An exploratory clustering approach for extracting stride parameters from tracking collars on free ranging wild animals.

First posted online on 3 November 2016 as 10.1242/jeb.146035 J Exp Biol Advance Access Online the most Articles. recent version First at posted http://jeb.biologists.org/lookup/doi/10.1242/jeb.146035 online on 3 November 2016 as doi:10.1242/jeb.146035 Access the most recent version at http://jeb.biologists.org/lookup/doi/10.1242/jeb.146035 An exploratory clustering approach for extracting stride parameters from tracking collars on free ranging wild animals. Authors: Oliver P. Dewhirst 1, Kyle Roskilly 1, Tatjana Y. Hubel 1, Neil R. Jordan 2,3,4, Krystyna A. Golabek 2, J.Weldon McNutt 2 and Alan M. Wilson 1 1 Structure and Motion Laboratory, Royal Veterinary College, University of London, Hatfield, AL9 7TA, UK. 2 Botswana Predator Conservation Trust, Maun, Botswana. 3 Centre for Ecosystem Science, School of Biological, Earth and Environmental Sciences, University of New South Wales, Sydney, NSW 2052, Australia. 4 Taronga Conservation Society Australia, Applied Eco-Logic Group, Taronga Western Plains Zoo, Obley Road, Dubbo NSW 2830, Australia. Corresponding Author: Oliver P. Dewhirst, odewhirst@rvc.ac.uk Abstract Changes in stride frequency and length with speed are key parameters in animal locomotion research. They are commonly measured in a laboratory on a treadmill or by filming trained captive animals. Here we show that a clustering approach can be used to extract these variables from data collected by a tracking collar containing a GPS module and tri-axis accelerometers and gyroscopes. The method enables stride parameters to be measured during free ranging locomotion in natural habitats. As it does not require labelled data it is particularly suitable for use with difficult to observe animals. The method was tested on large data sets collected from collars on free ranging lions and African wild dogs and validated using a domestic dog. 2016. Published by The Company of Biologists Ltd

Introduction Changes in stride frequency and length with speed are key parameters in human locomotion research (Maculewicz et al., 2016; Muro-de-la-Herran et al., 2014) and are routinely used in quadruped locomotion research (Heglund and Taylor, 1988; Jayne and Irschick, 2000; Smith et al., 2015; Sue et al., 2011; Witte et al., 2006). Measurement of these parameters enables the locomotor strategy used by an animal to attain a particular speed to be determined. They are commonly measured in laboratory based experiments using a treadmill or by filming trained captive animals (Hudson et al., 2012; Williams et al., 2014). These approaches provide estimates for movement over uniform terrain with a constant velocity (steady locomotion) (Bertram, 2016). They are, however, not ideal for species that are difficult to handle or observe (e.g. lions or African wild dogs). Captive animals may not show the same locomotor characteristics as wild animals (Hudson et al., 2012; Williams et al., 2014) and treadmill locomotion can modify gait patterns (Blaszczyk and Loeb, 1993). These limitations have been overcome by the development of animal tracking collars combining Global Positioning System (GPS) and inertial measurement units (IMUs) (accelerometers/gyroscopes) which can be sampled at high data rates (> 5 Hz). The detailed data these produce provide the potential to quantify how stride frequency and length vary with speed under natural conditions. In a typical deployment of several months these collars capture large quantities of data (tens of thousands of strides) so to achieve realistic workloads an automated analysis system is required. Such a system needs to be able to remove periods of non-steady locomotion and segment the data into strides. Previous studies trained animals to move at steady speeds and removed non-steady locomotion by using a threshold based on speed (Maes et al., 2008) and velocity heading (Daley et al., in press). Stride segmentation has been carried out using supervised machine learning (Mannini and Sabatini, 2012; Pfau et al., 2008). This method requires data to be collected while the animal is being viewed (labelled data) and this is challenging for difficult to observe wild species. Clustering (unsupervised machine learning) is an exploratory approach that aims to find groups in data. It is ideally suited for use with the data collected from collars on difficult to observe animals as it does not require labelled data. This approach has previously been applied to characterise the behaviours of birds (Sakamoto et al., 2009) and humans (Trabelsi et al., 2013). To our knowledge it has not been applied to the problem of stride segmentation in quadrupeds.

