Experimental subjects

All experiments were carried out on adult female mantises of the species Sphodromantis lineola. The mantises were housed in individual plastic boxes (7 cm length × 7 cm breadth × 9 cm height) which allowed for ventilation via holes in the lids. Mantises were free to move within the boxes. The boxes were stored in an insect housing facility maintained at 25 °C. The boxes were cleaned and misted with water twice a week and each individual was fed with a live adult cricket twice a week.

Stimuli and display

Stimuli were displayed on a DELL U2413 LED monitor, chosen because it has narrowband spectral output in the blue and green regions of the spectrum. The screen is 51.8 cm wide by 32.4 cm high, with a resolution of 1920 × 1200 pixels and a 60 Hz refresh rate. All stimuli were custom written in Matlab (Mathworks) using the Psychophysics Toolbox35,36,37. Our standard stimulus for behavioral experiments was the “spiraling disc” target presented on a bright background. This was a dark disc which appeared peripherally and spiraled in towards the center of the screen over the course of 5 s. On reaching the center, it stayed there quivering with a subtle jerky motion for a further 2 s, before vanishing. We have found that this stimulus reliably elicits strikes when presented within the mantis’ catch range at a size of 1 or 2 cm38.

Preparation and fixing of 3D glasses

We used green and blue filters distributed with a preprint of a previously published paper39. The 3D glasses were two teardrop shapes, one cut out from each filter, with a maximum diameter of about 7 mm (Fig. 4a). The filters had transmission peaks at 432 and 528 nm which are in the range of mantis spectral sensitivity27,34 (Fig. 1). When used with the DELL U2413 monitor, the light transmitted through each channel had almost no spectral overlap, except for a small leakage from the blue primary into the green range (Figs 1c and 2a). We can also estimate that, at the maximum digital driving level, the effective luminance of the blue primary viewed through the blue filter was about 70% that of the green primary viewed through the green filter (Fig. 2a).

In both techniques, prior to fixing the glasses, the mantis was first placed in its cage in a freezer (Argos Value Range DD1-05 Tabletop Freezer) for 5–7 minutes in order to immobilize it. Subsequently, the mantis was held in place under a microscope lens by holding down its legs with Plasticine® modelling clay (Flair Leisure Products plc). Previously cut out glasses were then affixed on the mantis with a mixture of beeswax and rosin that was melted and applied using a Denta Star S ST 08 wax melter. In addition to the glasses, a small component, designed for electronics, was glued onto the base of the mantis’s pronotum. This could later fit into a counterpart on the experimental stand and hold the mantis in place during experiments without restricting the movement of its head and forelimbs. After the glasses and the component were fixed, mantises were released and placed back in their cages where they were allowed a minimum of 24 hours to recover. Experiments were only carried out after this rest period.

Experimental set-up

For experiments, the mantises were attached to the frame of the experimental stand10,11 (Fig. 3b) with the components described above. The stand consisted of a Perspex® frame that could be easily rotated and raised vertically and was fitted with a card disc for the mantis to rest on. The disc was held in place by a copper rod with a weight on the opposite end and gave the mantis a feeling of flexibility and mobility11. The mantises were placed upside down, their preferred position and could then hold onto the disc with their legs (Fig. 3b). Once the mantis had been placed on the stand, the stand was placed in front of the monitor at the appropriate viewing distance.

