Mudskippers use tail thrusting to help crutching to move on mud of various wetness

Introduction

• Research has left relatively little known about how amphibious fishes adjust movement on wet flowable substrates of varying wetness.Previous studies of amphibious fishes on wet flowable substrates had not precisely controlled and systematically varied wetness.Source: §1 · pp. 4–5
• Mud poses linked locomotor challenges because its yield strength and stickiness vary with wetness, and it can penetrate weakly and pull downward and backward on animals.Highly cohesive mud can be up to two orders of magnitude weaker in resisting vertical penetration than dry or weakly cohesive wet sand.Source: §1 · p. 5
• The study tests mudskipper locomotion on clay mud of varying wetness, using clay as a controllable model for ecologically relevant muddy substrates.In the solid–transition regime, clay mud’s yield strength and cohesion depend on wetness, which can be varied through solid volume fraction.Source: §1 · p. 5
• The authors hypothesize that mudskippers adjust crutching or switch locomotor modes as mud wetness changes.They propose that mud affects locomotion in more complex ways than sand and that movement changes help cope with shifts in mud strength and stickiness.Source: §1 · p. 6
• To test these ideas, the study prepares clay mud at different wetness levels plus dry clay and measures mud properties with penetration, extraction, and horizontal-drag tests.The tests characterize how yield strength and stickiness vary with wetness.Source: §1 · p. 6

• Animal experiments tested crutching gait adjustment in relation to mud mechanics by measuring performance, sinkage, body– and fin–mud contact, 3-D kinematics, and weight support.The measurements included sinkage and weight support by the body and fins.Source: §1 · p. 6
• The experiments tested whether the animal switched to other locomotor modes by quantifying transitions to those modes.Source: §1 · p. 6

2.1. Mud wetness control

• Mud mixtures at ϕ = 27%, 34%, and 39% covered the solid–fluid transition, while ϕ = 42% represented fractured mud.Georgia Kaolin was mixed with water and prepared in a large container.Source: §2.1 · p. 7
• Dry fractured-regime mud was made by drying wet mud in an uncovered container for several days, but its exact ϕ could not be calculated.Plastic wrap, rubber sealing strips, and straps were used to limit evaporation during animal experiments.Source: §2.1 · p. 7

2.2. Characterization of mud yield strength and stickiness

• Yield strength was characterized with custom penetrometers by vertically penetrating and extracting a 3 cm-radius horizontal disc, measuring vertical force, with three trials per ϕ and upward lift force at 1 cm depth.For dry mud, force on a 3 cm-radius disc at 1 cm depth was estimated as ~6000 N.Source: §2.2 · p. 9
• During animal experiments, mud strength increased by 31–184% over 24–114 days for four tested ϕ values (Ramesh et al., submitted); sealing made this drift much smaller and slower than open drying’s 133-fold increase in 7 days.Source: §2.2 · pp. 9–10
• Stickiness across ϕ = 27%, 34%, and 39% was assessed by observing mud detachment in vertical penetration and horizontal drag tests.Horizontal tests dragged a cylinder across the mud surface; videos were used to observe how quickly mud flowed off the intruder.Source: §2.2 · p. 10
• A 200 g disc was allowed to sink into mud under its own weight, then extracted to measure sinkage and observe how much mud stuck to it.Side and oblique-view videos were recorded for these observations.Source: §2.2 · p. 11

2.3. Animals

• Five Atlantic mudskippers (Periophthalmus barbarous) were tested; mean mass was 19.33 ± 4.76 g and mean body length was 12.73 ± 1.65 cm.Mean height was 2.33 ± 0.48 cm.Source: §2.3 · p. 11

2.4. Experimental setup and protocol

• Six synchronized high-speed cameras recorded crutching to measure locomotor performance, 3-D kinematics, sinkage, mud contact, and mud sticking.The cameras recorded at 100 frames/s and 2592 × 2048 pixels.Source: §2.4 · pp. 11–12
• Two webcams recorded all daily sessions to quantify locomotor-mode transitions, crutching with or without tail thrusting, and jumping.The cameras captured top and side views at 30 frames/s.Source: §2.4 · p. 12
• Calibration produced a mean 3-D reconstruction error of 0.13 ± 0.07 cm, compared with a typical 0.5–4.5 cm range in measured crutching positions.The reported calibration error was small relative to the kinematic measurements.Source: §2.4 · p. 12
• Each mudskipper was accustomed to each mud wetness before testing and rested for 10–15 minutes in shallow water after each session.Animals that stopped moving were gently prodded; those drying out or heavily coated with mud were briefly cleaned in water.Source: §2.4 · p. 13
• Mud strength was measured at undisturbed locations after trials to track long-term drift, and disturbed mud was manually mixed and flattened between trials.Different mud wetnesses were used on different days.Source: §2.4 · p. 13