We developed an algorithm to estimate stride frequency and length during steady locomotion using a clustering approach. It was tested on large data sets collected from collars on African wild dogs (3290 strides) and lions (10480 strides) and validated using a domestic dog. Materials and Methods Data collection Data were collected from two female adult lions, a male and a female African wild dog and a lurcher using custom built Royal Veterinary College (RVC) GPS-enabled wildlife collars (Wilson et al., 2013) (Table S1). The lions and wild dogs are part of an ongoing study by the RVC and Botswana Predator Conservation Trust (BPCT) in Botswana (RVC CRERB 2013 1233 and a permit from the Botswana Ministry of Environment Wildlife and Tourism). MATLAB 2015a (Mathworks, Natick, USA) was used for data analysis. The collars contained a GPS module and an IMU (Hubel et al., 2016). The current study uses data from the highest resolution operating state (5 Hz GPS, 300 Hz accelerometer and 100 Hz gyroscope). The precision of the velocity and position data was improved by fusing GPS/IMU data with a Kalman filter (Wilson et al., 2013). Stride parameters were estimated from the Kalman filtered GPS measurements and data from the y/z-axis accelerometers (Fig. 1I). Typical measurements from a wild dog are shown in Fig. 1A to C. Pre-processing The reaction to gravity measured by the accelerometers was removed using a 3 rd order zerophase (Oppenheim and Schafer, 2013) high-pass Butterworth filter (0.5 Hz cut off frequency). The remaining signal was segmented using a sliding window approach (Fig. 1B,C). Windows (4 s long) were overlapped by 0.2 s (Fig. 1C) until steady locomotion was detected. Windows containing steady locomotion were not overlapped (Fig. 1C). Steady locomotion We assumed that there would be little variation in the phase difference between the signals from the y/z-axis accelerometers (over 4 s) during steady locomotion. The Phase Locking Value (PLV) was used to provide a measure of phase synchronisation between the two signals (Aydore et al., 2013). NN PPPPPP tt = 1 exp(jj) Θ(tt, nn) NN ii=ττ PLV ranges from 0 to 1, with 1 representing the case where the relative phase (RP) between signals is identical and 0 when there is no phase synchrony. RP, Θ(tt, nn), is

Θ(tt, nn) = φφ YY (tt, nn) φφ ZZ (tt, nn) where φφ YY aaaaaa φφ ZZ are the instantaneous phases (IP) of the windows of y and z-axis accelerometer signals respectively. IP was calculated using the Hilbert transform (Bracewell, 1999); as it is only meaningful for a narrow band signal the windows of accelerometer signals were filtered (zero-phase, 5 th order Butterworth band-pass filter; passband +/- 0.3 Hz the stride frequency). Transients introduced by the Hilbert transform were removed by extracting the middle 3.6 s of the windowed signal (Fig. 1D to F). Examples of band pass filtered accelerometer signals from a steady slow gallop, the transition to trot and steady trot are shown in Fig. 1Di to iii respectively. Fig. 1E and F shows the IPs and RPs of these signals. The phase synchronisation of the accelerometer signals during steady transverse gallop and trot can clearly be seen in Fig. 1D,E,Fi and D,E,Fiii (PLV for both gaits is 0.984). The lack of synchronisation that occurs during the gait transition can be seen in Fig. 1D,E,Fii (PLV = 0.521). A PLV threshold of 0.98 resulted in a balance between distinct clusters and retaining sufficient data (Fig. 1G and H). The total number of strides were reduced by 83 % for the lurcher, by 44 and 47 % for the two wild dogs and by 20 and 32 % for the two lions. Fig. S1 and Table S6 allows comparison between the PLV method and the speed threshold method used in previous studies (Maes et al., 2008; Schmidt and Biknevicius, 2014). Window stride frequency estimation The stride frequency for a window of data was estimated from the z-axis accelerometer signal using an autocorrelation approach. The biased autocorrelation estimate ( zzzz ) for a finite length (N) sampled signal is given by: NN zzzz = 1 zz(ii ττ)zz(ii) NN ii=ττ where zz is the window of data from the z-axis accelerometer and ττ is the lag (samples). For a cyclic signal, such as that measured during locomotion (Fig. 1C), the autocorrelation coefficients peak at lags equivalent to the periodicity of the signal. The lag of the first positive peak in the autocorrelation coefficients was found to represent the stride period (TT ss ) for galloping gaits and half the stride period for trotting and walking. Clustering To identify gait, clustering was performed on three features derived from the windowed accelerometer signals; features were selected using domain knowledge. The first two features

