Tracking the Lone Ranger: Continuous Locomotor Variation Along a 158 m Theropod Trackway

1. Introduction

Fossil footprints record direct interactions between organisms and substrates, preserving information on autopodial morphology, trackmaker affinity and body size, and palaeoenvironmental substrate conditions [1,2,3,4]. Where footprints occur in sequence as a trackway, they additionally preserve the spatial progression of an individual animal, providing evidence of locomotor and behavioural variation unavailable from isolated tracks [5,6,7,8,9].

Long, near-complete trackways extending over tens to hundreds of metres preserve repeated observations from the same trackmaker, providing opportunities to assess the persistence, change or recurrence of foot-placement patterns [6,7,9,10].

Such records have documented variations in gait, directional behaviour, and potential pathological or asymmetric locomotor signals [10,11,12,13,14,15,16,17]. Despite this potential, variation within very long trackways, they remain comparatively understudied. This may be in part because conventional field measurement becomes increasingly demanding as trackway length and footprint number increase [14,18,19,20]. Digital approaches including photogrammetry, georeferencing, and software-based spatial analysis reduce this logistical constraint by allowing extensive track surfaces and large numbers of footprints to be measured and reanalysed within a common spatial framework [10,17,21,22,23,24,25].

Long trackways also expose a limitation in the way locomotor data are commonly summarised. Trackway studies frequently report characteristic values such as mean pace, stride, or estimated speed [14,15,26,27]. Such values are useful descriptors, but when applied to long trackway sequences they can obscure the variation from which the mean was calculated. An animal traversing tens or hundreds of metres may vary its forward progression, lateral foot placement, or heading while remaining within the same broad gait category. Determining whether an observed pattern is sustained, transient, or continuously changed requires the ordered sequence itself to be analysed at the step-to-step scale rather than reduced solely to whole-trackway averages [5,6,9,10,28]

Such analyses require spatial records of sufficient fidelity, and fortunately, suitable datasets increasingly survive as products of earlier documentation campaigns. The Dinosaur Valley State Park, situated along the Paluxy River near Glen Rose, Texas, preserves one of the most extensively documented dinosaur track assemblages in North America, with numerous theropod and sauropod trackways occurring within the Lower Cretaceous Glen Rose Formation. Between 2008 and 2009, an international team working with the Texas Parks and Wildlife Department (TPWD) systematically documented exposed tracksites throughout the park [29,30,31]. Track surfaces were cleaned and gridded, footprints were georeferenced using survey-grade GPS, overlapping photographs were assembled into GIS-registered photomosaics, and footprint outlines were traced and measured directly [29]. This documentation was particularly important because the exposed track surfaces recorded decades earlier, have since been damaged or destroyed by river erosion and/or winter freeze-shattering [29,30,31].

TPWD subsequently made these records publicly available as georeferenced photomosaics and track overlays (with theropod and sauropod footprints distinguished by colour), distributed in KMZ format (TPWD, n.d.). Since footprint order and their spatial position within trackways can be derived, this can therefore be treated as a source from which new quantitative datasets may be generated. To the author’s knowledge, this analytical potential has not previously been exploited for the Dinosaur Valley overlays, with other published works of the park’s trackways relying principally on independently collected field measurements [29,31]. One long theropod trackway represented in the TPWD records, popularly known as the Lone Ranger, is recognised as the longest documented dinosaur trackway within Dinosaur Valley State Park [31,32]. Despite its extent, no comprehensive step-by-step quantitative analysis of the trackway has previously been published.

In the current study, footprint positions of the Lone Ranger trackway are derived directly from the publicly available TPWD overlays, with Acrocanthosaurus atokensis used only as a body-fossil candidate for model-based trackmaker estimates [29,31]. The objectives of this research are twofold: (1) to quantitively measure the trackway geometry in determining how pace, step, stride, lateral placement, and directional behaviour vary through the preserved sequence, while separately deriving model-based estimates of trackmaker locomotor progression and gait; and (2) to evaluate whether publicly available georeferenced tracksite records can function as reusable observational datasets for quantitative locomotor analysis without new field measurement.

2. Location and Geological Setting

The study area lies along the Paluxy River within Dinosaur Valley State Park, approximately 6.2 km west of Glen Rose, Somervell County, Texas (Figure 1). The dinosaur tracks occur within the Glen Rose Formation of the Lower Cretaceous Trinity Group (Upper Aptian–Lower Albian), which records marine to marginal-marine environments ranging from relatively low-energy lagoonal and subtidal settings to higher-energy tidal flats subjected to periodic subaerial exposure [31,33].

Figure 1. Geographic and stratigraphic context of the Paluxy River dinosaur tracksites, Dinosaur Valley State Park, of the lower Glen Rose Formation, Texas, USA. (A) Regional map of the western United States showing the location of Dinosaur Valley State Park (orange dot), Texas; (B) Locations of dinosaur tracksites along the Paluxy River. Red-coloured river sections indicate areas covered by publicly available KMZ overlays [32]. The black circle marks McFall Ledge (32.23733° N, 97.82449° W), used solely as the local coordinate origin (0, 0) for the Lone Ranger trackway maps in the subsequent figures (i.e., Figure 2 and Figure 3 and 5); the trackway itself occurs at Taylor; (C) Stratigraphic section in the Bowden-Baker Composite tracksite with track-bearing horizon indicated by the sauropod/theropod silhouettes [adapted from previous studies [29,33]. Satellite map image copyright Google Earth.