Behavioral data recording and analysis

All behavioral responses were recorded using a Kinobo USB B3 HD Webcam (Point Set Digital Ltd, Edinburgh, Scotland) placed directly beneath the mantis. The output of the camera was fed to a RM Expert 3040 computer where the video files were saved. Video recording was synchronized with the stimulus presentation and started when each stimulus first appeared on the screen, ending when the stimulus disappeared. The camera was placed at a position that ensured that the monitor was outside the visible range of the camera. The recordings could thus be analyzed blind to the stimulus. We coded the recordings for two different responses of the mantises: strikes and tensions. strikes involved a rapid release of the forearms typically in an attempt to capture perceived prey38 and tensions involved a tensing of the forearms in preparation for a strike that was eventually unreleased. We used the sum of strikes and tensions as our behavioral measure in the crosstalk experiments with around 87% of responses being strikes. The results did not change significantly if we used only strikes as our measure. In one experiment using polarizing filters (see Supplementary Material) we also used a third behavioral response: tracks. These were sharp, saccadic head movements that follow sudden movements in the visual field of the mantis38, The computer independently recorded the order of presentation of the stimuli, so that after manual coding we could assign the response to the correct condition.

Assessing interocular crosstalk

In a stereoscopic system, physical crosstalk is defined as the amount of luminance leaking through the “wrong” channel (e.g. green primary viewed through blue filter) relative to the luminance passing through the correct channel (e.g. blue primary viewed through blue filter):

In Fig. 2a, we evaluate this at the maximum luminance level. Recall that the definition of luminance takes into account the spectrum of the light emerging from the filter and the spectral sensitivity of the organism.

The definition of physiological and behavioral crosstalk additionally takes into account non-linearities in the organism’s response to luminance. For example, if at the maximum luminance of our display, the leak luminance is below threshold for eliciting a retinal response, then physiological crosstalk is effectively zero. To measure this, we compare the response to the maximum luminance presented in the wrong channel and ask how much luminance must be presented in the correct channel to elicit the same response:

where X is the crosstalk ratio and L is the maximum luminance. Where the response is a linear function of luminance, this is the same as the previous expression. Thus to compute the crosstalk in Fig. 2b,c, we draw a horizontal line from the value of the “wrong channel” response at 100% input and see where this intersects the “correct channel” curve.

Physical measurements (spectrophotometer)

To measure the physical crosstalk of the filters, we fixed a filter on the monitor directly in front of the Konica Minolta CS-2000 spectrophotometer such that it covered the entirety of the measurement area of the spectrophotometer. Measurements were subsequently made in complete darkness. A custom-written program then displayed a square target on the monitor that covered the entire measurement area of the spectrophotometer. The background of the display was kept white (i.e. the digital driving level was set to the maximum value, 255 in our 8-bit system, for all three primaries). The target square was presented in the blue or green primary only. The digital driving level in that primary was increased from 0 to 250 in 25 steps, with a spectrophotometer measurement taken at each step, while the digital driving levels in the other two primaries were kept at zero. These measurements were repeated for a blue/green target viewed through the blue/green filter.

Physiological measurements (electroretinograms)

The mantises were immobilized and tethered on a custom made holder. The mantises viewed the monitor through a cylindrical tunnel built from black cardboard (radius 6 cm, length 8.5 cm) that was blocked with card on either side except for a rectangular window (1.5 × 3 cm) for the mantis and a square window (of side 3 cm) that fit onto the monitor. A filter, either blue or green, was placed between the mantis and the tunnel. The construction prevented the photoreceptors being excited by reflections in the experimental setup. We used wick-electrodes or borosilicate micropipettes drawn on a microelectrode puller (Sutter Instruments P-97, USA) for the recordings. Responses were amplified (BA-03X amplifier; npi electronic, Tamm, Germany) digitized (CED1401 micro; Cambridge Electronic Design) and stored using a PC with Spike2 software (Cambridge Electronic Design, Cambridge, UK). We recorded electroretinograms in response to light flashes of increasing amplitude presented in either the blue or green primary of the monitor. The stimuli were slightly bigger than 3 × 3 cm window visible to the mantis, so they covered it completely. The results of Fig. 2a were used to calculate the luminance corresponding to each digital driving level. One stimulus sequence comprised 10 light flashes, each lasting 500 ms and separated by five or eight seconds of darkness. A new stimulus sequence was started manually about every 10 seconds. After several repetitions, the filter was changed and the procedure was repeated. In some electroretinograms, the filters were changed again and the procedure repeated. Amplitudes in response to light flashes were defined as the average potential over the last 100 ms of a 500 ms light flash, minus the average potential over the 100 ms before the flash onset. Electroretinograms were obtained from two recordings from each of two insects. The response was normalized for each recording and then averaged for each insect. The results in Fig. 2b show this mean response averaged across recordings and insects normalized such that the maximum response in each channel is 1. The signal response at the minimum value tested is greater than the maximum leakage response, so we cannot compute crosstalk exactly but only state that it is <2%.