Definition of crutching trials and cycles

• Crutching trials were straight-line sections of continuous movement, with each cycle running from one touchdown of both pectoral fins to the next.Cycles were divided into stance and swing according to whether the fins touched the substrate or moved in the air; trials near the testbed boundary were rejected.Source: §2.5 · pp. 13–14

Crutching performance analysis

• Performance analysis measured forward displacement per cycle (Δx) and average forward speed (vc), using ≥5 cycles on ϕ = 42% and dry mud, and 1–11 cycles on ϕ = 27%, 34%, and 39%.All trials were used on the latter muds because animals often stopped after 1–4 cycles; the sample sizes are listed in Table 1.Source: §2.5 · p. 14

Crutching 3-D kinematics analysis

• 3-D kinematics were compared across mud wetness in trials with at least four cycles and visibility in three or more camera views.Comparisons covered cycle start and end, mid-swing, and the timing of mid-stance, swing onset, and mid-swing; ϕ = 27% was excluded because mud obscured tracking.Source: §2.5 · pp. 14–15, Table 1 · p. 15

Crutching mud interaction analysis

• Mud-interaction analysis measured body sinkage, body–mud and fin–mud contact length, fin sinkage, upward substrate force, and mud sticking to the animal.These measurements tested Hypotheses 1 and 2; sample size is reported in Table 1, data row 2.Source: §2.5 · p. 14

Locomotor transitions and other mode analysis

• Locomotor-mode analysis quantified transitions, normal crutching and tail-thrusting variants, jumps, and forward jump displacement from animal-initiated modes inside the testbed.Modes and transitions were identified from webcam video; jump displacement used webcam and high-speed videos, excluding jumps near the testbed boundary.Source: §2.5 · pp. 14–15

2.6. Crutching performance measurements

• Snout-marker tracking from top-view high-speed video provided forward displacement per cycle along the direction of each straight trial.The marker was manually digitized using DLTdv.Source: §2.6 · p. 16
• Cycle speed was averaged across cycles to obtain trial-average forward speed, with each cycle spanning one pectoral-fin touchdown to the next.Forward displacement per cycle was tracked from the snout marker over each straight trial.Source: §2.6 · p. 16

2.7. Crutching body sinkage and mud contact measurements

• Body sinkage was measured from near-side video by comparing the animal’s height with the mud surface at mid-swing, when sinkage was maximal.The researchers tracked the second dorsal-fin marker and the mud rise on the body directly below it.Source: §2.7 · p. 16
• The animal’s height above the mud was estimated from the second dorsal-fin marker and the lowest body point below it while the animal was off the mud.That height and the mud-surface height were used to calculate sinkage via Eqn. 2.Source: §2.7 · p. 16
• Body–mud contact length was measured from side-view video at mid-stance, when lifting was maximal.Source: §2.7 · p. 17
• Fin–mud contact length was assessed at mid-stance, and fin and body contact areas were estimated from their contact-length ratio.Because fin size made direct measurement challenging, contact lengths were used as proportional to contact areas, measured from top-view video; near-side video helped identify contact.Source: §2.7 · p. 17
• High-speed videos were also visually inspected for mud interactions, including whether mud stuck to the animal and whether it struggled to get out.Source: §2.7 · p. 17

2.8. Crutching fin sinkage and body and fin lift calculations

• Because substrate force on the animal’s body and fins could not be measured, vertical force on a penetrating disc and horizontal force on a dragged rod served as estimates.The section refers to Sec. 2.2 for these measurements.Source: §2.8 · p. 17
• Body and fin lift were estimated as F_b = C_L · A_b · d_b and F_f = C_L · A_f · d_f, assuming lift scales with sinkage and contact area.The proportionality assumption applies to shallow disc penetrations up to 4 cm, the range observed in the mudskipper.Source: §2.8 · pp. 17–18
• At mid-stance, body lift was calculated from crutching sinkage and body–mud contact, while fin sinkage was inferred from fin–mud contact and fin-generated upward force.Fin sinkage was difficult to measure directly; the body and fins together were treated as supporting the body.Source: §2.8 · p. 18
• Expected fin sinkage across the tested mud wetnesses was also calculated assuming constant fin contact area, using the area measured at ϕ = 42%.These estimates are shown as dashed lines in panel D of Fig. 9.Source: §2.8 · p. 18