Figure 1. Geographic and stratigraphic context of the Paluxy River dinosaur tracksites, Dinosaur Valley State Park, of the lower Glen Rose Formation, Texas, USA. (A) Regional map of the western United States showing the location of Dinosaur Valley State Park (orange dot), Texas; (B) Locations of dinosaur tracksites along the Paluxy River. Red-coloured river sections indicate areas covered by publicly available KMZ overlays [32]. The black circle marks McFall Ledge (32.23733° N, 97.82449° W), used solely as the local coordinate origin (0, 0) for the Lone Ranger trackway maps in the subsequent figures (i.e., Figure 2 and Figure 3 and 5); the trackway itself occurs at Taylor; (C) Stratigraphic section in the Bowden-Baker Composite tracksite with track-bearing horizon indicated by the sauropod/theropod silhouettes [adapted from previous studies [29,33]. Satellite map image copyright Google Earth.

Figure 2. Trackway parameters for the Lone Ranger theropod trackway, from the Dinosaur Valley State Park, the lower Glen Rose Formation, Texas, USA. (A) Pace length, and (B) pace angulation. Bar-scatter plots show their distribution across the trackway length with black/grey representing right/left parameter, respectively. Violin plots summaries the distribution of values for each parameter as a combined distribution (‘All’), and as ‘left’ and ‘right’ values. Grey shading in ‘pace angulation’ scatter plot denotes values exceeding 180° (i.e., crossover events). Co-ordinate plot of the LR trackway colour-codes the corresponding parameter to the associated footprints positions.

Figure 2. Trackway parameters for the Lone Ranger theropod trackway, from the Dinosaur Valley State Park, the lower Glen Rose Formation, Texas, USA. (A) Pace length, and (B) pace angulation. Bar-scatter plots show their distribution across the trackway length with black/grey representing right/left parameter, respectively. Violin plots summaries the distribution of values for each parameter as a combined distribution (‘All’), and as ‘left’ and ‘right’ values. Grey shading in ‘pace angulation’ scatter plot denotes values exceeding 180° (i.e., crossover events). Co-ordinate plot of the LR trackway colour-codes the corresponding parameter to the associated footprints positions.

Figure 3. Trackway parameters for the Lone Ranger theropod trackway, from the Dinosaur Valley State Park, the lower Glen Rose Formation, Texas, USA. (A) Stride length, (B) trackway width, and (C) relationship between stride and trackway width. Bar-scatter plots show their distribution across the trackway length with black/grey representing right/left parameter, respectively. Co-ordinate plot of the LR trackway colour-codes the corresponding parameter to the associated footprints positions. Grey shading in scatter plots denotes crossover events.

Figure 3. Trackway parameters for the Lone Ranger theropod trackway, from the Dinosaur Valley State Park, the lower Glen Rose Formation, Texas, USA. (A) Stride length, (B) trackway width, and (C) relationship between stride and trackway width. Bar-scatter plots show their distribution across the trackway length with black/grey representing right/left parameter, respectively. Co-ordinate plot of the LR trackway colour-codes the corresponding parameter to the associated footprints positions. Grey shading in scatter plots denotes crossover events.

The local stratigraphy of the Glen Rose Formation comprises seven principal beds, here described from oldest to youngest [31,33]. The Main Track Layer was deposited under subtidal to intertidal conditions on a periodically exposed dolomitic mud surface and preserves Arenicolites burrows together with well-preserved dinosaur footprints. It is overlain by four fully marine, non-track-bearing units — the Hardground Bed, Steinkern Marl, Corbula Bed, and Serpulid Bed — representing alternating higher- and lower-energy shallow-marine deposition. Above these, the Taylor Track Layer records a marginal-marine to tidal-flat setting with periodic subaerial exposure, including variably preserved dinosaur footprints and mudcracks. The uppermost Diplocraterion Bed represents a calm, shallow-marine setting characterised by firm subaqueous sediment and U-shaped Diplocraterion burrows [31,33].

The Paluxy River track-bearing exposures are conventionally divided into seven named areas (Figure 1B). From upstream to downstream, these are McFall, Taylor, Highline, Blue Hole, Main, Buckeye Branch, and the Bowden-Baker Composite area, each encompassing one or more individual tracksites. Dinosaur tracks occur within three stratigraphic units — the Main Track Layer, Taylor Track Layer, and Diplocraterion Bed — spanning an approximately 6 m vertical interval (Figure 1C; Table 1) [29,31].

The Lone Ranger trackway lies wholly at the Taylor section within and the Taylor Tracklayer, where it is preserved as two portions. The first preserved footprint lies at the Lone Ranger Site to the north-east (32.239201°, −97.820529°) and the last at the West Taylor Site to the west (32.238466°, −97.821881°).

3. Materials and Methods

3.1. Trackway Nomenclature

In this study, the Lone Ranger trackway is abbreviated as LR, with the eastern portion designated LR-1, separated by a >20 m gap to the western portion designated as LR-2. Individual tracks within each portion are identified using a numerical suffix indicating their sequential order; for example, LR-2-4 refers to the fourth track in the second trackway portion. An alternative naming convention (i.e., IID Trail) is documented elsewhere [29,34].