were the standard deviation (STD) of the windowed y and z-axis accelerometer signals, the third was the autocorrelation estimate of the stride frequency (Fig. 1G,H). Features were normalised to have zero mean and unit STD before they were clustered using the k-means algorithm. The number of clusters was determined using the Davis-Bouldin criterion (Davies and Bouldin, 1979) and human inspection. Stride parameters Once the windows of data had been assigned a gait it was possible to extract stride segments using the MATLAB peak find method. This enabled the individual stride frequency, length (GPS position data) and speed to be estimated. The vertical accelerations in each stride were registered using Dynamic time warping (DTW) (Ramsay and Silverman, 2005) so they were independent of speed; their magnitude was normalised to be between -1/1. Statistical Parametric Mapping (SPM) and Random Field Theory (RFT) were used to test for differences between registered stride traces (Pataky et al., 2013). Validation Validation was carried out by comparing stride parameter estimates from collar data measured on a male lurcher (moving freely off the lead) with those from video footage of the animal moving along a line at a range of speeds and gaits on a level playing field (RVC repository). Two video cameras were positioned parallel to the line (Hero3, GoPro Inc., San Mateo, California) (120 frames/s, 720x1280 pixels). Footage was calibrated using a 0.8 m long stick placed on the line in front of each camera. To allow gait identification and calculation of stride parameters we recorded the foot on/off events. Two symmetrical (lateral walking and trotting) and two asymmetrical (transverse and rotary gallop) gaits were identified using anteroposterior sequence (APS) analysis (Abourachid, 2003; Maes et al., 2008). Lines were fitted to the stride frequency vs. speed data and the stride length vs. speed data for each method and gait using the least squares algorithm (Heglund and Taylor, 1988; Hudson et al., 2012; Wilson et al., 2013). The slopes of the linear regressions estimated from collar and video data were compared using analysis of covariance (AOC). Further validation was carried out by fitting lines to the stride speed estimates calculated from the stride length and frequency values vs. the stride speed estimate from the Kalman filtered GPS speed data. We assumed accurate parameter estimates would result in a line with a slope not significantly different to one.

Results The variation of stride frequency and length with stride speed (collar data), for a lurcher, two wild dogs and two lions is shown in Fig. 2A to F. Stride frequency increased linearly with speed for the lurcher and lions within all gaits and for wild dogs during trotting and galloping but not during walking (Fig. 2A to C) (Table S2). The rate of change of stride frequency decreased as the animal moved faster (Fig. 2A to C) (Table S2). During galloping stride frequency increased gradually with speed (Fig. 2A to C) (Table S2). Our results are consistent with previous work (Heglund and Taylor, 1988; Maes et al., 2008). The lions used a lower stride frequency at a given speed than the smaller lurcher and wild dogs (Table S1). Stride length increased linearly with increasing speed (Fig. 2D to F) (Table S2). This relationship has been found in other studies (Hudson et al., 2012; Maes et al., 2008). Our method was validated against estimates from video data from the lurcher (Fig. 2G to N). The slopes and intercepts of the linear regressions estimated from both methods were compared using AOC; no significant differences in slope (p < 0.05) were found (Table S3); the intercepts were significantly different (p < 0.05) (note large data variability for stride frequency, Fig. 2G to J, and low r 2 value, Table S3). While the range of speeds for each gait varies with the method used, they both return values which are reasonable compared to other work (Maes et al., 2008) and predictions from dynamic similarity (Heglund et al., 1974; Iriarte- Díaz et al., 2006). Dynamic similarity predicts that the walk to trot transition occurs at a Froude number between 0.5 and 1 and the trot to gallop transition between 2 and 3 (Heglund et al., 1974; Iriarte-Díaz et al., 2006) (Table S4). Further validation was carried out by fitting regression lines to the GPS measured stride speeds and the stride speed predicted from stride length and frequency estimates obtained from GPS position data and accelerometer data (Fig. S2). The slopes of the lines were not significantly different to one (p < 0.05) (Table S5). Fig. 3 shows the mean and two STDs of the stride cut vertical accelerations for each gait and animal. The traces recorded during trotting for all species are similar (Fig. 3 D to F) (visual comparison). The lower signal to noise ratio of the accelerometer signal during walking makes comparison between species difficult (Fig 3. A to C). The timing of the first positive and negative peaks in the traces for the slow (Fig. 3 G,H; first positive peak marked by (a), negative by (b)) and fast (Fig 3. I,J; first positive peak marked by (c), negative by (d)) gallops in the dogs appears to be different. Analysis using SPM/RFT found significant differences (p < 0.05) between the traces at these locations and over the majority of the stride (Fig. S3).

