Behavioural evidence for a visual and proprioceptive control of head roll in hoverflies (Episyrphus balteatus)

Gaze stabilization plays a crucial role in many tasks performed by insects during flight such as obstacle avoidance, hovering, chasing, landing and take-off. In the presence of a wide range of physical and visual perturbations, gaze is stabilized by combining cues provided by various sensory channels (Hengstenberg, 1993; Taylor and Krapp, 2007).

The main parts of this complex system, described in more detail below, are: halteres, which respond to fast body rotation; articular proprioceptive hairs, which measure joint angles; and vision, which is composed of compound eyes and ocelli. The halteres form a mechanosensory gyroscopic system that is sensitive to Coriolis forces (Nalbach, 1993; Hengstenberg, 1993,, 1998; Huston and Krapp, 2009) and measure the rotational speed of the body during fast perturbations or manoeuvres and drive opposite head roll movements (Schwyn et al., 2011). An example of proprioceptive structure, the prosternal organs, consisting of a pair of mechanosensitive hair fields located symmetrically on the neck on the anterior part of the thorax of insects (Pringle, 1938; Preuss and Hengstenberg, 1992; Paulk and Gilbert, 2006), are stimulated by the head position through ‘contact sclerites’ (Peters, 1962). Differential stimulation of opposite sclerites during head roll movements generates mechanoreceptive cues about the head-in-body roll orientation (Preuss and Hengstenberg, 1992). Although the mechanosensory sensors located on the neck are involved in compensatory reflex responses realigning the head with the body in flies (Horn and Lang, 1978; Preuss and Hengstenberg, 1992) and are connected neuroanatomically to an insect's neck motor system (Strausfeld and Seyan, 1985; Milde et al., 1987), the exact contribution of these sensors to head control during flight has not yet been clearly established. Vision is also involved in gaze stabilization processes. It was recently established that the ocelli are able to resolve modicum spatial information (Berry et al., 2007; Hung and Ibbotson, 2014) and that the ocellar neural pathway is connected to motion-sensitive visual neurons (Parsons et al., 2006). The idea that the ocelli detect a rotation rate rather than an absolute head roll (Stange, 1981; Stange et al., 2002; Taylor, 1981a,b) has been supported by electrophysiological studies showing phasic responsiveness of ocelli to light change (Hu et al., 1978; Simmons et al., 1994; Parsons et al., 2006) and a behavioural study in which phasic head roll (∼25% of compound eye maximal response) was induced by differential illumination of lateral ocelli (Schuppe and Hengstenberg, 1993), related to measurements of high-pass filter characteristics and rotational rate. The finding that head roll responses can be driven by ocellar stimulation alone has confirmed that this structure is able to operate some stabilizing reflexes (J. van Kleef, T. Massey and M. M. Maharbiz, personal communication). Moreover, on the roll axis, compound eyes are sensitive to rotational optic flow and induce compensatory head roll movements, which feature slower processing times than the ocelli (Schuppe and Hengstenberg, 1993; Hengstenberg, 1993).

Although the compound eye and the ocelli assess the rate changes in the orientation of the fly's head, they are also involved in the dorsal light response (DLR) (Mittelstaedt, 1950; Hengstenberg, 1993), which aligns the dorsal part of the head and body with the brightest part of the visual field. In the walking fly, Horn and Knapp (1984) observed the occurrence of an invariant head orientation response to the orientation of an artificial horizon despite the various body roll orientations imposed on the flies. In addition, Hengstenberg (1984) has pointed out the importance of the horizon in head roll orientation during flight and the fact that no gravity information was used to perform this task. In locusts, compensatory head roll movements were also observed in studies using an artificial horizon (Goodman, 1965; Hensler and Robert, 1990), where body roll stabilization resulted from the head stabilization that occurred in response to the DLR reaction and the changes in the horizon's orientation. All in all, these results suggest that visual cues predominate over gravity sense during flight, and thus support the idea that the DLR may be involved in attitude stabilization. However, although the DLR had been found to be closely linked to head and body roll steering, the interactions between gaze and the body control system still remain to be established.

Based on previous studies on the DLR, we assumed that head control in hoverflies is based solely on visual cues. The horizon is certainly a useful means of reference frame for ensuring flight stability, as we established in a first set of experiments in which the tethered flying hoverflies aligned their head with the artificial horizon presented in various orientations. These findings were supported by comparing them with the predictions of a model based on visual inputs. We then raised the question as to how the visual errors are processed when the control input signals are transmitted to both head and body. To answer this question, we perturbed the purely visual control of the head with respect to the horizon by reversing the polarity of the horizon combined with a body roll perturbation paradigm. The results obtained in this condition show that head control in hoverflies does not rely solely on a visual feedback loop and suggest that neck proprioception may act as a gateway between head and body reference frames. A new model based on both vision and neck proprioception was then drawn up in line with this assumption.