Crutching 3-D kinematics measurements

• Kinematics were analyzed for mud strengths ϕ = 34%, 39%, 42%, and dry mud, but not ϕ = 27%, where mud covered the fins and most of the body.Source: §2.9 · p. 18

Tracking

• Three high-speed views tracked the snout, tail tip, body midline, and pectoral fin tips and shoulders to measure crutching movements.DeepLabCut was used for tracking.Source: §2.9 · p. 18

3-D reconstruction

• Tracked points were reconstructed in 3-D, aligned so each trial’s forward direction was the +x-axis, and used to calculate marker velocities.Velocities included fore-aft, lateral, vertical, and total velocity.Source: §2.9 · p. 19

Angle calculation

• Fin retraction, lateral ending, fin depression, and vertical ending angles were calculated, with minimum fin retraction and depression angles during stance compared across mud wetness.Source: §2.9 · pp. 19–20

Cycle averaging

• Cycle-averaged kinematics were calculated by offsetting time and kinematic data to each cycle’s start and normalizing time within the cycle.Source: §2.9 · p. 20

Kinematic features comparison

• Comparisons across wetness included duty factor, mid-swing time, maximal snout vertical displacement, and maximal fin displacements; fin lateral displacement identified mid-swing and swing onset.Source: §2.9 · p. 20

• Small-tail-bending crutching added a slight tail bend at stance that straightened slowly, generating little propulsion and no or partial body lift for only one or two cycles.Source: §2.10 · p. 21
• On mud at ϕ = 27%, large-tail-bending crutching persisted across multiple cycles and propelled part of the body upward and forward, likely generating upward substrate force and forward thrust.Source: §2.10 · p. 21
• In forward jumps, the mudskipper bent and rapidly straightened its tail while pushing its tail and fins downward and backward to launch upward and forward, usually landing without self-righting in the air.Occasionally on dry mud, it self-righted on the ground after landing on its side.Source: §2.10 · p. 22
• In vertical jumps, the mudskipper tilted its head farther upward and pushed its tail and fins downward and backward, then extended its fins while falling and landed on its belly and fins.Source: §2.10 · p. 23
• Other defined actions included wiggling both fins against mud to dig in and rapidly bending the head and tail into a shape to turn.Source: §2.10 · p. 23

Locomotor mode transitions

• Webcam-recorded session sequences were used to map locomotor transitions and calculate each transition’s frequency relative to transitions from its start mode.Diagrams retained non-self transitions above 0.089 and newly emerging transitions below that threshold.Source: §2.11 · p. 24

Relative frequency of crutching with/without tail thrusting

• Crutching-mode frequencies were calculated from average counts across animals and sessions for normal crutching and small- or large-tail-bending crutching.Each mode’s relative frequency was its average count divided by the summed average counts of these three modes.Source: §2.11 · p. 24

Jumping frequency and displacement

• They measured vertical- and forward-jump frequency per session and forward-jump horizontal displacement by tracking the snout at each jump’s start and end.Snout positions were manually tracked with the DLTdv digitizing tool.Source: §2.11 · pp. 24–25

Crutching performance statistical tests

• Crutching displacement, speed, and stride frequency showed no trial or individual effects, while cycle count varied by trial but not individual.Trial averages were pooled by mud wetness for the performance measures.Source: §2.12 · p. 25

Crutching sinkage, mud contact and mechanics statistical tests

• Body sinkage, body–mud and fin–mud contact, mid-stance weight support, and fin sinkage were tested across wetness, with no individual effects detected.The analyses used linear mixed-effects models with individual as a random effect.Source: §2.12 · pp. 25–26

Jumping statistical tests

• Jump frequency and forward jump displacement were compared across mud wetness, and neither showed an individual effect.Linear mixed-effects models treated individual as a random effect.Source: §2.12 · p. 26

Crutching 3-D kinematics averaging

• Crutching 3-D kinematics were interpolated to normalized time, with linear interpolation filling missing segments up to 5%T before averaging across trials and individuals.The measures included velocities, cycle displacements, body bending, and fin retraction and depression angles.Source: §2.12 · p. 26

Body 3-D position and fin placement instance statistical tests

• Maximum snout vertical displacement and mid-stance timing, plus swing-start and mid-swing timing, showed no trial or individual effects.These measures were tested across mud wetness using linear mixed-effects models.Source: §2.12 · p. 27