3.2. Digital Landmarking and Data Acquisition

3.2.1. Source Data and Provenance

Georeferenced track overlays of the Lone Ranger trackway and neighbouring mapped areas (Area5_Loan_Ranger_g.kmz and Area5_West_Taylor_g.kmz; file names as published by TPWD) were downloaded from the Texas Parks and Wildlife Department “Mapping Dinosaur Tracks” webpage [32]. Each KMZ archive contains an embedded KML document and an associated RGBA raster image represented as a ‘GroundOverlay’. The raster annotations identify theropod footprints in red and sauropod tracks in blue [32]. The KML documents contain no Placemark or KML coordinates elements and therefore provide no discrete vector coordinates or polygons for individual footprints.

3.2.2. Import and Coordinate Transformation

The KMZ files were imported into Blender 4.2 using a purpose-written Python importer (Supplementary Code S1). The importer read the geographic bounds and rotation stored in each ‘LatLonBox,’ extracted the associated raster and converted the WGS84 geographic coordinates to a metre-scaled local Cartesian coordinate system. Within Blender, X represents east and Y represents north; Z was used only to separate display layers and carries no elevation information. All overlays shared a fixed WGS84 working origin at the McFall Ledge coordinate (32.237330°, -97.824490°). Each raster was positioned at its calculated local centre, scaled to its geographic ground dimensions and rotated according to its KML rotation value.

Photo mosaics were imported only as visual context and were not subjected to colour analysis. Within the track-overlay rasters, red and blue pixels were classified into theropod and sauropod colour classes (respectively) and grouped into eight-connected components. Components with a mapped colour area below 0.0025 m² or a mapped dimension below 0.04 m were excluded. For each accepted component, the importer calculated its mapped colour area, centroid, bounding dimensions and convex-envelope outline. The centroid of the mapped coloured area served as the footprint landmark, while the convex envelope provided an outline snap target. These components were treated as graphical representations rather than automatically as individual biological footprints because coloured regions could merge, fragment or include non-footprint annotations. Trackway membership, footfall sequence and left–right identity were not inferred by the importer but were assigned by the author as described in Section 3.2.3.

3.2.3. Landmarking and Trackway Construction

Trackway geometry was digitised as a polyline by placing vertices sequentially at the centroid landmark of each successive footprint in the inferred direction of travel. Footprint laterality (left versus right) was assigned by the author according to its position relative to the inferred trackway midline. When viewed in the direction of travel, footprints consistently offset to the left of the midline were classified as left, and those offset to the right were classified as right. These user-defined sequence and laterality assignments were used in the subsequent trackway measurements.

For missing footprints (LR-1-22, -65, -114, -115, and -123; LR-2-14), positions were tentatively estimated by placing vertices equidistant between the flanking preserved tracks. The 21.53 m gap separating LR-1 from LR-2 was taken to represent 24 missing footprints, with equidistant points marking their inferred positions. This count was constrained by the requirement for an even number, maintaining alternating left–right footfall, and by the near-average step lengths of the flanking portions, which yield an estimated range of 23–26 missing footprints. Varying this estimate to 22 or 26 would not affect any measured trackway parameter or modelled biometric calculation, as missing footprints were excluded from quantitative analyses (with the exception of ttrackway length, and traditional straightness index; the latter see Section 3.4.1). Footprint length was not measured from the georeferenced overlays but was taken as 38 cm for biometric estimation, following the average track length reported for the Lone Ranger trackway by Kuban [34].

All trackway parameter and modelled trackmaker biometric calculations were digitally as described previously [10].

3.3. Trackway Parameter Calculations

Length measurements (pace and stride) were determined as the Euclidean distance between the starting point (x₁, y₁) and end point (x₂, y₂) of the respective measurement. Pace angulation and step angle were determined following Thulborn [1]. As the trackmaker narrows the width between its legs during locomotion, the pace angulation approaches 180° and the step angle approaches 0°, both reaching these values when three successive footprints come inline. Pace angulation was measured as the angle between two successive pace lengths (Equation 1), while step angle was measured as the angle between the pace and stride (Equation 2):

Cos (pace angulation) = ((pace₁)² + (pace₂)² − (stride)²)/ (2 × pace₁ × pace₂)

(1)

Cos (step angle) = ((pace₁)² + (stride)² − (pace₂)²)/ (2 × pace₁ × stride)

(2)

The cosine returns only angle magnitude (0°-180°), so the sign was assigned from the side of the stride axis on which the intervening footprint fell. Negative values (for step angle and trackway width [see below]), or values above 180° (for pace angulation), mark crossover, where a left footprint lands on the right of the trackway, and vice versa.

Trackway width was defined as the perpendicular distance of the intervening footprint from the stride orientation (Equation 3):

Trackway width = pace × sin (step angle)

(3)

To compliment the forward-only distance of pace, step length was calculated as the distance between successive footprints measured parallel to the stride (Equation 4):

Step length = (pace² − trackway width²)^0.5

(4)

The trackway length was calculated by summing all step lengths to represent the distance covered by the trackmaker along its trajectory. The orientation of stride and step lengths was recorded as both azimuth and cardinal direction.

