## Introduction

Surface-tension-dominated locomotion of water striders has attracted the attention of researchers at the interface of biology and engineering1,2,3, who are interested in designing biomimetic devices that move on the water surface. This multidisciplinary research has indicated that escape efficiency of jumps by the water striders should depend on the ability to adjust their leg movements to jumping conditions3. In order to maximize body velocity during jumping and to minimize latency till leaving the water surface, a jumping water strider should push the water surface downward with its long midlegs4 at the speed that is high enough to produce fast take-off but not higher than the upper threshold value, above which the legs break the water surface and the take-off velocity is dramatically reduced3 (Fig. 1a). Theoretically, this optimal leg speed depends on the body mass and on the leg length of a water strider, which vary by species3,4. Empirical data confirmed that different species use angular downward speeds of legs that are close to these theoretical optima calculated for each species from the species-specific body mass and leg length3, which assure that legs interact with un-broken surface of water. This ability might have aided5 adaptive evolution of leg morphology and micro-structures for optimized exploitation of water surface tension, which is associated with evolutionary colonization of water surface habitats by water striders4,6. It is not known how water striders achieve this optimal angular leg speed that matches the theoretical predictions and assures that legs interact with unbroken surface of water. It is possible that natural selection produces a fixed action pattern of the species-specific mid-leg movements that, on average, maximizes jumping performance for the species’ body mass and leg length. However, it is also known that many organisms, including insects, adjust their behaviour to changing environmental conditions through developmental or behavioural phenotypic plasticity7,8,9,10,11,12,13,14,15,16. Therefore, it is possible that individual water striders adjust their leg speed via personal experience through frequent jumping, which may result in the species-specific angular leg speed that are near the predicted optimum3. Therefore, we asked if water strider use experience to adjust their leg speed during locomotion (Fig. 1a).

The degree of behavioural plasticity in response to personal experience may vary not only among individuals or among species17,18,19, but also between sexes within a species20 if males and females face different selective pressures. Sexually selected behaviours may expose males and females to different experience, and this may result in the sex difference in the ability to adjust to environmental conditions. Water striders are a good study system to explore this issue in the context of locomotory behaviour because female water striders experience dramatic weight change while mating on the water surface. A male water strider mounts a female during mating and remains mounted for a long period, which may last for hours or even days, and females experience multiple mating bouts during their life21,22,23,24,25,26,27,28,29,30,31,32. Therefore, females, but not males, repeatedly experience periods of additional weight followed by periods of normal weight, and even when mating are able to perform jumps on the water surface either in response to predators or in attempts to shrug off the mating males. The frequent changes in weight are associated with changes in female’s predation risk24,25,26, and may pose a selective pressure for the female-specific abilities to adjust locomotion on the water surface to changes in the weight that is supported by the legs.

In this study, we conducted experiments (Fig. 1b) to determine whether male and female water striders Gerris latiabdominis use their experience to modify their leg movements during their jumps in the manner that depends on the body weight supported by their legs. We predicted that this behavioural change may be more pronounced in females, who naturally experience frequent changes in the weight that is supported by the legs. We also predicted that behavioural adjustments of jumping should be performed within the upper limits set by the physical properties of water surface.

## Results

Jumping behaviour and the physical constraints on performance—In the theory of water strider’s surface-tension dominated jumps3, one dimensionless variable plays a crucial role: ΩM1/2. It is a complex variable and its full definition and formula are given in the Methods section: “Physical constraint from water surface: theoretical upper threshold of performance” . Its value increases as the Angular leg speed; ω), insect body mass (m), and the length of midleg sections that interact with water surface (combined length of midleg tibia and tarsus referred to here as the wetted leg length; ls), and increase. A water strider of a given body mass and leg morphology (i.e. when body mass and wetted leg length are constant) can affect the value of the variable ΩM1/2 by controlling the Angular leg speed during jump. The theory3 predicts that for a given total length of midlegs (L; see details in the Methods section) there is a threshold value of ΩM1/2 above which surface breaking will occur and the jump will be inefficient. We calculated this critical threshold for males and females separately (see Methods for details) and compared it with the values of ΩM1/2 observed in our experiments. Although Angular leg speed varied among the treatments and among individuals, the water striders (except one individual) did not cross the theoretical threshold value of ΩM1/2 above which meniscus breaking is theoretically expected (Fig. 4). This suggests that the observed adjustments of Angular leg speed were kept within the theoretical limit set by the physical properties of water surface. It is notable that the males’ Angular leg speeds were much below the threshold value, and female’s Angular leg speeds were closer to the critical value.