Fin 3-D position and fin angle statistical tests

• Lateral fin placement and fin retraction and depression angles showed no trial or individual effects; forward fin displacement had a trial effect likely due to inaccurate tracking.The text also reports an individual effect for forward displacement as P < 0.05.Source: §2.12 · p. 28

3.1. Dependence of mud yield strength and stickiness on wetness

• Yield strength increased monotonically as mud dried and rose exponentially from ϕ = 27% to 42%.Weaker mud at ϕ = 27% was 1–2 orders of magnitude weaker than dry and wet sand.Source: §3.1 · p. 29, Figure 4 · p. 30
• Stickiness peaked at intermediate wetness, rising from medium at ϕ = 27% to high at ϕ = 34%, then falling to low at ϕ = 39% and 42%.Mud stuck to the disc or cylinder and pulled opposite to their motion.Source: Figure 4 · p. 30, §3.1 · pp. 30–31
• Mud stuck most to the disc at ϕ = 27%, despite peak stickiness at ϕ = 34%, because weaker mud allowed greater sinkage and contact area.The animal likewise sank more deeply on mud at ϕ = 27% than at ϕ = 34%, causing more mud to stick and pull downward and backward as it moved.Source: Figure 4 · p. 30, §3.1 · p. 31

3.2. Crutching performance and behavior

• On wetter mud, the animal used lower stride frequencies and sustained fewer crutching cycles: near 1 Hz and usually one cycle at ϕ = 27%, versus near 2 Hz and 4–5 cycles on drier mud.The animal regularly sustained 4–5 cycles as mud became drier.Source: §3.2 · p. 32
• Crutching performance improved as mud dried from ϕ = 27% to 42%, with speed and displacement per cycle rising, then declined slightly on dry mud.The animal predominantly crutched at all tested wetnesses except the wettest mud (ϕ = 27%).Source: §3.2 · pp. 31–32, Figure 5 · p. 33

3.3. Animal–mud interaction during crutching

• Body sinkage was about 10 times deeper on mud at ϕ = 27%, 37%, and 39% than at ϕ = 42% and on dry mud, with body–mud contact length reaching 90% BL at ϕ = 27%.Pectoral fins also sank farther into weaker, wetter mud.Source: §3.3 · p. 32, Figure 5 · p. 33
• As ϕ fell from 42% to 27%, fin support declined from 94% to about 2/3 of average body weight, while body support rose from 3% to 1/3.The passage associates these changes in support with increased fin and body sinkage on wetter, weaker mud.Source: Figure 7 · p. 35, §3.3 · p. 35
• On very weak mud, the fish spread its fins to limit sinkage, but greater body and fin contact plus mud sticking and extraction forces impeded crutching.At ϕ = 27%, fin sinkage under a constant-contact-area estimate was ~50% deeper than actual; the animal struggled to raise itself, reducing displacement per cycle and stride frequency.Source: §3.3 · pp. 36–37

3.5. Crutching kinematics

• Despite major changes in animal–mud interaction, crutching kinematics remained mostly conserved across mud wetness, with lifting then falling during stance and forward propulsion.Maximal body lifting and fin motions were also similar across wetness; lateral motion was almost absent.Source: §3.5 · p. 37, Figure 8 · p. 38

3.6. Tail bending to assist crutching on challenging mud

• At ϕ = 34% mud, small and large tail bending assisted crutching 5% and 8% of the time; on dry mud, they occurred 3% and 1% of the time.At ϕ = 34%, large bending generated upward lift and forward thrust; on dry mud, quickly dried mucus made the fins stick and increased body friction.Source: §3.6 · p. 39
• On the wettest mud (ϕ = 27%), large-tail-bending crutching dominated (79% of attempts), while normal crutching occurred only 5% of the time.Small-tail-bending crutching occurred 16% of the time, but was less effective and the animal could move only one cycle.Source: §3.6 · p. 39, Figure 9 · p. 40