3.4. Asymmetry

Lateral differences were assessed by comparing the mean left- and right-associated values for each parameter across the trackway sections. Individual measurements were grouped according to their anatomical association (right-to-left versus left-to-right), and a mean and standard deviation were calculated for each group and statistically tested (i.e., Welch’s unequal-variance two-sample t-test was applied to the measurements in the two groups to assess whether their means differed, yielding a t-statistic and two-tailed p-value for each parameter). Differences between the means of each group were considered statistically significant at p < 0.05.

3.5. Straightness Index (Tortuosity) and Directional Analysis

Two complementary approaches were used to characterise the straightness and directional behaviour of the LR trackway. The first, straightness index, quantifies how much the trackway deviates from a straight line and is expressed as the ratio of the straight-line distance to the total path length (0 for a closed loop, 1 for a perfectly straight path). The second, directional analysis, quantifies how much the trackmaker’s heading changed from step to step and is expressed in degrees. While these metrics are related, they capture different aspects of locomotor behaviour. For example, a trackway can be spatially very straight (a straightness index near 1) while still exhibiting substantial step-to-step heading instability, because frequent small angular corrections may cancel out over distance. Conversely, a single large turn can lower the straightness index while leaving most of the trackway’s step-level directional consistency high. Together, the two approaches provide a more complete picture of the trackmaker’s navigational behaviour than either alone.

3.5.1. Straightness Index (Tortuosity)

The straightness index was calculated for the entire LR trackway, spanning from the first to the last of 188 footprints (i.e., LR-1, gap, and LR-2). This ratio was derived by dividing the direct linear distance (DL) between the first and last footprint by the cumulative trackway length (TL) [35,36].

In addition to this single whole-trackway value, an incremental straightness index was calculated across all possible multi-footprint windows within each trackway portion. For each window, a DL/TL ratio was computed, identifying the specific footprint intervals where the trackway deviated most from a straight spatial path (Equation 6). This approach captures local-scale sinuosity that may be masked by the high whole-trackway straightness index of an overall near-linear trajectory. Missing footprints were excluded from the analysis.

Straightness Index = DL_i,j/TL_i,j

(6)

3.5.2. Directional Consistency Analysis

To assess whether the steps held a stable or variable path, a directional consistency analysis was conducted. Each step was treated as a vector combining step length (magnitude) with the azimuth of the local stride axis (heading), in which the magnitude of the heading change (i.e., relative to the preceding step) was taken as the angular deviation. Two evaluations were made from this: the magnitude of the local heading change (i.e., at the step level); and the persistence of the deviation (i.e., whether it reflected a genuine, sustained change of course). The magnitude of the local heading change was graded into four bands: very direct (<2°), direct (2–5°), variable(5–10°), and highly variable (>10°). Missing footprint could not be so defined and were excluded from the analysis.

Persistence was evaluated only for steps whose magnitude was graded as highly variable (i.e., >10°) and assessed whether it persisted or not, using a window across the three following steps. Those with a heading the remained shifted were classified as a re-aiming event, while those that returned towards its prior bearing were regarded as a transient swerve. Only the former (i.e., persistent re-aiming events) were used to define boundaries between successive directional segments of the trackway. It is worthwhile noting that this test is not sensitive to an accumulation of gradual course changes (i.e., <10°), which would appear as the segment drifting in its heading, rather than being a discrete re-aiming event.

3.6. Trackmaker Biometrics (Model-Based)

Biometric estimates (relative stride, gait, speed) for an unobservable dinosaur trackmaker are model-based, and while informative in relative terms, these are not to be read as accurate absolute values [37]. Velocity equations were calibrated on extant quadrupedal animals moving at consistent, steady-state gaits [38], while Ruiz and Torices [39] adapted the formula using human athletes as a proxy for bipedal trackmakers. As such, both treat each stride as a sample from a sustained locomotor regime.

The continuous variation in stride length along trackways (including the Lone Ranger) suggest that steady-state locomotion may have only rarely or momentarily been held by a trackmaker, and consequently, each biometric (stride-based) estimate is therefore considered as an instantaneous snapshot rather than a measure of sustained velocity. The relative pattern nonetheless remains informative, with the inference here being that longer strides corresponding to faster travel and shorter to slower, and in this context, variation in calculated velocity serves as a meaningful proxy for changes in locomotor intensity even where the absolute magnitudes are uncertain.

Hip height is also needed to estimate trackmaker biometrics. Following convention, the Paluxy River theropod tracks are attributed tentatively to Acrocanthosaurus atokensis [29], so this taxon was used as the candidate trackmaker for the Lone Ranger trackway. Limb proportions were taken from Scott Hartman’s skeletal reconstruction of Acrocanthosaurus atokensis (skeletaldrawing.com). Assuming a flexed-legged posture, this reconstruction gives a hip height of 3.74 times foot length. Applying this to a footprint length of 38 cm [34] yields a hip height of 1.42 m. Velocity was then estimated using the equation of Ruiz and Torices [39] (Equation 7):

v = 0.226 × (9.8^0.5) × (stride^1.67) × (hip height^-1.17)

(7)

Relative stride (stride length divided by hip height) was used to classify gait following Alexander [38]. Values below 2.0 indicate walking, values above 2.9 indicate running, and intermediate values indicate a gait equivalent to the quadrupedal trot. Speed at gait transitions was estimated using Equation 6, substituting stride values of 2× hip height (walk-trot) and 2.9× hip height (trot-run).