Discussion As the collared animal does not have to be directly observed our method reduces demands on field staff, equipment and enables the study of free ranging locomotion at self-selected speeds. It extends the range and numbers of species and habitats in which locomotion can be investigated providing a tool to improve understanding of energetics, resource selection and the impact of human intervention on animal populations. While it does not suffer the drop in performance associated with a surrogate approach (Campbell et al., 2013) it does require the correct number of clusters to be chosen. This simply requires a visual check and comparison with expected gait transition values (Heglund et al., 1974). Our results fit with previous observations (Biancardi and Minetti, 2012), that dogs perform transverse and rotary gallops at low and high speeds respectively (Fig. 2 A,D and B,E and Fig. 3G,I) and that lions perform a rotary gallop regardless of speed (Fig. 2 C,F and Fig. 3K). It is unlikely, however, that our method would allow the separation of transverse and slow rotary galloping (Maes et al., 2008). Further work may enable other gait parameters, such as foot contact times, to be determined and this would allow finer gait classification and the ability to distinguish between transverse and slow rotary galloping. Our method could be extended to the classification of animal behaviour (Grünewälder et al., 2012) with the potential to reveal unseen behaviours (Brown et al., 2013), increase our understanding of elusive species and reduce observer effects. Acknowledgements We thank J. Lowe, S. Amos, J. Usherwood, B. Smith, S. Wilson, S. Hailes, A.R. Wilson and BPCT. Author contributions O.P.D/A.M.W conceived and designed the study. O.P.D analysed and interpreted the data and wrote the paper with extensive input from all authors. Funding We thank the ERC (Ad-G 323041), EPSRC (EP/H013016/1), Paul G Allen Family Foundation, Myhrvold Family Charitable Fund, Sunset Fund, Brookfield Zoo, Dallas Zoo, Woodland Park Zoo, and private donors (Tusk Trust/Wild Entrust International).

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Fig. 1. Examples of the signals recorded by the animal tracking collar, steady locomotion detection and gait classification. Signals were measured from a free ranging African wild dog (male). (A) GPS speeds, (B) y axis and (C) z-axis accelerations (see I) measured during steady slow gallop (SG) the transition to a trot and steady trotting. The modified sliding window signal segmentation approach is shown beneath the plots in (C). (D) to (F) Steady locomotion detection is shown. (D) Shows the results of filtering the windowed y and z-axis accelerometer signals with a band pass filter (pass band ± 0.3 Hz around the stride frequency). (E) The instantaneous phase of the filtered x and y accelerations. (F) The relative phases for steady SG, the gait transition and steady trotting (i to iii respectively). The Phase Locking Value (PLV) for steady SG and trotting are 0.984 and 0.983 respectively. The PLV value for the gait

transition is 0.802. (G) Feature space (calculated from multiple high sample rate recordings collected from African wild dog) for all locomotion (n = 1992, 4 s windows) and steady state (n = 622, 4 s windows) locomotion. Note features have been calculated from a 4 s window of data. (H) Result of k-means gait classification into walking (n = 21, 4 s windows), trotting (n = 116, 4 s windows), slow (n = 396, 4 s windows) and fast (n = 89, 4 s windows) (SG and FG) galloping clusters. Note the large separation between trotting and the other gaits and the clear distinction between the two galloping gaits. (I) The alignment of the three axis accelerometer in the animal tracking collar.

