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As Rossel noted, these different behaviours suggest that mantids, like humans, possess at least two distinct forms of stereopsis [103]. To stretch the analogy further, in both species, one stereo system seems to be suitable for getting the eyes into the right position (turning to fixate the target, in the case of mantis saccades) and the other for subsequent depth perception (releasing the strike).
Figure 14, reproduced from [44], shows how a model animal would respond to targets with a range of sizes and distances, if its probability of striking at any moment is proportional to the instantaneous activity of this simple binocular neuron. The three dashed lines compare data from real mantises. Remarkably, this very simple, single-neuron model is able to reproduce the qualitative features of real mantis behaviour. The most strikes are elicited for stimuli of approximately 10 diameter, approximately 2.5 cm from the animal. The number of strikes falls off very rapidly with changes in distance (halving or doubling the distance produces less than half the number of strikes), and less rapidly with changes in size (halving or doubling the size reduces the number but not by half). The model even reproduces the interaction between size and disparity: larger angular sizes are preferred when stimuli are more distant (the opposite direction from that which would produce a constant preference for physical size, in centimetres). In the model, this occurs because of false matches made between the leading and trailing edges of the moving target (see [44] for details).
Size and disparity tuning of the model sketched in figure 13, reproduced from [44] but correcting an error in the empirical results as plotted in that publication. Solid lines show the mean number of strikes elicited from the model animal by a moving target at the distance indicated by the colour, and with the diameter indicated on the horizontal axis. Dashed lines show corresponding empirical results with praying mantises [111]. In the model, the mean number of strikes elicited by each trial is taken to be proportional to the time-averaged activity of the binocular neuron. (Online version in colour.)
Schematic drawing showing model proposed by Kral & Prete [42] for mantis stereo-guided strikes. LGMD, lobula giant movement detector; DCMD, descending contralateral movement detector. Redrawn from fig. 3.15 of [42]. (Online version in colour.)
As shown above, the single-sensor model gives a good account of current data on mantis striking behaviour, including the preference for size, vertical and horizontal disparity, and the lack of response to ghost matches. If so much is achieved by a single disparity sensor, why does the mantis brain have more than one? Most obviously, mantids do not strike solely at objects directly ahead of them. Having multiple disparity sensors, at different azimuths and elevations, could enable the animal to trigger strikes targeted towards the appropriate direction [113]. Secondly, a single disparity sensor necessarily confounds size and disparity, and indeed other stimulus dimensions like contrast or speed: for example in figure 14, the sensor is activated equally by a target at the preferred size but sub-optimal distance as by a target of sub-optimal size but preferred distance. Rossel [6,101] has provided compelling evidence that mantids do not confound size and disparity in this way. For example, when disparity indicates that a virtual object is very close, mantids may switch from attacking to defensive strikes [6]. Detailed measurements in one mantis showed that it systematically adjusted its strike trajectory depending on disparity, even when size is fixed ([101], figure 17). Importantly, the extent of the strike trajectory increases monotonically with distance, while the strike rate varies non-monotonically, which is not consistent with the idea that a single sensor is controlling both behaviours. This behaviour could be accounted for by multiple disparity sensors with different preferred disparities (and perhaps also sizes). The strike would be triggered by whichever sensor was most strongly activated and the strike trajectory would reflect the properties of the sensor triggering it.
Mantids tailor strike trajectories according to stereoscopic disparity, for a given angular size. Reproduction of figure 3b from [101] showing data for a single mantis. The origin is the centre of the mantis head and the y-axis indicates the direction of the target. Curves show the path of the femur tip, each curve averaged over 30 strikes, for targets at stereoscopic distances of 25, 35, 45, 55 mm. The target was physically always at 55 mm with an angular diameter of 20; nearer distances were simulated with prisms. Fifty-five millimetres is out of range and so no prey contact occurred during any of the strikes. I have superimposed the average strike rates for each distance, taken from of fig. 5 of [101]. These are the average over six animals, and it is not known whether these included the animal whose strike trajectories are plotted here.
Next, I considered a system suitable for triggering predatory strikes when prey is in the catch range. Here, we could assume that the head-saccade system has already ensured that the prey is already roughly directly ahead of the animal. For triggering strikes, greater accuracy is required, since mantids rarely strike at monocular stimuli or at prey which is out of their catch range [6,28,105,106]. Here, we found that we did need a disparity sensor which achieves weak correspondence: our model fitted a strong expansive output nonlinearity (raising to the power of 5). As well as greatly enhancing the response to optimal stimuli, this also boosts the average response to matching stimuli, relative to non-matching stimuli with the same average monocular value. This is formally very similar to the binocular simple cell, the building-block of current models of primate stereopsis. However, monocular processing before binocular combination renders the mantis disparity sensor insensitive to properties of the stimulus which are fundamental to primate stereopsis, such as the direction of local motion or the sign of contrast (bright versus dark) [34,35]. This again seems very poor design from the point of view of primate stereopsis and conventional machine stereo.
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