How human runners regulate footsteps on uneven terrain

Running stably on uneven natural terrain takes skillful control and was critical for human evolution. Even as runners circumnavigate hazardous obstacles such as steep drops, they must contend with uneven ground that is gentler but still destabilizing. We do not know how footsteps are guided based on the uneven topography of the ground and how those choices influence stability. Therefore, we studied human runners on trail-like undulating uneven terrain and measured their energetics, kinematics, ground forces, and stepping patterns. We find that runners do not selectively step on more level ground areas. Instead, the body’s mechanical response, mediated by the control of leg compliance, helps maintain stability without requiring precise regulation of footsteps. Furthermore, their overall kinematics and energy consumption on uneven terrain showed little change from flat ground. These findings may explain how runners remain stable on natural terrain while devoting attention to tasks besides guiding footsteps.

. Uneven terrain experiments. a, We conducted human-subject experiments on flat and uneven terrain while recording biomechanical and metabolic data. The reflective markers and the outline of the force plate are digitally exaggerated for clarity. b, Footsteps were recorded to determine whether terrain geometry influences stepping location, illustrated here by a meansubtracted contour plot of terrain height for an approximately 6 foot segment of uneven II overlaid with footsteps (location of the heel marker). Blue and red circles represent opposite directions of travel and transparency level differentiates trials. the range of strategies used to run on naturalistic uneven terrain. This is suggested by studies that 86 examine walking on a variety of outdoor terrain and show that stride variability and energetics 87 significantly depend on terrain complexity (Kowalsky et al., 2021). Undulating uneven terrain have 88 been studied in the context of walking (Kent et al., 2019;Kowalsky et al., 2021), but not running. Fig. 2. Details of the experiment design. a, Schematic of the running track, camera placement, force plate positions and the LED strip with a 3 m illuminated section. b, The terrain was designed so that the range of its height distribution h was comparable to ankle height h pp ∼ h f and peak-to-peak distances λ (along the length of the track) were comparable to foot length λ ∼ l f . c, Histograms of the mean subtracted heights h of the uneven terrain. d, Histograms of the peak-topeak separation λ of the uneven terrain.

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Terrain unevenness was heuristically specified so that peak-to-valley height variations were approx-124 imately equal to the height of the malleolus while standing barefoot on level ground, and peak-to-125 peak horizontal distances were similar to foot length (Fig. 2b). Large terrain height variations may 126 elicit obstacle avoidance strategies, which is not the subject of this paper, and peak-to-peak hori-127 zontal separation longer than the step length may make the slope variation too gentle. Conversely, shell which was coated with a slurry of sand and epoxy to create a surface that texturally resembles 134 weathered rock. The width at the ends of the uneven track were broadened to approximately 1 m to 135 allow for runners to change direction while remaining on the terrain. The terrain was then digitized 136 using a dense arrangement of reflective markers that were recorded by the motion capture system.  Stance was defined as when the heel marker's forward velocity was minimized and its height 143 was within 15 mm of the marker's height during standing. The threshold of 15 mm was chosen to 144 account for terrain height variations so that stance may be detected even when the heel lands on 145 a local peak of the uneven terrain. 146 The center of mass forward speed v = d step /t step was found from the distance d step covered by 147 the center of mass in the time duration t step between consecutive touchdown events. Leg angle at 148 touchdown was defined as the angle between the vertical and the line formed by joining the heel 149 marker to the center of mass. Virtual leg length at touchdown is defined as the distance between 150 the heel marker and the center of mass. Foot length l f is defined as the average distance in the 151 horizontal plane between the toe and heel marker, across all subjects. The center of mass trajectory 152 during stance was fitted with a regression line in the horizontal plane. The step width was found as 153 twice the distance of nearest approach of the stance foot from the regression line. This definition 154 allows for the runner's center of mass trajectory to deviate while preserving a definition of step 155 width that is consistent with those previously used (Donelan et al., 2001;Arellano and Kram, 156 2011). We estimated meander, i.e. the deviation of the center of mass from a straight trajectory, at the moment just prior to touchdown. Leg retraction rate ω is determined using ω = v f /||l||, 163 where v f is the component of the foot's relative velocity with respect to the center of mass that is 164 perpendicular to the virtual leg vector l (vector joining heel to center of mass).

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Step width, step length and virtual leg length at touchdown are normalized by the subject's leg 166 length, defined as the distance between the greater trochanter and lateral malleolus.