Hoverfly pupae [Episyrphus balteatus (De Geer 1776)] purchased from a bio-control company (Koppert, Berkel en Rodenrijs, The Netherlands) were placed in a cage (53 cm×29 cm×29 cm) at an ambient temperature of 25±1°C until they hatched. Shortly after they hatched (less than 5 days later), males (N=8) and females (N=15) were sorted and placed in two different cages. To handle the flies and fix them on the tiny actuated clip of the roll generator, a strip of cardboard was glued (with 50% beeswax, 50% rosin) to their thorax. The state of the animals was then checked by observing their flight behaviour before returning them to the cage. They were given water ad libitum, surrounded by artificial flowers (carrying wet brewed pollen and sugar) and real flowers (which were replaced every 3 days). As the raising room had no windows, a photoperiod was applied artificially, using a halogen light bulb (42 W) to simulate long days lasting from 08:00 h to 21:00 h. Experiments were carried out on animals aged 3 to 21 days. The state of the animals was checked again prior to all experiments by observing their flight behaviour in the cage.

The experimental set-up used in this study was very similar to that used by Viollet and Zeil (2013) in their study on wasps. It consisted basically of a stepper motor, an opaque tube and a digital camera (see Fig. 1A). These three parts were firmly mounted onto an optical bench (Spindler and Hoyer, Gottingen, Germany) to ensure perfect alignment of the camera's optical axis with the shaft of the stepper motor (Sanyo Denki, Roissy, France; 103H5208-0440, Tokyo, Japan; 200 steps per round), which was connected to a fast electronic driver (Sanyo Denki US1D200P10). Flying animals were tethered to a tiny clamp fixed to two miniature perpendicular stages (Edmund Scientific, Lyon, France). Accurate alignment of the motor's shaft facing the camera (DALSA Genie HM640, Stemmer Imaging, Suresnes, France) was also ensured by adding two further perpendicular stages (Spindler and Hoyer) on which the motor was mounted. The motor and the camera were controlled via a data acquisition board (USB, 6128; National Instruments, Austin, TX, USA) and a fast ethernet bus connected to the camera. The stepper motor and the image acquisition set-up were synchronized with a custom-written LabVIEW-based program (National Instruments, Austin, TX, USA) running on a PC. Movie sequences were stored frame by frame in the form of uncompressed 8-bit tiff images (resolution: 640×480 pixels) for off-line processing. Special attention was paid to the choice of ethernet board (Intel Pro/1000 GT Desktop Adapter) to ensure a maximum rate of 200 frames s⁻¹ without any loss of images during the experiments. Each experiment lasted 20 s. Hoverflies were placed inside an opaque tube (internal diameter, 9.5 cm; length, 20 cm) illuminated frontally by an fibre optic ring light (Schott, KL 1500, Clichy, France; 8.32×10⁻⁹ W m²) fitted with a halogen light source (Xenophot HLX, OSRAM, Molsheim, France) and three pairs of infrared LEDs were used to light the hoverfly when the ring light was turned off. The digital camera was used to film the head and body movements (see Fig. 1C). After introducing a hoverfly into the tube, it was presented with various patterns: a tilted artificial horizon (a half-black, half-white roll of paper presented in various orientations, as shown in Fig. 1B) and a uniform white background. A gentle air stream generated by a compressor (Silent Air System SAS-038, Oil-free, Dürr Technik, Bietigheim-Bissingen, Germany) connected to a small flexible tube (diameter, 6 mm) was directed towards the fly during all the experiments in order to induce and sustain flight behaviour.

In light of previous studies showing that visual systems (including compound eyes and ocelli) are involved in the gaze stabilization reflex, the DLR was a priori modelled in the form of a single visual feedback loop, which is presented in detail in Fig. 2. The visual error (ε_visual) results here from the difference between the horizon orientation (θ_horizon) and that of the head (θ_head). At each time-step, the ‘head in body’ orientation (θ_headbody) is adjusted in response to the horizon's orientation based on the visual error. Then, by definition, the output of the system θ_head was obtained by adding θ_headbody with θ_body. Behavioural experiments will allow us to validate this model.

The angular position of the motor's shaft was adjusted to keep the hoverfly's body horizontal. Once a hoverfly had been placed in the tube and the light turned on, it was surrounded by an artificial horizon oriented in any of five different directions: −90 deg, −45 deg, 0 deg, 45 deg and 90 deg (negative angles with clockwise tilts and positive ones with counterclockwise ones; see Fig. 1B). The head response was also measured in the absence of any orientation cues (with a uniform white background). At the end of each run, the fly was removed from the tube, the orientation of the pattern was changed and after a short rest, further runs were conducted until all five orientations and the uniform background had been experienced by the insect. The same hoverfly could not undergo more than one set of runs per day, and if any of them showed a complete lack of flight motivation, the experiment was stopped and possibly resumed later in the day. Flight behaviour was induced and maintained by a gentle frontal air flow.