4. Results

4.1. Trackway Completeness and Parameters

The Lone Ranger (LR) trackway extends 158.11 m along the track surface and comprises an estimated 188 footprints, of which 158 are preserved (84.0% complete; Figure 2). It consists of two segments separated by a gap. The first segment (LR-1) is 110.12 m long and contains 130 of an expected 135 footprints (96.3% complete); tracks LR-1-22, -65, -114, -115, and -123 are absent. A 21.50 m gap, oriented ~243° (WSW) and inferred to have had 24 footprints, separates LR-1 from the second segment (LR-2). LR-2 is 26.49 m long and contains 28 of an expected 29 footprints (96.6% complete; LR-2-14 absent).

Trackway parameters for LR-1 and LR-2 are summarised in Table 2 (see also Figs 2–3). Strides were longer in LR-2 than in LR-1 (mean 189.4 vs 164.9 cm), as were paces (mean 102.0 vs 87.8 cm). LR-2 was also wider (mean trackway width 36.6 vs 26.1 cm) and had a lower mean pace angulation (135.8° vs 143.7°). Crossover steps, in which a footprint lies across the trackway midline, occurred only in LR-1, at three of 120 assessed steps (2.5%; LR-1-111, -112 and -131). Stride orientation shifted from predominantly southwestward in LR-1 (mean azimuth 229.8°; first stride 208.4° SSW, last 267.0° W) to predominantly westward in LR-2 (mean 263.7°; first 250.4° WSW, last 284.4° WNW; Figure 5A).

4.2. Asymmetry

No significant differences were found between right-to-left and left-to-right measurements in either segment (Welch’s t-tests; Figure 4; Table 3). In LR-1, the two sides had nearly identical means for all six parameters (all p ≥ 0.67). In LR-2, left-to-right paces and steps were nominally longer than right-to-left ones (pace 107.4 ± 23.0 vs 96.6 ± 11.9 cm; step 100.1 ± 26.7 vs 86.7 ± 17.6 cm; mean ± SD), but neither difference was significant (both p = 0.151). The remaining parameters also showed no significant differences (all p ≥ 0.35).

4.3. Straightness Index and Directional Consistency Analysis

4.3.1. Straightness Index (Tortuosity)

The LR trackway is nearly straight. The straight-line distance (DL) from the first to the last footprint is 151.37 m and the trackway length (TL) is 158.11 m, giving a straightness index of 0.957 (Table 4). Each segment is straighter on its own (LR-1: 0.977; LR-2: 0.989), because the whole-trackway value also captures the change in heading between LR-1 and LR-2 (Figure 5A). In the incremental analysis, the least straight sections were LR-1-1 to -7 (0.937), at the start of the trackway, and LR-2-7 to -11 (0.956).

Figure 5. Trackway orientation and directional consistency for the LR-1 and LR-2 portions of the Lone Ranger theropod trackway, from the Dinosaur Valley State Park, the lower Glen Rose Formation, Texas, USA. Stride orientation represented as (A) scatter plot, (B) Rose diagram, and (C) polar plot. (D) Coordinate plot of the LR trackway with intra-trackway directional variation colour-coded, with cool colours having low directional change and warm colours being more variable. Asterisks denote segment boundary, marking change in direction; grey line within trackway indicated missing footprints.

Figure 5. Trackway orientation and directional consistency for the LR-1 and LR-2 portions of the Lone Ranger theropod trackway, from the Dinosaur Valley State Park, the lower Glen Rose Formation, Texas, USA. Stride orientation represented as (A) scatter plot, (B) Rose diagram, and (C) polar plot. (D) Coordinate plot of the LR trackway with intra-trackway directional variation colour-coded, with cool colours having low directional change and warm colours being more variable. Asterisks denote segment boundary, marking change in direction; grey line within trackway indicated missing footprints.

4.3.2. Directional Consistency

Although the trackway is nearly straight overall, its heading changed continuously at the step scale in both portions (Table 5). In LR-1, the heading shifted from 208.4° (SSW) at the first stride to 267.0° (W) at the last, a net reorientation of 58.6°. The mean change per step was 6.0°, and the largest single change (31.9°) occurred between LR-1-24 and LR-1-25. Of 124 steps, 31 (25%) were classed as very direct, 32 (26%) as direct, 40 (32%) as variable and 21 (17%) as highly variable, and 13 directional segments were identified.

In LR-2, the heading shifted from 250.4° (WSW) to 284.4° (WNW), a net reorientation of 34.0°. The mean change per step was 5.9°, and the largest single change (31.6°) occurred between LR-2-9 and LR-2-10, within the least straight section identified in Section 4.3.1. Of 25 steps, 5 (20%) were very direct, 8 (32%) direct, 9 (36%) variable and 3 (12%) highly variable, with three directional segments.

4.4. Trackmaker Biometrics

The LR trackmaker had an estimated hip height of 1.41 m (Figure 6C). Relative stride indicated a walking gait throughout both segments, ranging from 0.50 to 1.54 in LR-1 (mean 1.17) and from 0.76 to 1.84 in LR-2 (mean 1.34), all below the walk–trot threshold of 2.0 (Figure 6A; Table 6). Estimated velocity was correspondingly higher in LR-2 (mean 5.04 km/h; range 1.91–8.38 km/h) than in LR-1 (mean 3.98 km/h; range 0.96–6.21 km/h; Figure 6B). For a hip height of 1.41 m, the walk–trot and trot–run transitions (relative stride 2.0 and 2.9) correspond to 9.6 and 17.9 km/h, respectively, so even the fastest stride in LR-2 remained below the walk–trot transition.