Behavioural measurements

Mantises, not fitted with glasses, viewed stimuli through a blue or green colored filter of dimensions 4.5 by 4.5 cm. The filter was fixed directly to the screen, at the centre of the screen over the location where the stimulus comes to rest. The mantises were placed 3 cm from the monitor, a distance at which they will reliably strike at computer-generated stimuli presented on a 2D screen in the normal way. “Spiraling disc” stimuli, with a diameter of 1 cm on the screen, were then presented in either only the green or blue color channels or both. For the background, the digital driving level was set to 128 in both the blue and green primaries. To present a dark target in the blue or green channel, the digital driving level of that primary was reduced to one of five possible values (0, 32, 64, 96, 128) which were randomly interleaved across trials. The last value corresponds to no stimulus, since the “target” was the same as the background. Again, Fig. 2a was used to translate each digital driving level into the luminance of the background, B and target, T. Figure 2c shows response rate as a function of target contrast relative to the background, (B−T)/(B + T). In one experimental run each combination of the three channel conditions (blue, green, both) and five contrast conditions was presented three times in random order for a total of 45 trials per experimental run. Four mantises were tested with each of the two filters and with 3 trials each for every combination of contrast and disparity condition. Note that in this experiment, both eyes always viewed the same stimulus, so there was no binocular disparity. The target was always presented at the same location in blue and green channels.

Demonstrating illusory 3D depth

In this experiment, the mantises were fitted with 3D glasses so that different images could be presented to the two eyes; there was no other filter in front of the monitor. Each eye was fitted with one or the other color filter and across animals we alternated whether the left or the right eye was fitted with the blue or green filter. The stimulus was again the “spiraling disc” target, this time presented with maximum contrast in the three disparity conditions as described above. As before, the digital driving level in the background was set to 128 in both the blue and green primaries. In the zero disparity condition, the disc was black in both channels (RGB = [0 0 0]). In the crossed and uncrossed disparity conditions, the stimulus consisted of separate ‘blue’ (RGB = [0 0 128]) and ‘green’ (RGB = [0 128 0]) discs. The discs in the two channels had the same spiral motion, but were separated horizontally by a constant offset as described in the text. Note that the blue disc matches background luminance in the blue channel and is therefore invisible through the blue filter but is darker than the background in the green channel and can therefore be seen through the green filter. The converse is true for the green disc.

During the experiment, mantises were presented with ten trials in each of the three disparity conditions, randomly interleaved, for a total of thirty presentations. There was a pause of 60 seconds between presentations of the stimuli. We ran the experiment at three viewing distances: 5, 7 and 10 cm. We tested six mantises at a viewing distance of 5 cm and four each at 7 cm and 10 cm. The size of the disc on the screen was increased with the physical viewing distance (Table 1, Fig. S1), so that in each case it subtended a visual angle of 22.6o when at the center of the screen. This is the angle subtended by a physical disc of diameter 1 cm viewed at 2.5 cm. The disparity between the images visible in each eye was calculated to simulate a target at a distance of 2.5 cm from the mantis using a mantis interocular distance of 0.4 cm. Thus, the physical separation between the images ranged from 0.4 cm when the viewing distance was 5 cm, to 1.2 cm when the viewing distance was 10 cm. Since the disparities were always equal to or greater than the interocular distance of the mantis, the images in the uncrossed condition are divergent.