Fig. 2. Variation of stride frequency and length with speed for steady locomotion estimated from data collected using an animal tracking collar (cl) during walk, trot, slow and fast galloping (SG and FG respectively). (A, D) Stride frequency and length estimates for a lurcher. (B, E) Stride frequency and length estimates from two African wild dogs. (C, F) Stride frequency and length estimates from two lions. Note each point represents one stride. For the lurcher n = 49, 392, 174 and 76 for the walk, trot, slow and fast gallops. For the wild dogs n1 = 19, 802, 1229 and 321 and n2 = 26, 316, 430 and 147 for the walk, trot, slow and fast gallops. For the lions n1 = 766, 3101 and 385 and n2 = 1865, 3928 and 435 for the walk, trot, and gallop. (G to N) Comparison of stride frequency and length estimated from data collected using an animal

tracking collar (cl) and from video footage (v) for a lurcher. Note that stride parameter estimates from video data are calculated over individual strides. The anteroposterior sequence (APS) method was used to identify walking (G, K), trotting (H, L) and slow (I, M) and fast (J, N) gallop (SG and FG respectively) from video footage. Collar data were segmented into different gaits using the k-means algorithm. Linear regression lines are shown using solid lines, and 95 % confidence intervals using dash/dotted lines. We found no significant difference between the slope of the lines fitted to the stride parameter estimates from collar or video data (analysis of covariance, p > 0.05). The number of strides from the video footage for walk, trot, slow and fast galloping gaits was 25, 41, 21 and 15 respectively.

Fig. 3. Stride cut vertical accelerometer signals returned by clustering algorithm (data recorded by animal tracking collar). (A, D, G, I) results from Lurcher. (B, E, H, J) results from two African wild dogs (animal 1, n1, represented by pink line; animal 2, n2, represented by green line). (C, F, K) results from two lions (animal 1, n1, represented by blue line; animal 2, n2, represented by red line). The acceleration was normalised to be between -1 and 1. The animal s gait was determined using the k- means algorithm. Slow and fast gallops are represented by SG and FG respectively. The solid lines represent the average of the strides (n1/n2 represent the number of strides). The variability of the signal is represented by plotting two standard deviations of the values (shaded region). Features used to distinguish between slow and fast gallops are marked by (a), (b), (c) and (d). Analysis using Statistical Parametric Mapping (SPM) and Random Field Theory (RTF) found significant differences between SG and FG traces at these locations and over the majority of the stride (Fig. S3).

Journal of Experimental Biology 219: doi:10.1242/jeb.146035: Supplementary information Fig. S1. The speed variation (fluctuation) within each stride for strides classified as steady locomotion by the phase difference method developed in the current study to allow comparison with the speed threshold method used in previous work. Stride speed (m/s) is the mean speed over each stride (x-axis). The individual stride speeds (5 Hz) within each stride (speed fluctuation) are plotted on the y-axis. The +/- 10 % and +/- 20 % speed variation limits are shown by the green and black lines respectively. Journal of Experimental Biology Supplementary information

Journal of Experimental Biology 219: doi:10.1242/jeb.146035: Supplementary information Fig. S2. Validation of stride frequency and length parameter estimates obtained from animal tracking collar data by comparison of the speed estimate from these parameter with that measured by the GPS module. Data from the lurcher for walking, trotting, slow and fast galloping (SG and FG respectively) gaits are shown in A, F, K and N. The data from the two African wild dogs are shown in B, G, L and O (animal 1) and C, H, M and P (animal 2). The data from the two lions are shown in D, I and Q (animal 1) and E, J and R (animal 2). Regression lines were fitted to the GPS (Kalman smoothed) measured mean stride speeds and the mean stride speed calculated from stride length and frequency estimates obtained from GPS (Kalman smoothed) position data and accelerometer data. The slopes of the regression lines are not significantly different to one (p<0.05). Journal of Experimental Biology Supplementary information

