aI7CSv5rAbpTpGbbEXlAWnbkOk4LnclhF+wU1E4q+ov9xXfcIegbGVz8L4aKWKXEX3KPpcg/2MfnzmW1bUFR42beBj8U+XDGqMcBF6H5TI6SRFWI90xJzvj03pR3trroF+uo6Yr9Y7S7FxX/K/Fn+SMawlOI48VXPHaYpCxRZXxyqcu2kbKuBO3+W0aPvPw1zjfOiIdmCjSrRb9N8qOE2CNhGuqLflhALef2i7Yq9i/+V+IvSxgxMnSB9Tr5RzYw66KPHZtFL3496Li2dFjfIkgXtOwpEqL+FLC81I3SbUVHbpdV9EfrNSag2J8+4n5S/C/FTIk/ekWWV6RlB3EY9Roe2+Wf/w9jmOnpPem4NAAAAABJRU5ErkJggg==)
Where U is speed, g is the acceleration due to gravity and h is the functional hip height. Fr is a dimensionless number that by equalising the centripetal to gravitational force ratio allows the locomotion of terrestrial animals to be compared equally across all sizes. Geometrically similar animals of different sizes will move in a dynamically similar way at any given Fr. In practice, not all animals are geometrically similar, but it was argued that despite this, the ratio of stride length (lstride) to h gave a highly predictable relationship across a broad size range of mammals and birds [10, 11]. By using this empirically derived relationship with the Fr concept, it was further suggested [10] that the forward U of a terrestrial animal can be calculated from:
![](data:image/png;base64,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)
Fr may also allow the U at which gait transition occurs (e.g. walking to running) to be estimated [36]. Alexander (10) and Thulborn (37) suggest that gaits will shift from walking to a bouncing gait (e.g. trotting) when lstride/h reaches 2.0, and the transition from trotting to running (or galloping) at an lstride/h of 2.9. Equation 2 is therefore probably applicable to walking animals only [38]. For highspeed gaits where lstride/h is greater than 2.9 the following is advocated as being more appropriate for estimating U [23, 38]:
![](data:image/png;base64,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For trotting U is better estimated by the mean of predictions derived from equations 2 & 3 [23]. Irrespective of the equation used, the reliability of estimates of U may be compromised if there is lack of certainty on h –in particular in extinct animals where h is not available [39-42]– and the use of lstride boundaries that may not be compatible with bipedal gaits [39]. Trackways are therefore restricted in the information that they can provide as much of the information needed for accurate locomotion analysis, such as leg morphology and stride frequency, depends on data from the animal itself. It is worth remembering that anecdotally the vast majority of extant animal movement does not leave evidential tracks. Aside from seeing occasional footprints in the sand or on muddy ground, overwhelmingly animals are not moving over substrates where their feet will leave lasting impressions. An exception to this is locomotion over snow which will, in the vast majority of cases, leave tracks. Regions of the world, like the Arctic are seasonally covered in snow which provides an opportunity to examine trackways and the kinematics of locomotion in context of the real-world influence of variations in substrate. Svalbard rock ptarmigan are endemic to the high Arctic Archipelago of Svalbard meaning they spend approximately half a year locomoting over snow and they are also one of the few species in which a comprehensive laboratory treadmill dataset exists which can be used for comparison. Recently one of the first comparisons of the kinematics of locomotion under field and laboratory treadmill conditions was undertaken in the Svalbard rock ptarmigan [1]. The kinematics of locomotion were conserved for ptarmigan moving in the field and during laboratory treadmills studies but only for walking and aerial running gaits. Important differences were found when the birds were grounded running, with the birds taking faster and shorter steps in the field when compared to the movement on the treadmill. These kinematic differences were attributed to differing substrate when moving over snow compared to a treadmill belt [1]. Our ptarmigan studies also highlighted the importance of understanding the influence substrate can have on locomotion [1]. Studies in extant animals have demonstrated that substrate can influence the neuromuscular control of locomotion to maintain stability [43-45] and can affect the energetic cost [46, 47] and the speed [48] of locomotion. Furthermore, despite the obvious links between trackways and the ground, substrate is rarely considered when inferences into speed and gait are made from tracks. Not taking any potential effect of substrates into account is surprising as information derived from tracks depends more on the substrate properties than the anatomy of the foot itself [49]. When substrate is considered it is most often examined in terms of the formation of the physical tracks themselves [see 49]. Consideration of substrates and tracks has also been used to demonstrate that in extant species foot morphology can vary with stance and gait [50, 51] and highlighted the interaction of the feet with different sedimentary substrates [52, 53].
The principle objective of our study was to develop a species-specific model to examine gait and speed predictions directly from lstride of trackways of the Svalbard rock ptarmigan. The accuracy of these trackway derived speed predictions and gait transitions was determined by ground truthing data extracted from videos of the birds taken as the tracks were being made. Finally, a comparison between the predictions obtained using our ptarmigan species-specific model and existing Fr based models [10, 23, 38] were made to elucidate the accuracy of each approach. Further, we discuss how reliable information extracted from trackways is for examining the predicted speed of locomotion in both extant and extinct animals.