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To correct for slight angular misalignments between the motion capture reference frame and 168 the long axis of the running track, we align the average CoM trajectory over the entire track length 169 to be parallel to the y-axis of the motion capture reference frame. This correction reflects the 170 experimental observation that the subjects run along the center of the track. Force plate data were low-pass filtered using an 8 th order, zero-phase, Butterworth filter with a 173 cut-off frequency of 270 Hz. Touchdown on the force plates was defined by a threshold for the 174 vertical force of four standard deviations above the mean unloaded baseline reading.

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The forward collision impulse, defined as the maximal decelerating fore-aft impulse J * y , was 176 found by integrating the fore-aft component F y of the ground reaction force during the deceleration 177 phase as (1) 179 We normalized J * y by the aerial phase forward momentum mv y , where v y is the forward speed of 180 the center of mass during the aerial phase. Net metabolic rate is defined as the resting metabolic power consumption subtracted from the power 183 consumption during running and normalized by the runner's mass. Metabolic power consumption 184 is determined using measurements of the rate of O 2 consumption and CO 2 consumption using 185 formulae from Brockway (Brockway, 1987 range of heights (h IQR ) in each patch was used as a measure of its unevenness.

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Starting from an initial position (x i , y i ), the model takes the next step to (x i+1 , y i+1 ) in the open-loop stage: x noise process:

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In the open-loop stage, the model takes a step forward and sideways dictated by the experimentally

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At the ends of the track, the x position of the runner is reset so that the runner is at the center 237 of the track, and the direction of travel is reversed (j value is toggled). We simulate for 100,000 238 steps to ensure that reported terrain statistics at footstep locations as well as step length and step 239 width converge, i.e. errors between simulations in these parameters are less than 1% of their mean 240 value. This average S is used to normalize each f i,j to yield the foot placement index p i,j according to, additional segments representing the thigh and torso and calculating the fore-aft collisional impulse.

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The collision is assumed to be instantaneous and inelastic, with a point-contact between the leg 278 and the ground. Such collision models are widely used to capture the stance impulse due to ground 279 forces in walking (Donelan et al., 2002;Ruina et al., 2005) and running (Srinivasan and Ruina,280 2006; Dhawale et al., 2019). Because the collision is assumed to be instantaneous, only infinite 281 forces contribute to the impulse (Chatterjee and Ruina, 1998;Lieberman et al., 2010). Therefore,

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to investigate the effect of joint compliance, we model the hinge joints connecting the links as either 283 infinitely compliant or perfectly rigid. The advantage of these contact models is their ability to 284 accurately capture the impulse without the numerous additional parameters needed to represent 285 the complete force-time history when contact occurs between two bodies (Chatterjee and Ruina,286 1998).

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We use experimental data on center of mass velocity and leg retraction rate just prior to landing, and angular velocity Ω − collides with the ground at angle θ. G represents the center of mass. Leg length and body mass are obtained from data and scaled according to Dempster (Dempster, 1955) to obtain segment lengths and masses. Free-body diagrams show all non-zero external impulses: b, collisional impulse J acting at O, and panels c, d, e, show reaction impulses R 1 , R 2 , and R 3 acting at B, C, and D respectively.
Due to the instantaneous collision assumption, finite forces like the gravitational force do not 311 contribute to the collisional impulse, and the ground reaction force at point O leads to the impulse 312 J (Fig. 4b). Angular momentum balance about the contact point O yields the relationship between 313 pre and post collision velocities, where The total mass M b is the sum of the masses of the torso M , thigh M t , shank M s , and foot m f . 315 We solve for ω + in equation (6) and obtain the post-collision center of mass velocity v + G using 316 equation 6b. From this, the collision impulse J and the normalized fore-aft collisional impulse and Compliant joints: If the L-bar has compliant joints, then the post-collision velocities for each 319 segment may vary. Therefore, we write additional angular momentum balance equations for each 320 segment to solve for the post-collision state. Since the only non-zero external impulse acting on 321 the shank, thigh, and torso segments is the reaction impulse R 1 acting at B (Fig. 4c), the only 322 non-zero external impulse on the thigh and torso portion of the leg is the reaction impulse R 2 323 acting at C (Fig. 4d), and the only non-zero external impulse acting on the torso portion of the leg 324 is the reaction impulse R 3 acting at D (Fig. 4e), we write angular momentum balance equations for the entire body and these three segments as, where and Simultaneously solving equations (8)-(9) yields the post-collision velocities for each segment of the using equation (7).  to be normally distributed about zero and account for inter-subject variability of the intercept.

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The model residuals are ϵ ij which are also assumed to be normally distributed about zero.