Even though the behaviours of water striders were within the theoretical threshold values, meniscus breaking was occasionally observed (in 25% of jumps: 21 of 62 in females, 10 of 62 in males). We found no statistical evidence for the effect of Additional weight or Jumping experience on the occurrence of meniscus breaking either in First or Second jump (Table 3). The breaking, if happened, typically occurred in the very late stage of jumping when an individual had already reached, or was about to reach, the final take-off velocity, and the legs’ downward push against the water surface was completed. Therefore, it is not surprising that Take-off velocity was not statistically significantly affected by the presence of meniscus breaking either in First (Wilcoxon rank sum test: female, W = 120, P = 0.379; male, W = 10, P = 0.155) or in Second jump (Wilcoxon rank sum test: female, W = 122, P = 0.765; male, W = 89, P = 0.912).

## Discussion

Males did not show significant weight-specific changes in their jumping behaviour, which may suggest that predation-mediated natural selection for the ability to adjust the jump to the body weight may be weaker in males. This is expected because males do not experience frequent changes in their weight and because they are exposed to lower risk of predation24,25. Additionally, males’ jumping behaviour was far below the theoretical threshold where the meniscus breaking occurs and the jump becomes less efficient in escaping predation. Therefore, even if they lack the ability to modify the leg movements to their body mass, they may mostly stay below that critical threshold. We hypothesize that the relatively larger distance to the critical threshold visible in Fig. 4 is related to their smaller size and consistent with published data: Yang et al.3 have realized that the smaller water strider species (G. comatus, G. latiabdominis; Fig. 4 in3) are more distant in their jump performance from the threshold, and speculated why this may be the case. Here we see this trend between lighter males and heavier females within one species (G. latiabdominis).

The theoretical threshold of the downward leg speed is an outcome of the physical properties of water, which imposes constraints on the water striders’ jumping performance2,3. In the optimal jump, the leg downward movement in the theoretical model should not exceed the critical threshold angular velocity associated in the model with meniscus breaking, which dramatically decreases jumping performance3. Although the angular speed of legs in nearly all the jumps (except one individual) was indeed below the critical threshold determined from our modifications of the theoretical model of Yang et al.3 (explained in Methods), the breaking of the meniscus occurred in some jumps (Table 3) at the late stage of jumping when the individual had already accumulated most of the momentum that shaped the take-off velocity. Therefore the observed meniscus breaking did not affect the jump performance, and did not invalidate the theoretical threshold model. We can provide two hypothetical reasons for the observed meniscus breaking. Usually, the tibia of the water striders was bent during the jump, which prevents the meniscus breaking35. However, in some jumps it seems that the tibia did not curve enough, which resulted in meniscus breaking by the tip of the midleg just before the critical depth was reached. In other cases, the model assumptions of symmetrical simultaneous downward movements of left and right legs were not fulfilled, in which cases the average meniscus depth (average of the depths of the left and the right legs was used in calculations of the theoretical critical threshold of leg angular speed) did not correctly represent the depth of the leg that moved deeper and broke the water surface because it pushed the meniscus beyond the critical depth.

In summary, we provide empirical evidence that semi-aquatic insects are able to use personal experience during locomotion (jumping) to adjust their locomotory performance in response to the changes in body weight, and that they do it within the constraints set by the physical properties of environment (physics of water surface). Hence, in addition to reacting to changes of their physical circumstances such like changes in body weight, water striders are able to deal with the relatively dramatic physical constraint on jump biomechanics. While the behavioral ability to match locomotion to physical or biological circumstances has been known in other insects [e.g. 36,37,38,39,40], this is the first demonstration that this ability can be acquired through repeatedly experiencing the circumstances. This behavioral ability of short-term changes through experience is reminiscent of developmentally acquired (long-term) modifications of jump biomechanics in response growing up in environments of different predation risk41. The behavioural adjustments through personal experience were statistically significant in females. We propose that the observed difference between the sexes in the use of individual experience to adjust their locomotory performance to the changing body weight may be a female-specific adaptation to frequent mating that involves males riding on the back of females. As both sexes across different species seem to match their leg movements to their morphology during jumps3, our results suggest that the fine adjustments from experience observed in our experiments are not the sole mechanism that contributes to the optimal species-specific match between morphology and leg movements. This mechanism is likely to play a role in females of many water strider species because their mating behaviour is similar to our study species21,22,23,24,25,26,27,28,29,30,31,32. These findings allow us to think about a biologically inspired scheme to make robots learn to optimize their performance using repeated experience based on physical or computational intelligence42.