3.7. Use of other locomotor modes on challenging mud

• The fish also used forward and vertical jumps, turning, and digging, and transitions among locomotor modes varied with mud wetness.On the wettest mud (ϕ = 27%), it never jumped vertically or turned, which the authors attributed to deep sinkage and substantial mud sticking.Source: §3.7 · pp. 41–42
• On all drier mud, normal crutching was the most frequent locomotor mode, followed by forward jumping; vertical jumps occurred only on dry mud.The animal sometimes jumped vertically after stopping and switched repeatedly among locomotor modes and stopping.Source: §3.7 · pp. 42–43
• Jumping was more frequent on weaker, stickier mud (ϕ = 34%) and dry mud than on stronger mud (ϕ = 39% and 42%; P < 0.005).The comparison combines vertical and forward jumps.Source: §3.7 · p. 42
• On mud with ϕ = 34%, tail thrusting during forward jumps propelled the body upward and forward to overcome drag from mud sticking to it.On dry mud, jumping helped the fish leave the surface, mitigating ice-like fin stickiness and increased body friction.Source: §3.7 · p. 42
• On the weakest mud (ϕ = 27%), deep sinking and mud adhesion made jumping rare and prevented takeoff even with strong tail thrusting.Forward-jump displacement was lowest at ϕ = 27%, increased as mud became stronger, and decreased slightly on dry mud (P < 0.005).Source: §3.7 · pp. 42–43

4.1. Summary of findings about hypotheses

• Mudskippers predominantly retained crutching with mostly conserved kinematics, making fine adjustments as mud weakened and became stickier.These responses included reducing stride frequency, shifting more weight onto the fins, and using tail bending to assist crutching.Source: §4.1 · pp. 43–44

4.2. Greater challenges to move on mud than sand

• Mud resists downward penetration up to two orders of magnitude less than sand and can stick to an intruder, pulling it downward and backward.Assuming equal substrate deformation during penetration, energy lost to mud is twice that lost to sand because mud resists extraction as well as intrusion.Source: §4.2 · p. 44

4.3. Modest performance loss on weaker substrate relative to other crawling animals and robots

• 60% performance loss in forward displacement per cycle occurred from ϕ = 42% to ϕ = 27% as mud yield strength fell 25-fold.The discussion characterizes this loss as modest despite the substantially weaker, stickier substrate.Source: §4.3 · p. 44

4.4. Less performance reduction over consecutive cycles than other animals and robots

• The mudskipper’s performance reduction over consecutive cycles was less than that of some other animals and robots, and it stepped into disturbed mud only at ϕ = 27%.There it stopped normal crutching after one cycle, assisting with tail bending or switching to jumping.Source: §4.4 · p. 45

4.5. Mostly inflexible control of mudskipper crutching

• Crutching kinematics remained mostly inflexible, resembling a stereotypical gait-control template, with tail use as the main exception.The paper suggests this inflexibility may reflect crutching’s adaptation to mudflats, but identifies tail use as an exception to the largely fixed gait pattern.Source: §4.5 · pp. 45–46

4.6. Tail thrusting as a main strategy to assisting crutching on challenging mud

• When weaker, stickier mud made crutching less effective, tail thrusting assisted crutching and powered forward or vertical jumps.Small or large tail bends generated upward lift and forward thrust, making tail thrusting a major strategy on challenging mud.Source: §4.6 · p. 46

Supplementary figures

• Figure S1 plots trial-average snout forward speed against stride frequency across days for mud at ϕ = 27%, 34%, 39%, and 42%, and dry mud.Dashed lines fit each day’s data, while solid lines fit all data for each mud wetness.Source: Figure S1 · p. 53, Supplementary figures · p. 54
• Figure S2 tracks forward displacement per crutching cycle over sustained cycles across five mud wetnesses; the 27% average slope is not statistically meaningful because it uses one day.The figure reports average slopes of linear fits across experimental days.Source: Figure S2 · p. 55, Supplementary figures · p. 56
• Figure S3 compares stance duty factor, mid-stance and mid-swing times, snout vertical displacement, and fin forward and lateral displacements across four mud wetnesses.Fin forward displacement is measured at touchdown and lateral displacement at mid-swing.Source: Figure S3 · p. 57, Supplementary figures · p. 57
• Body and pectoral-fin three-dimensional displacement and velocity profiles were relatively conserved over a normalized crutching cycle across mud wetnesses.The profiles include fore-aft, lateral, and vertical displacement and velocity, plus total velocity; dashed lines mark the end of stance.Source: Figure S4 · p. 58, Supplementary figures · p. 59
• Normal-crutching kinematics were relatively conserved across mud wetnesses, with minimal body bending at most marker locations and similar fin rotations.Body bending angles and fin retraction and depression angles were measured over the cycle; mud comparisons covered four wetnesses.Source: Figure S5 · p. 60, Supplementary figures · p. 61

• Movie 1 shows a passive weight sinking test on mud of different wetness.Source: Supplementary Movies · p. 62
• Movie 2 shows mudskippers crutching normally and with small or large tail bends.Source: Supplementary Movies · p. 62
• Movie 3 shows mudskippers jumping forward and vertically, digging in, and turning.Source: Supplementary Movies · p. 62