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The second linear mixed model uses stepwise data where each step is grouped by subject and 369 terrain type. Each of the 1086 steps in this dataset contains a value for subject number, terrain 370 type, touchdown leg angle, decelerating fore-aft impulse, and forward foot speed at touchdown.

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The linear model for the dependent variable y (touchdown leg angle or fore-aft impulse) is,

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the value of y on flat terrain when foot speed = 0, β i for terrain factor, and the slope β f for the 375 dependence of y on forward foot speed at touchdown. The variable µ 1j account for inter-subject 376 variability of the intercept, and the variables µ 2j and ν i account for inter-subject and terrain-specific 377 variability of the slope β f , respectively. The residuals ϵ ij are assumed to be normally distributed. where k = 1, 2 for the two uneven terrain and l = 1 → 9 for the 9 subjects. The dependent variable 383 y is the probability of landing in a foot-sized cell p i,j and the independent variable 'terr' refers to the

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The experimentally measured stepping patterns are the same as the blind scheme on both 400 uneven I and II in terms of the terrain unevenness as quantified by h IQR (human subjects versus 401 blind scheme in Fig. 5). However, the directed scheme finds substantially more level landing patches,

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showing that it was possible for the runners to land on more level ground (directed scheme in Fig. 5).

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These trends are also borne out in a subject-wise analysis (Fig. 5-figure supplements 1, 2). The fore-aft ground reaction force in stance initially decelerates the center of mass before acceler-419 ating it forward (Fig. 6a). We find that less than 6 ± 1% (mean ± S.D.) of the forward momentum 420 is lost during the deceleration phase of stance and there is no dependence on terrain or subject 421 (Fig. 6b). The low variability of the fore-aft impulse, just 1% of the forward momentum, suggests 422 that it is tightly regulated across runners, terrain and steps.

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The regulation of foot speed is unlikely to be the primary determinant of the low variability in  Fig. 6. Regulation of fore-aft impulses. a, The fore-aft impulse J * y (gray shaded area) is found by integrating the measured fore-aft ground reaction force F y (black curve) during the deceleration phase. b, Mean J * y mvy . c, Measured J * y mvy (green circles) versus relative forward foot speed at landing (forward foot speed/center of mass speed) for each step recorded on all terrain types (total 1081 steps). The green line is the regression fit for the data. The dark and light gray lines are the predicted fore-aft impulse for the mean stiff and compliant jointed models, respectively. Per step model predictions in Fig. 6-figure supplement 1. d, Measured versus predicted fore-aft impulses for every step. The dotted line represents perfect prediction.
fore-aft collision impulses varied only by 17% of its mean. A statistical analysis lends further 427 support and shows that the dimensionless fore-aft impulse depends significantly, but only weakly, impulse while the stiff model overestimates it (Fig. 6 c, d, and Fig. 6-figure supplement 1). This 436 is expected because the muscle contraction needed for weight support and propulsion would induce 437 non-zero but non-infinite stiffness at the joints. Although both models overestimate the dependence 438 of the fore-aft impulse on foot speed, the slope of the compliant model is closest to the measurements 439 (Fig. 6c, Fig. 6-figure supplement 1). The slope of measured speed-impulse data is 0.01 ± 0.003 440 (p = 0.001, Fig. 6-table supplement 1), closer to compliant model than the stiff model, whose 441 slopes are 0.0203 ± 0.010 (p < 0.0001) and 0.056 ± 0.005 (p < 0.0001), respectively. The measured 442 fore-aft impulse for most steps was below 0.07 (whiskers extend to 1.5 times the interquartile 443 range in Fig. 6b). The compliant model's predicted fore-aft impulses show good agreement with 444 measurements when the impulse is below 0.07 (measured versus predicted in Fig. 6d), and disagree 445 only for the occasional steps when runners experience more severe fore-aft impulses. Unlike the 446 compliant model, the stiff model consistently over-estimates the measured fore-aft impulse over its 447 entire range. Thus, we propose that maintaining low joint stiffness at landing helps maintain low 448 fore-aft impulses despite variations in touchdown foot speed.