5. Discussion

The Lone Ranger trackway extends 158.11 m and comprises an estimated 188 footprints, of which 158 are preserved, making it the longest theropod trackway documented along the Paluxy River [29,31]. Both segments are more than 96% complete, so despite the 21.50 m gap between them, the trackway provides an unusually long sequential record of a single trackmaker.

5.1. One Gait, Continuously Modulated Locomotion

The Lone Ranger trackway shows that a constant gait need not mean constant locomotion. Footprint spacing varied throughout both segments, with stride length ranging from 71 to 260 cm, and LR-2 was shifted towards wider spacing than LR-1 (mean pace 88 vs 102 cm; step 83 vs 94 cm; stride 165 vs 189 cm). These are direct measurements of trackway geometry and do not depend on how gait is modelled.

The gait interpretation is necessarily more inferential. Under the Alexander framework [38], relative stride (0.50–1.84) stays below the walk–trot threshold of 2.0 throughout, so every preserved stride is consistent with walking. Within that single category, the corresponding velocity estimates range from 0.96 to 8.38 km/h, with means of 3.98 km/h in LR-1 and 5.04 km/h in LR-2. Because these velocities are calculated from stride and a fixed hip height, they re-express the measured variation in terms of speed rather than providing independent evidence for it. They are best treated as proxies for progression rate rather than measurements of the animal’s actual speed [37,40,41,42].

The distinction matters because gait classification is coarse: “walking” covers every relative stride below 2.0. In the Lone Ranger trackway, substantial variation occurs within that range, both from step to step and between segments. This variation does not indicate a steady acceleration or a series of discrete behavioural states. Rather, it reflects repeated adjustment of stride around a gait that remained broadly stable. The 21.50 m gap also cautions against treating LR-1 and LR-2 as discrete states, because how locomotion changed between them is unknown. A stable gait category and variable locomotion are therefore features of the same record, seen at different scales.

5.2. A Straight Trackway Made by Continuous Steering

At the scale of the complete trajectory, the Lone Ranger trackway is remarkably direct. Its whole-trackway straightness index of 0.957 approaches the value of 1 expected for a perfectly straight path [35,36,43], while the two preserved portions are straighter still (LR-1, 0.977; LR-2, 0.989). Considered only through this metric, the trackway could reasonably be characterised as near-linear. That description is geometrically correct, but it does not describe how that trajectory was produced.

Preserving the order of successive footfalls reveals continuous modulation of heading within the near-linear path. Across LR-1, heading shifted overall from 208.4° to 267.0°, while successive steps differed in heading by a mean of 6.0°. LR-2 similarly underwent stepwise directional adjustment, with a mean change of 5.9°, despite a smaller net reorientation from 250.4° to 284.4°. These changes are unlikely to be artefacts of digitising: to produce a mean change of 6.0° by measurement error alone, footprint-centre positions in LR-1 would need an error with a standard deviation of about 11 cm, more than a quarter of footprint length. Thus, neither preserved portion records maintenance of a single fixed bearing. Instead, the apparently straight trajectory emerged from successive directional adjustments. Straightness in this sense is an outcome of the locomotor sequence, rather than evidence of directional constancy within it.

The two portions also show why directional variability cannot be reduced to a single measure. Mean stepwise heading change is similar in LR-1 and LR-2 (6.0° and 5.9°). Once sequence length is accounted for, so is the frequency of directional segments (13 in 124 steps vs 3 in 25, or about 10 and 12 per 100 steps), although the LR-2 count is small. Net reorientation, however, differs: LR-2 turned 34.0° over 26.49 m, more than twice the rate of LR-1 (58.6° over 110.12 m; 1.28 vs 0.53° per metre). Mean stepwise change, net reorientation and directional segmentation therefore describe different properties of the ordered trajectory and should not be treated as interchangeable summaries of directional behaviour.

These differences expose complementary limitations of conventional directional summaries. The straightness index reduces a trackway to the ratio of direct displacement to path length, so it cannot show where directional adjustments occurred or whether successive deviations accumulated or cancelled [35,36,43]. A rose diagram retains the distribution of headings but discards their order (Figure 5B), and it is often reduced further to a single mean direction. Two trackways with the same distribution of headings would therefore produce identical rose diagrams, even if one changed bearing progressively and the other oscillated back and forth. Neither representation is incorrect; each describes a different property of the trackway [36]. An order-preserving, step-resolved analysis adds the missing sequential structure, distinguishing sustained reorientation from transient or self-cancelling variation [10].

The Lone Ranger trackway therefore remained spatially direct without being directionally invariant. Its near-linear form was maintained while heading was continuously modulated from step to step, showing that an apparently simple trackway can contain a considerably richer locomotor record than its overall geometry suggests. The same issue of scale extends beyond direction: variation that appears transient when individual steps are considered may acquire, or lose, biological significance only when evaluated across a sufficiently long sequence.

5.3. Long Trackways Distinguish Sustained Patterns from Local Variation

Unequal left- and right-initiated pace or step lengths have been reported from a range of dinosaur trackways and are conventionally interpreted as evidence of limping, although behavioural laterality has been proposed as an alternative explanation for at least some cases [11,12,13]. Distinguishing between these interpretations, or between either of them and ordinary step-to-step variation, requires knowing whether the disparity is sustained [10,16,44]. That is what a short trackway cannot establish and an unusually long one can.