Journal of Experimental Biology 219: doi:10.1242/jeb.146035: Supplementary information Fig. S3. Statistical testing using Statistical Parameter Mapping (SPM) and Random Field Theory (RFT) shows were in the stride that the stride cut vertical accelerometer signals vary during slow and fast galloping gaits (SG and FG respectively). We found significant (p < 0.05) differences at the locations of the first and second peaks (marked by (a) and (b) on the SG trace, and (c) and (d) on the FG trace) (B,D,F shaded regions). These points were selected by visual analysis as appearing to differ. Significant differences (p < 0.05) were between the SG and FG traces found over the majority of the stride (B,D,F shaded regions). The solid lines represent the average of the strides (A,C,E). The variability of the signal is represented by plotting two standard deviations of the values (shaded region) (A,C,E). Critical t = 2.979, 2.971 and 2.957 for the Lurcher (A,B) and African wild dogs n1 (C,D) and n2 (E,F) respectively. Journal of Experimental Biology Supplementary information

Journal of Experimental Biology 219: doi:10.1242/jeb.146035: Supplementary information Table S1. Animal age and leg lengths. Animal Age (yrs) Leg length (mm) lurcher 8 470 wild dog 1 3 542 wild dog 2 3 528 lion 1 Adult 960 lion 2 6 920 Table S2. Linear regression parameters from stride frequency and length estimates obtained from collar data from a domestic dog (lurcher), two African wild dogs and two lions. Stride frequency Gait Animal m c r 2 p lurcher 0.39 1.09 0.28 <0.001 wild dog 1 0.08 0.79 0.01 0.75 Walk Trot SG FG wild dog 2 0.09 0.87 0.03 0.41 lion 1 0.20 0.65 0.12 <0.001 lion 2 0.19 0.67 0.16 <0.001 lurcher 0.26 1.50 0.33 <0.001 wild dog 1 0.11 1.49 0.12 <0.001 wild dog 2 0.09 1.51 0.10 <0.001 lion 1 0.13 1.16 0.29 <0.001 lion 2 0.10 1.24 0.22 <0.001 lurcher 0.05 2.18 0.22 <0.001 wild dog 1 0.04 1.93 0.18 <0.001 wild dog 2 0.03 1.93 0.11 <0.001 lion 1 - - - - lion 2 - - - - lurcher 0.04 2.45 0.29 <0.001 wild dog 1 0.05 1.94 0.18 <0.001 wild dog 2 0.05 1.90 0.11 <0.001 lion 1 0.05 1.66 0.24 <0.001 lion 2 0.06 1.54 0.33 <0.001 Stride length Gait Animal m c r 2 p lurcher 0.49 0.19 0.70 <0.001 wild dog 1 1.13 0.06 0.51 <0.001 Walk Trot SG FG wild dog 2 0.88 0.18 0.66 <0.001 lion 1 0.84 0.33 0.56 <0.001 lion 2 0.83 0.33 0.65 <0.001 lurcher 0.36 0.27 0.78 <0.001 wild dog 1 0.46 0.25 0.78 <0.001 wild dog 2 0.49 0.21 0.82 <0.001 lion 1 0.45 0.55 0.74 <0.001 lion 2 0.50 0.41 0.81 <0.001 lurcher 0.37 0.19 0.97 <0.001 wild dog 1 0.40 0.32 0.92 <0.001 wild dog 2 0.44 0.18 0.95 <0.001 lion 1 - - - - lion 2 - - - - lurcher 0.31 0.38 0.94 <0.001 wild dog 1 0.31 0.89 0.74 <0.001 wild dog 2 0.31 1.06 0.59 <0.001 lion 1 0.38 0.72 0.84 <0.001 lion 2 0.38 0.91 0.84 <0.001 Journal of Experimental Biology Supplementary information