## Methods

### Study animals

Between June and August 2014, male and female Gerris latiabdominis were collected using insect nets from small ponds and an old swimming pool at Seoul National University, Seoul, South Korea. The number of water strider collected weekly varied depending on the current experimental requirements. In total, we collected near 100 individuals and used 62 of them in the experiments reported here. Collected water striders were housed in plastic containers (52 × 42 × 18 cm, 2–4 individuals/container) with aerated water, foam resting platforms, and two frozen large crickets per container per day. Each water strider’s thorax was marked with three unique color-coded dots using enamel paints. Females and males were housed separately.

### Experiments

#### Effect of weight addition on the performance of first jumps

After the weight was added to the water strider, the animal was allowed to rest with 2–3 other individuals of the same sex in a container filled with water (20 × 14 × 10 cm). After three hours, the water strider was placed in a box where the 3-D slow motion movie of the jump was recorded (labeled as the First jump; see below for the details). In weight-not-added group the individuals were treated similarly and handled for similar duration but no extra weight (neither wire nor the glue) was put on their backs. Triggering repeated jumps successively many times in the small container in which they were filmed likely leads to changes in performance due to repeated jumps within relatively short time and due to accumulated effect of the heat of the lights needed for high speed filming. We decided to use the design in which we took one jump per individual. The final sample sizes differ between treatments because some movies were discarded at the analysis stage for technical reasons.

#### Effect of jumping experience on adjustment of jumping performance

In order to test the effect of individual’s experience on adjustments of jumping behaviour we subjected the males and females from the preceding First jump to two conditions of Jumping experience [JE] treatment: presence and absence of frequent jumping during a three-day period (Fig. 1). For three days following the filming of First jump, water striders were kept in groups of 3–4 individuals per container (20 × 14 × 10 cm; filled with aerated water) and fed two frozen crickets per day. Each container was assigned to either JE-present or JE-absent treatment. In the former, we used an aluminum wire bent in the shape of a hook to touch or poke the insect’s underside in order to trigger 3–5 jumps/hour over 5 h/day. Jumps provide individuals with repeated experience of their jumping performance and the opportunity to adjust jumping behaviour. In the latter, individuals were not exposed to these procedures. At the end of the three days, the jumps (Second jump) were recorded in the same manner as for First jump. Sample sizes (listed in caption to Fig. 3 and in Supplementary Table 7 in Supplementary Materials PART 4) differ between treatments because some movies were discarded for technical reasons (see below) and some animals escaped or died.

### High speed filming of jumps

We used three synchronized high-speed cameras (FasTec Troubleshooter Model #: TS1000ME), with lens axes perpendicular to one another (Supplementary Fig. 2b in Supplementary Materials PART 4). Lights (Photon Super Energy Light, Aurora CCD-250 W, and PLTHINK Photo Light Think with Metal Halide bulbs) were placed directly opposite to each camera lens (Supplementary Fig. 2b). At the center of the setup was a 10 × 10 × 10 cm clear Plexiglas box filled with water. The jumps were invoked by an aluminum wire bent in the shape of a hook underneath the water surface. Jumps were recorded at 500 frames per second. Clips with insects that were accidentally pushed upward by the wire were excluded from the analyses. Examples of jumps extracted for the movies are shown in the Supplementary Movie.

### Variables extracted from the videos

We tracked the locations of body parts of water striders frame by frame in a three dimensional x, y, z, coordinate system (x, y are horizontal axes, z-coordinates are on the vertical axis, and origin is located at the level of undisturbed water surface) using video tracking software MaxTRAQ 3D (Innovision Systems). We tracked three markers; body center (defined as point between midleg and hindlegs), right midleg dimple depth, and left midleg dimple depth. Dimple depth is the deepest point of water surface deflection under the pressure from a midleg. From this data we calculated upward (vertical) and forward (horizontal) body velocities. For each pair of consecutive frames, we calculated the raw upward velocity of body center (along the vertical axis z) by dividing the vertical shift of body center (vertical distance between z coordinates of body center in the two consecutive frames) by the duration (2 ms between frames in 500 fps movie). Then, we calculated smoothed vertical velocity (m/s) by using rolling three-point average of three successive velocities. In an analogical manner we calculated the values of smoothed horizontal velocity (m/s) during a jump. From the data we extracted four variables used in analyses:

Angular leg speed (rad/s): Legs move downward as a result of downward angular femur movement powered by insect’s muscles, and the rotational rate of the leg downward movement is termed Angular leg speed (rad/s). To match the angular leg speed calculations in the theoretical model3, we calculated the Angular leg speed in several steps using empirical data and theoretical formulas from the existing model3. The coordinate system included vertical axis (z) with origin (z = 0) at the level of undisturbed water surface. First, for each frame we calculated average dimple depth as an average z from the left and right dimple depths’ z values, and the downward leg reach as the distance between body center’s z and the average dimple depth. Then, for each pair of consecutive frames, we calculated the downward velocity of dimple depth relative to body center (along the vertical axis z) by dividing the change in the downward leg reach between two consecutive frames by the duration (2 ms between frames in 500 fps movie). By using rolling three-point average from three successive downward velocities we obtained smoothed leg speed (m/s). Finally, we calculated the maximal downward speed of legs vs,max (m/s) as an average from the three largest smoothed velocity values. The downward Angular leg speed (ω) was calculated according to Yang et al.3 by approximation starting from the previously approved formula3 for the maximal downward speed of legs vs,max containing leg length ll: $$v_{s,\max } \approx \omega *\left( { l_{l} - y_{i} } \right)*\sin \left( {2\omega t} \right)$$ (yi indicates distance from the surface to insect body at rest and t indicates time during jump). See “Physical constraint from water surface: theoretical upper threshold of performance” below for more details about the model. The calculations resulted in the variable (Angular leg speed) that was directly relevant to the theoretical predictions of the optimal jumping behaviour3.

Take-off angle (deg): We defined take-off angle (deg) as the angle of trajectory to the water surface when the water strider leaves the surface of water. Takeoff angle was calculated from the ratio of horizontal and vertical vectors of the smoothed body center velocities.

Take-off velocity (m/s): Take-off velocity (m/s) is the vertical velocity of body center when the water strider leaves the surface of water. We determined the moment of leaving the water surface as the frame when legs disengage from the surface. Vertical velocity indicates how fast the animal removes itself from surface of water. A high take-off velocity is important when predators attack from underneath the water surface. This variable is a crucial component of the theoretical model of optimal jumping performance by water striders3.

Meniscus breaking (binary): Sometimes jumping water striders break the water surface. When left or right midleg pierced the water surface by more than a quarter of its full leg length the jump was categorized as a jump with meniscus breaking-present. Otherwise the jump was categorized as a jump with meniscus breaking-absent.

### Statistical analyses

Effect of weight addition on jumping performance—To analyze the effect of Additional weight on jumping performance of First jumps, we used Wilcoxon rank sum tests (Mann–Whitney test) to compare weight-added with weight-not-added groups for each sex separately. We used nonparametric statistical methods here because of small sample size that does not allow to confirm the parametric methods’ assumptions with high reliability (nevertheless the tests indicated that the parametric assumptions were probably met and in Supplementary Materials PART 1we also provide results from parametric comparisons: t-tests and Welch’s t-tests. In order to investigate whether Additional weight effect is statistically significantly different between sexes we switched to parametric analyses and run two-way ANOVA tests including the interaction effect between two independent variables (Additional weight and Sex) separately for the three dependent variables: Angular leg speed, Take-off angle and Take-off velocity.

Effect of jumping experience on adjustments of jumping performance—For each individual, we calculated three indices of adjustment (change) in performance between First and Second jumps. For each of the three dependent variables, we subtracted the value at First jump from the value at Second jump (for analysis of Second jump solely—see Supplementary Materials PART 3). Linear regression model was used to investigate the effect of Jumping experience and Additional weight treatments on jumping adjustments. Because of the small sample sizes, estimates and 95% confidence intervals of regression coefficients were reported using nonparametric bootstrap procedure with 10,000 replications of each linear model (‘boot’ package in R).

Meniscus breaking—To analyze the effect of Jumping experience and Additional weight treatments on the probability of breaking of the water surface (Meniscus breaking-present) we used Fisher’s exact test. To determine the effect of Meniscus breaking on Take-off velocity we used Wilcoxon rank sum test separately for males and females. All statistical analyses were performed using R (version 3.3.2;43).