The Lone Ranger sequence contains an apparent disparity of this kind. In LR-2, left-to-right paces average 107.4 cm compared with 96.6 cm for right-to-left paces, a difference of approximately 11 cm. Across the complete portion, however, neither pace nor step asymmetry is statistically significant (pace, p = 0.151; step, p = 0.151), and no significant left–right difference occurs in the substantially longer LR-1 portion or among the other tested trackway parameters. The analysis therefore provides no statistical support for a persistently expressed lateral asymmetry in either preserved portion, and the present measurements do not require either a marked limp or a sustained lateral preference to explain the observed variation.

The value of that negative result lies in the distinction it permits. With about 13 paces per side, LR-2 could only have detected a pace disparity of roughly 20 cm (about 20% of mean pace; two-tailed α = 0.05, 80% power), so the observed 11 cm difference cannot be distinguished from step-to-step variation over that span. LR-1, with 125 paces, could have detected a difference of roughly 7 cm, yet its left-to-right and right-to-left paces differ by only 0.1 cm. Had a disparity of the size seen in LR-2 persisted through LR-1, the longer sequence would very likely have revealed it. Within a continuously modulated trackway, local runs of unequal left–right measurements can therefore arise without characterising the trackmaker’s locomotion across the larger record. The Lone Ranger trackway shows why apparent asymmetry over a restricted interval should not, by itself, be treated as evidence of either pathology or behavioural lateralisation.

As shown in Section 5.1, stride length varies widely within a single modelled gait category (i.e., walking). A short sequence of comparatively long or short strides could therefore provide a valid description of that local interval while revealing little about how persistent that locomotor state was along the broader trackway. Long trackways add more than additional measurements: they provide the sequential extent needed to distinguish a locally expressed state from a sustained locomotor pattern.

5.4. From Trackway Geometry to Trackmaker Behaviour

The walking gait recorded along the Lone Ranger trackway varied in three respects: the forward spacing of successive footprints, their lateral placement relative to the trackway midline, and the direction of travel. LR-2 has greater mean pace, step and stride lengths than LR-1. It is also wider and differently oriented, and lacks crossover steps. The difference between the portions is therefore multidimensional: LR-2 records a different combination of forward progression, lateral placement and direction of travel, not simply a longer version of the same step geometry.

The greater forward spacing of footprints in LR-2 is consistent with faster progression within the same modelled walking category. The more informative question is whether the accompanying changes in lateral placement and orientation reflect locomotor adjustment by the trackmaker, differences in track–substrate interaction, or both [45].

Trackway width shows that LR-2 is not simply a scaled-up version of LR-1. Mean width increases by about 40% (from 0.26 to 0.37 m), whereas mean stride increases by about 15%. The wider geometry could represent a genuine change in limb placement associated with directional or postural adjustment. Alternatively, variation in substrate properties could have altered how successive footprints were registered [27,46,47,48]. Because the overlays record two-dimensional track positions but not impression depth or sediment deformation, these possibilities cannot presently be distinguished (Section 5.6).

Lateral placement also varies within LR-1. Three crossover steps occur late in that portion (LR-1-111, -112 and -131), whereas none occurs in LR-2. As only 3 of 120 assessed steps, they represent brief departures from the usual alternating placement rather than a persistent configuration. The data do not establish whether these events reflect locomotor adjustment, turning, substrate interaction or another cause. What they show directly is that lateral foot placement was itself variable.

The portions also differ in orientation: LR-1 is predominantly southwestward, whereas LR-2 is predominantly westward. Some of the differences in spacing and width may have accompanied this reorientation, but the two-dimensional record cannot establish their order or separate them from substrate-related effects. The 21.50 m gap compounds this. Because the footprints that would record the transition are missing, the data show only that LR-1 and LR-2 differ, not whether the change between them was gradual or abrupt. The two portions are therefore best treated as samples from one continuously varying sequence, not as two ways of walking with a switch somewhere in the gap. Even the difference in mean orientation (229.8° vs 263.7°) does not mark a switch, because the last stride of LR-1 (267.0°) is already westward.

5.5. Legacy Georeferenced Records as Observational Data

The Lone Ranger analysis shows that a georeferenced archival record can support quantitative questions beyond those it was produced to answer. The TPWD overlays were created during the 2008–2009 mapping programme to document the Dinosaur Valley State Park tracksites, yet they retain enough positional information to derive footprint locations, trackway geometry and ordered locomotor parameters retrospectively. Here they supported analysis of the full 158.11 m trackway without new field measurement.

This matters most for long trackways. Field measurement becomes increasingly demanding as trackway length and footprint number increase, in addition to accessibility to challenging sites [7,14,15,24,25,27]. Long trackways also expose a limitation in the way locomotor data are commonly summarised. Trackway studies frequently report characteristic values such as mean pace, stride, or estimated speed [14,26], whereas a georeferenced record, once imported into a digital environment, can be assessed repeatedly. The KMZ-to-Blender workflow used here reconstructed footprint positions in a common metre-scaled coordinate system and subjected the sequence to automated trackway, directional and model-based analyses (Supplementary Code S1). This does not replace field observation or 3D documentation. It does separate many spatial analyses from the need for new fieldwork, and it makes comprehensive treatment of long sequences practical wherever comparable records exist.