Journal of Experimental Biology 219: doi:10.1242/jeb.146035: Supplementary information Table S3. Linear regression parameters estimated from the stride frequency and length data extracted from the collar using the clustering method and data from the video method. Data were obtained from a domestic dog (lurcher) running on a grass playing field. Slow and fast gallops are SG and FG respectively. Stride frequency Gait Method m c r 2 p Walk Trot SG FG Collar Collar Collar Collar 0.39 1.09 0.28 <0.001 0.26 1.50 0.33 <0.001 0.05 2.18 0.22 <0.001 0.04 2.45 0.29 <0.001 Video Video Video Video 0.59 0.84 0.55 <0.001 0.34 1.38 0.68 <0.001 0.03 2.24 0.04 <0.001 0.05 2.27 0.12 <0.001 Stride length Gait Method m c r 2 p Walk Trot SG FG Collar Collar Collar Collar 0.49 0.19 0.70 <0.001 0.36 0.27 0.78 <0.001 0.37 0.19 0.97 <0.001 0.31 0.38 0.94 <0.001 Video Video Video Video 0.49 0.22 0.79 <0.001 0.36 0.25 0.93 <0.001 0.41 0.06 0.96 <0.001 0.32 0.41 0.88 <0.001 Table S4. Min/Max animal speeds and Froude numbers for a domestic dog (lurcher), two African wild dogs and two lions estimated from collar data. Animal speed (m/s) Froude no. Gait Animal Min Max Min Max lurcher 0.70 1.44 0.31 0.65 wild dog 1 0.53 1.05 0.23 0.46 Walk Trot SG FG wild dog 2 0.51 1.76 0.22 0.77 lion 1 0.58 1.79 0.19 0.60 lion 2 0.50 1.74 0.16 0.57 lurcher 1.40 3.35 0.63 1.52 wild dog 1 1.53 3.96 0.66 1.72 wild dog 2 1.80 3.76 0.79 1.66 lion 1 2.01 4.90 0.67 1.63 lion 2 1.20 5.11 0.39 1.67 lurcher 2.02 10.72 0.91 4.84 wild dog 1 2.45 12.48 1.06 5.42 wild dog 2 2.71 11.11 1.19 4.89 lion 1 - - - - lion 2 - - - - lurcher 3.42 14.43 1.54 6.52 wild dog 1 6.13 15.48 2.66 6.72 wild dog 2 7.22 15.24 3.17 6.70 lion 1 3.30 13.31 1.10 4.43 lion 2 3.65 12.98 1.19 4.23 Journal of Experimental Biology Supplementary information

Journal of Experimental Biology 219: doi:10.1242/jeb.146035: Supplementary information Table S5. Validation of stride frequency and length parameter estimates obtained from animal tracking collar data. Regression lines were fitted to the GPS (Kalman smoothed) measured average stride speeds and the average stride speed calculated from stride length and stride frequency estimates obtained from GPS (Kalman smoothed) position data and accelerometer data. The slopes of the regression lines are not significantly different to one (p < 0.05). Validation linear regression Gait Animal m c r 2 p lurcher 1.00 0.00 1.00 0.00 wild dog 1 0.99 0.00 1.00 0.00 Walk wild dog 2 0.99 0.00 1.00 0.00 lion 1 0.99 0.00 1.00 0.00 lion 2 0.99 0.00 1.00 0.00 lurcher 1.00 0.00 1.00 0.00 wild dog 1 0.99 0.00 1.00 0.00 Trot wild dog 2 0.99 0.00 1.00 0.00 lion 1 0.99 0.01 1.00 0.00 lion 2 0.99 0.00 1.00 0.00 lurcher 1.00 0.00 1.00 0.00 wild dog 1 0.99 0.00 1.00 0.00 SG wild dog 2 0.99 0.00 1.00 0.00 lion 1 - - - - lion 2 - - - - lurcher 1.00 0.00 1.00 0.00 wild dog 1 0.99 0.02 1.00 0.00 FG wild dog 2 0.99 0.02 1.00 0.00 lion 1 0.99 0.01 1.00 0.00 lion 2 0.99 0.01 1.00 0.00 Journal of Experimental Biology Supplementary information

Journal of Experimental Biology 219: doi:10.1242/jeb.146035: Supplementary information Table S6. Percentage of values in strides classified as steady locomotion by the phase difference method developed in the current study falling within the mean stride speed +/- 10 % and +/- 20 % to allow comparison with previous studies which have used a speed threshold for steady locomotion detection. Animal % of values within mean +/- 10 % % of values within mean +/- 20 % lurcher 66.59 92.94 wild dog 1 79.97 96.87 wild dog 2 73.00 95.66 lion 1 70.10 94.50 lion 2 83.19 97.57 Journal of Experimental Biology Supplementary information