### Physical constraint from water surface: theoretical upper threshold of performance

During a water strider’s jump, the water surface can be pushed downward only so much before breaking. Thus, a theoretical upper threshold of performance exists. The mathematical model of surface tension dominated jumping3 allows to predict the moment of surface breaking and the optimal behaviour of vertically jumping water striders without surface breaking. The model contains a non-dimensional variable: ΩM1/2. Its value depends, among others, on the Angular leg speed used by water striders during jump and on morphology: body mass and midleg’s tibia and tarsus length—the leg parts on which water strider’s body is supported on the water surface. The theory predicts that for a given total length of midlegs there is a threshold value of ΩM1/2 above which surface breaking will occur and the jump will be inefficient. We determined if water striders used Angular leg speed values that resulted in theoretical values of ΩM1/2 below this critical threshold. In order to more precisely predict the theoretical threshold value of ΩM1/2we modified the original model3. The original model used a simple average length of all four legs (mid-legs and hind-legs) and did not reflect a difference between the length of hind and mid legs. We changed the original equation into systems of differential equations using information about midlegs and hindlegs separately. Modified predicted threshold values of ΩM1/2 were compared with empirically observed values of ΩM1/2in order to determine if the observed adjustments of leg speed by water striders lie within the theoretical limit of performance set by physical properties of water. We used the same parameters as in3 for, lc, capillary length, g, gravitational acceleration, ρ, density of water. Because of the short length of legs, we approximated C, flexibility factor, as 1. Downward angular velocity of leg rotation, ω, was calculated by approximation, $$v_{s,max} \approx \omega {\Delta }l\sin \left( {2\omega t} \right)$$. The averaged length of femur, tibia and tarsus were measured from 24 individuals of each sex in G. latiabdominis and yi, the distance from body center to the undisturbed water surface in the resting position of the water strider was measured from 4 movie clips of each sex. Measured variables were averaged (Supplementary Table 8 in Supplementary Materials Part 4) and used to determine lt, average length of tibia plus tarsus, ll, average leg length, and Δl = ll − yi, maximal reach of the leg. Note that, the average length of tibia plus tarsus of hind and mid legs, lth, ltm, and the average length of maximal reach of leg of hind and mid legs, Δlh, Δlm, can be represented as:

$$l_{th} = 0.77l_{t} ,l_{tm} = 1.23l_{t} ,\Delta l_{h} = 0.84\Delta l,\Delta l_{m} = 1.16\Delta l$$
$$\frac{{d^{2} H_{m} }}{{d\left( {\omega t} \right)^{2} }} + \frac{4 \cdot 1.23}{{{\Omega }^{2} M}}H_{m} \left( {1 - H_{m}^{2} /4} \right)^{1/2} + \frac{4 \cdot 0.77}{{{\Omega }^{2} M}}H_{h} \left( {1 - H_{h}^{2} /4} \right)^{1/2} - 2 \cdot 1.16L\cos \left( {2\omega t} \right) = 0,$$
(1)
$$\frac{{d^{2} H_{h} }}{{d\left( {\omega t} \right)^{2} }} + \frac{4 \cdot 1.23}{{{\Omega }^{2} M}}H_{m} \left( {1 - H_{m}^{2} /4} \right)^{1/2} + \frac{4 \cdot 0.77}{{{\Omega }^{2} M}}H_{h} \left( {1 - H_{h}^{2} /4} \right)^{1/2} - 2 \cdot 0.84L\cos \left( {2\omega t} \right) = 0,$$
(2)

where $$H_{m} = h_{m} /l_{c}$$ is the dimensionless dimple depth of mid legs (hm, dimple depth of mid legs), $$H_{h} = h_{h} /l_{c}$$ is the dimensionless dimple depth of hind legs (h1, dimple depth of hind legs), $${\Omega } = \omega \left( {l_{c} /g} \right)^{1/2}$$ is the dimensionless angular velocity of leg rotation, $$M = m/\left( {\rho l_{c}^{2} Cl_{t} } \right)$$ is the dimensionless index of insect body mass (m, insect body mass), and $$L = {\Delta }l/l_{c}$$ is the dimensionless maximum downward reach of leg. The variable ΩM1/2 is calculated, as the name suggests, by multiplying the above-defined Ω by square root of M3. For a given L, the optimal value of ΩM1/2 for maximal take-off velocity is achieved when the maximal hm is equal to the critical depth, $$\sqrt 2 l_{C}$$, just before meniscus breaking. Wetted leg length, ls, was measured from 24 individuals of each sex in G. latiabdominis and initial height, yi, was measured from 12 recorded videos of females (6 individuals) and 9 recorded videos of males (5 individuals) (Supplementary Table 8 in Supplementary Materials Part 4). The ode45 function in Matlab was used to solve Eqs. (1) and (2) to get the optimal ΩM1/2 of male and female water striders (red lines in Fig. 4).