Public availability also makes the analysis reproducible. TPWD did not supply footprint coordinates as vector data; they were derived from the published georeferenced raster overlays (Section 3.2). Because that transformation is documented, the footprint positions and every parameter calculated from them can be independently regenerated, checked and reanalysed.

The kind of signal recovered here shows why this matters. Although the Lone Ranger trackway is exceptionally long, it records no gait transition and no statistically supported lateral asymmetry. Much of its information lies instead in step-to-step changes in stride and heading that emerge only when the sequence is analysed in order. Recovering them requires a record that retains footprint positions and their sequence, not just summary measurements. A trackway without a conspicuous behavioural anomaly can therefore still preserve substantial sequential structure.

Legacy spatial datasets thus allow new questions to be asked of existing tracksite records. Where their spatial fidelity is adequate, they also allow long locomotor sequences to be analysed at a resolution that may not have been practical when the sites were first documented. That potential is ultimately limited by the quality and dimensionality of the archival record, which makes the uncertainties of the TPWD overlays central to assessing how far the present interpretations can be taken.

5.6. Limitations

The evidential strength of the present analysis differs among the quantities derived from the TPWD overlays. Inter-footprint distances, orientations and trackway geometry are calculated from the spatial positions of footprint landmarks and therefore depend principally on the positional fidelity of the georeferenced source record. The depicted footprint outlines, by contrast, are simplified and near-uniform, and their correspondence to the original track margins is uncertain [49]. This distinction particularly affects quantities derived from footprint dimensions: the estimated hip height, and consequently relative stride, velocity and the other trackmaker biometrics, inherit uncertainty from both footprint-length measurement and the anatomical scaling model [40]. These quantities should therefore be regarded as model-based interpretations of the spatial record rather than measurements equivalent in status to pace, stride or orientation.

The absence of three-dimensional track morphology imposes a different limitation. The overlays contain no information on impression depth, displacement rims or subsurface deformation, and substrate conditions were not characterised sedimentologically along the trackway. Variation in substrate consistency, moisture content or depth of foot penetration can influence both the morphology of individual tracks and the registered spacing between them [45,50,51,52,53], meaning that changes along the sequence cannot be attributed uniquely to changes in locomotor behaviour. This bears particularly on differences between the two preserved portions, including their contrasting stride geometry and trackway width. The present data establish that the registered trackway geometry varies; they cannot resolve how much of that variation originated with the trackmaker and how much with changing track–substrate interaction.

Directional measurements depend on the positional fidelity of the footprint landmarks. Positional error has not been independently quantified for the TPWD overlays, so no empirical uncertainty can be assigned to individual headings, and single step-to-step differences should be treated with caution. The aggregate pattern is more robust: as shown in Section 5.2, measurement error alone would require footprint-centre errors with a standard deviation of about 11 cm to produce the mean heading change observed in LR-1.

Trackway incompleteness has a more restricted effect than its overall percentage might suggest. Of the 30 inferred footprints that are absent, 24 fall within the 21.50 m gap between LR-1 and LR-2, leaving five isolated missing footprints in LR-1 and one in LR-2. The gap prevents direct reconstruction of how trackway geometry and heading changed between the two portions. LR-2 nevertheless contains far fewer observations than LR-1, which limits the size of left–right difference it can resolve (Section 5.3).

These limitations constrain different levels of interpretation rather than weakening the same result uniformly. Confidence is greatest that the Lone Ranger trackway records substantial variation in spatial geometry and heading across an unusually long preserved track sequence. Confidence is lower in assigning particular components of that variation exclusively to locomotor adjustment, and lower again in treating absolute model-derived speeds or other biometric quantities as exact properties of the trackmaker. Three-dimensional documentation coupled with sedimentological characterisation would provide the most direct means of separating locomotor changes from foot-substrate-interactions [45], and would allow the spatial patterns identified here to be tested against the morphology of the individual tracks themselves.

6. Conclusions

The Lone Ranger trackway is the longest theropod trackway documented along the Paluxy River, extending 158.11 m across two highly complete portions and providing an unusually long sequential record of theropod locomotion. Its principal significance lies in the contrast between stability at one scale and variability at another. Relative stride consistently indicates a walking gait, while the trackway geometry shows substantial change of stride length, lateral foot placement and heading. Likewise, a near-linear overall path is built from repeated step-to-step directional adjustment: spatial straightness does not imply directional constancy.

The length of the record also allows local variation to be distinguished from a sustained pattern. An apparent difference between left-to-right and right-to-left paces is present in LR-2 but is not statistically significant, whilst LR-1 shows none. The trackway therefore provides no evidence of a persistent limp or lateral preference. More generally, short intervals of a variable trackway may accurately describe local locomotion without characterising the broader movement sequence.

These findings support treating long trackways as continuous locomotor records rather than reducing them to mean parameters. They also show that publicly available georeferenced tracksite records can be reused as observational datasets for new spatial measurements and behavioural questions. Combining conventional trackway parameters with order-preserving directional analysis can recover locomotor modulation concealed within apparently simple trackways. Separating the trackmaker’s contribution from that of the substrate, however, will require three-dimensional and sedimentological documentation.