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Leg retraction 450 Increased leg retraction rate results in reduced forward foot speed at touchdown, thereby altering 451 the fore-aft impulse (Karssen et al., 2015;Dhawale et al., 2019). The mean non-dimensional forward 452 foot speed at landing is terrain-dependent and lower by 0.17±0.04 (p = 0.001) on uneven I compared 453 to flat ground, and by 0.15±0.04 (p = 0.002) on uneven II compared to flat ground (Fig. 7a, Fig. 7-454 table supplement 1). For the mean subject, these correspond to reductions in forward foot speed 455 of 0.48 ± 0.11 m/s on uneven I and 0.42 ± 0.11 m/s on uneven II compared to flat ground. 456 We find that touchdown angle depends significantly but only weakly on forward foot speed at 457 landing (p ≈ 0, slope = 0.07 ± 0.01 rad, Fig. 6-table supplement 1). If the dimensionless forward 458 foot speed at landing varied through its entire observed range from −0.2 to 1.1, it would result in 459 a change in landing angle of 0.08 rad or 5 • .
Step 463 width variability, i.e. the interquartile range of step widths within a trial, is also terrain dependent 464 (p = 0.05, Fig. 7c, Fig. 7-table supplement 1) and greater on uneven II versus level ground by c, Box plot of the step width variability. Central red lines denote the median, boxes represent the interquartile range, whiskers extend to 1.5 times the quartile range, and open circles denote outliers. The distribution of step widths within a trial deviated from normality and hence we report the median and the interquartile range of the distribution for each trial (Fig. 7-figure supplement 1), instead of the mean and standard deviation as is reported for all other variables. d, Net metabolic rate normalized to subject mass. Whiskers represent standard deviation across subjects. step width variability (IQR) increased by 6 ± 2 mm.

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The approximately 5% increase in metabolic power consumption on the uneven terrain compared 469 to flat we measured was not statistically significant (p = 0.08, Fig. 7d, Fig. 7-table supplement 1).

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Our primary finding is that runners do not use visual information about terrain unevenness to guide 472 their footsteps. In addition, the fore-aft collisions that they experience seem almost decoupled from 473 the forward speed with which their foot lands on the ground. Based on the modeling estimate 474 of collisional impulses and comparison with measurements, we propose that low joint stiffness 475 underlie the regulation of fore-aft impulses, likely contributing to stability (Dhawale et al., 2019).

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Taken together, these results suggest that runners rely not on vision-based path planning, but 477 on their body's passive mechanical response for remaining stable on undulating uneven terrain.

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Additionally, the changes in step-width kinematics on the uneven versus flat terrain may reflect 479 sensory feedback mediated stepping strategies similar to those reported previously (Seipel and 480 Holmes, 2005;Seethapathi and Srinivasan, 2019), but more work is needed to investigate whether 481 the differences were the result of feedback control or simply the result of variability injected by the 482 terrain's unevenness.

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Measurements of fore-aft impulses have not been previously examined in the context of stability.

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A previous theoretical analysis hypothesized that reducing tangential collisions and maintaining low 485 fore-aft impulses reduces the risk of falling by tumbling in the sagittal-plane (Dhawale et al., 2019).

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Our data are consistent with this model. We find that only 6 ± 1% of the forward momentum was 487 lost in stance although the forward foot speed at landing varied by nearly 50%. This reduction 488 in variability is surprising because, all else held the same, speed and impulse are expected to be 489 linearly related. This suggests that the fore-aft impulse is tightly regulated by other means. By 490 examining the role of leg joint compliance using model-based analyses of the data, we found that 491 the measured fore-aft impulses were partly consistent with an idealized extreme of zero stiffness 492 in the joints at the point of landing. However, joint stiffness in a real runner cannot be too small 493 because it is needed to withstand the torques for weight support and propulsion. Thus, we propose that the low variability in fore-aft impulses arises from active regulation of joint stiffness.

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Past studies on running birds Birn-Jeffery et al., 2014) provide some hints on 496 why leg compliance, and not foot speed, might be the preferred means to regulate fore-aft impulses.

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To deal with abrupt changes in terrain height, running birds regulate foot speed and leg retraction 498 rates to maintain consistent leg forces and reduce discomfort or injury risk. Although our terrain 499 has smoothly varying terrain and not the step-like blocks used in the bird studies, our runners 500 may still have encountered sudden height changes because they did not precisely regulate their 501 stepping pattern to avoid uneven terrain areas. Like the running birds, they may have regulated 502 foot speed to mitigate discomfort and high forces. Thus, by employing leg compliance to reduce 503 the fore-aft impulse, the runners could deal with stability independent of foot speed regulation for 504 safety and comfort. However, caution is warranted when comparing our results with these past 505 studies. The bird studies used SLIP models to interpret their findings, but such models are energy 506 conserving and unaffected by slope variations that were part of our terrain design. Furthermore, 507 the peak-to-peak height variation of our terrain was less than 6% of the leg length, Blum et al.

