Water strider females use individual experience to adjust jumping behaviour to their weight within physical constraints of water surface tension
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
Experimental design is graphically summarized in Fig. 1b (also see Supplementary Materials PART 4). To determine the effect of increase in body mass on the behaviour, we tested water striders in two conditions of the Additional weight treatment: weight-added (11 females and 16 males) and weight-not-added (20 females and 15 males). After measuring the weight with an Ohaus electronic scale with the precision of 0.1 mg, the water striders were randomly assigned to either of the treatment group. In weight-added group, a flat coiled aluminum wire (~ 7.5 mg weight in males, ~ 10.5 mg weight in females) was secured to the backs of water striders with a tiny drop of non-water soluble glue gel (applied only on top of thorax). Added weights caused an increase of body mass by about 50% (54.5% ± 9.2 (mean ± SD) in males and 52.8% ± 5.7 in females). The body weight of a male is about 70% of female body weight on average (similar based on median or average body weights). Preliminary theoretical calculations using the model of surface-tension dominated jumping3 suggested that an average female with the extra weight equivalent to the average male body mass would be able to jump and to achieve take-off velocity of about 0.75 m/s for the leg angular velocity of about 40 rad/s. However, based on our observations, when a male sits on the female’s back during copulation and mate guarding the male’s hindlegs are always on the water, probably adding to the support for the mating pair on the water surface. The tips of male midlegs can also be on the water surface, possibly also helping in support on the water surface. All evidence suggests that the male’s support on the water surface contributes to some extent to the forces maintaining the mating pair on the surface of water. Hence, the female does not perceive the full body weight of the mating male. Our preliminary trials with additional weight of different masses indicated that the weight similar to the male body mass is too heavy for the purpose of our experiments because some females were not able to stay on the surface for extended time periods. This was not observed for the extra weights used in our experiments.
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( {2omega 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 }lsin left( {2omega 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:
$$l_{th} = 0.77l_{t} ,l_{tm} = 1.23l_{t} ,Delta l_{h} = 0.84Delta l,Delta l_{m} = 1.16Delta l$$
$$ frac{{d^{2} H_{m} }}{{dleft( {omega t} right)^{2} }} + frac{4 cdot 1.23}{{{Omega }^{2} M}}H_{m} left( {1 – H_{m}^{2} /4} right)^{1/2} + frac{4 cdot 0.77}{{{Omega }^{2} M}}H_{h} left( {1 – H_{h}^{2} /4} right)^{1/2} – 2 cdot 1.16Lcos left( {2omega t} right) = 0, $$
(1)
$$ frac{{d^{2} H_{h} }}{{dleft( {omega t} right)^{2} }} + frac{4 cdot 1.23}{{{Omega }^{2} M}}H_{m} left( {1 – H_{m}^{2} /4} right)^{1/2} + frac{4 cdot 0.77}{{{Omega }^{2} M}}H_{h} left( {1 – H_{h}^{2} /4} right)^{1/2} – 2 cdot 0.84Lcos left( {2omega t} right) = 0, $$
(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). More