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We found variability in step-to-step kinematics that are largely consistent with previous studies 515 on step-like terrain, but with some notable differences. Studies of running birds hypothesize that 516 crouched postures could aid stability on uneven terrain (Blum et al., 2011;Birn-Jeffery and Daley, 517 2012), as do human-subject data from treadmill running (Voloshina and Ferris, 2015). We find 518 a slight decrease in the virtual leg length at touchdown on the most uneven terrain compared to 519 flat, but the difference was only around 1% of the leg length ( Fig. 7-table supplement 1), whose 520 effect on stability would be negligible. We find higher leg retraction rates on uneven terrain, as 521 also reported in running birds (Birn-Jeffery and Daley, 2012;Blum et al., 2014). Leg retraction 522 has been hypothesized to improve running stability in the context of point-mass models by altering 523 leg touchdown angle to aid stability (Seyfarth et al., 2003;Blum et al., 2010). However, we find 524 only a weak dependence between leg retraction rate and leg touchdown angles. Human-subject 525 treadmill experiments report that step width and step length variability increased by 27% and 526 26%, respectively, and mean step length or step width were the same for flat and uneven terrain 527 (Voloshina and Ferris, 2015). Like those studies, we find 24% greater step width variability on 528 uneven terrain compared to flat, but no significant changes in step length variability (Fig. 7b, 529 Fig. 7-table supplement 1). We additionally find that the median step width increased on uneven 530 terrain by 13%. The increase in median step width that we measure could be due to lateral stability 531 challenges of running on relatively more complex terrain with smoothly varying slope and height 532 variations in all directions.

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Unlike treadmill running studies, we do not find a statistically significant increase in metabolic 534 power consumption on uneven terrain versus flat ground, but the mean increase of around 5% 535 is similar to Voloshina and Ferris (2015). The acceleration and deceleration when subjects turn 536 around during our overground trials could affect the metabolic energy expenditure. Therefore, cau-537 tion is warranted in comparing the absolute value of our reported energetics data with other studies 538 on treadmills or unidirectional running. But several aspects of the experimental design allow us to 539 compare the respirometry data between the different terrain types. For every subject, we ensured 540 that the breath-by-breath respirometry data stabilized within the first 3 minutes and only used the 541 stabilized value for further analyses (Methods 2.1.4). If the transients had dominated the respirom-542 etry measurements, the measurements would not have stabilized ( Fig. 7-figure supplement 2).

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The use of the moving light bar on either side of the track ensured that the subjects maintained 544 the same speed on all the terrain types. Moreover, the turnaround patches were designed to have 545 the same terrain statistics (flat, uneven I, uneven II) as the rest of the track, thus ensuring that 546 there were no abrupt terrain transitions. This allowed us to control for and mitigate the effects of 547 the turnaround phases when comparing the results between the different terrain types. 548 We find no evidence that subjects used visual information from the terrain geometry to plan 549 footsteps despite predicted advantages to stability (Dhawale et al., 2019). This finding differs 550 from walking studies that highlight the role of vision in guiding step placement on natural, uneven 551 terrain (Matthis et al., 2018;Bonnen et al., 2021). The stochastic stepping model was able to 552 consistently find landing locations with lower unevenness than the human subjects, while matching 553 the measured mean stepping statistics and even reducing step-to-step variability, thus showing that 554 the absence of a foot placement strategy was not due to a lack of feasible landing locations. We 555 speculate that foot placement strategies are used for obstacle avoidance (Matthis and Fajen, 2014) 556 on more complex terrain while our terrains were designed to be continuously undulating and not 557 have large, singular obstacles. While our data suggest that terrain-guided foot placement strategies Footsteps were not directed towards flatter regions of the terrain despite predicted benefits to 564 stability. Instead, we found evidence for a previously uncharacterized control strategy, namely that 565 the body's stabilizing mechanical response due to low fore-aft impulses was used to mitigate the 566 destabilizing effects of stepping on uneven areas. The limited need for visual attention may explain 567 how runners could employ vision for other functional goals, such as planning a path around large 568 obstacles, or in an evolutionary context, tracking footprints to hunt prey on uneven terrain without 569 falling. Whether other animals employ similar strategies on uneven terrain is presently unknown 570 but data from galloping dogs show that they do not alter their gait on uneven terrain (Wilshin et al.,571 2020), thus suggesting that other adept runners potentially employ similar principles for stability. 572 We propose that our results could translate to new strategies for reducing the real-time image 573 processing burden in robotic systems, and could also help in training trail runners by emphasizing 574 limber joints when dealing with uneven terrain.

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Data availability statement: All data points are plotted in either the main text or the electronic 576 supplementary material. Raw data are available on the Dryad repository associated with this paper.

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Author Contributions: MV conceived the study. ND conducted the experiment. ND and MV 578 performed the data analysis and wrote the paper.