To identify the dynamic of the control underlying head locking to an artificial horizon we measured the response to a step. The motor's shaft was adjusted to keep the fly's body horizontal. Once a hoverfly had been introduced into the tube lined with an artificial horizon oriented in one of the four different positions (−90 deg, −45 deg, 45 deg and 90 deg) with the light turned off, the light was switched alternately on and off approximately every 5 s manually during the run, giving two dark sequences followed by two illuminated sequences per 20 s run. Flight was filmed during the dark phases under infrared LED lighting in front of the animal. The flies were removed from the tube at the end of the run and the horizon's orientation was changed until the insect had been exposed to all four orientations. Flight behaviour was induced and maintained by a gentle air flow from the front.

with K and τ the identified parameters of the closed-loop transfer function G(s) and s is the Laplace variable. Simulations were made with MATLAB-Simulink, with a time-step of 0.005 s, to confirm the identification (see blue line in Fig. 6). Only roll around the animal's longitudinal axis was considered, allowing us to describe a single input–single output (SISO) system. The model was restricted to the effects of a static horizon, and the responses elicited via motion-sensitive and mechanosensory channels (modelled in Schwyn et al., 2011) were not taken into account.

To test the model to its limits we put hoverflies in an uncommon visual environment. The artificial horizon was settled in an upside-down configuration (black on top and white on bottom of the visual field, 180 deg of the 0 deg horizon). The step motor's shaft was rotated to orient the hoverfly's body at an angle of approximately 30 deg in the initial state. A series of brisk angular steps rotating the fly's body by ±60 deg within 0.05 s (rotational speed of 1200 deg s⁻¹) was applied every 5 s (0.2 Hz). Flight behaviour was induced and maintained by a gentle frontal air flow.

Head orientation (θ_head) was obtained during the body rotation experiments by tracking two natural markers on the fly's head (Fig. 1C) with a semi-automatic marker-tracking software program running under MATLAB (Hedrick, 2008). Body orientation (θ_body) was taken to be 0 deg under static and light off/light on conditions and measured via the orientation of the cardboard during rotation, which was determined automatically with another custom-made MATLAB program. The θ_headbody angle was calculated in the form of the difference between θ_head and θ_body.

Two variables were used to analyse the results of the static experiments. The first was the mean head orientation (denoted ⁠). One value of was extracted from each run analysed.

where Q_head is half the difference between the maximum and minimum values of 80% of θ_head data, in view of the fact that 10% were excluded on both sides of the data distribution (2×2 s at most) in order to prevent occasional artefacts from increasing the value of Q_head. Therefore Q_head was our proxy for θ_head stability during each run: the more the θ_head values were scattered during a run, the higher the Q_head value tended to be and the lower the stability of the head was. One value of Q_head was extracted from each run.

Linear mixed-effects (LME) models were used to discriminate between the effects of the artificial horizon, its orientation (θ_horizon) and the sex of individuals (fixed effects) on both and Q_head. As each individual was liable to undergo several trials, the date of the experiments was also included as a fixed effect in order to rule out the potential effects of habituation processes, and individuals were included as a random effect. The Akaike information criterion (AIC) was used to compare and select the best LME model and an ANOVA analysis was then applied to this model to determine the significance (the P-value) of the effects. All the statistical analyses were conducted with freeware R software (www.r-project.org).

Typical time courses of θ_head during tethered flight with an artificial horizon or a uniform background are shown in Fig. 3A. The uniform background condition induced visible drifts in the head orientation, whereas no drifts were observed in the presence of the artificial horizon and the head remained very still in space. In both conditions, we observed small-amplitude head saccades, around 5 deg for the artificial horizon and 10 to 20 deg for the uniform background.

As shown in Fig. 3B, in the presence of the artificial horizon, the range of hoverflies' head orientations decreased significantly (bottom panels) during tethered flight (P<0.01). Their mean head orientations also shifted slightly counter-clockwise (top panels) during flight by a median value of less than 5 deg (shift was not significant, P=0.08) between the uniform pattern and the trials with an artificial horizon in the case of both males and females. As shown in the boxplots, the inter-run variability of increased with the uniform background, especially in the case of males.

Fig. 4 shows one typical time-course corresponding to each orientation of the horizon (see Fig. 1B) except for the horizontal orientation (0 deg, see Fig. 3). As expected from previous experiments (Hengstenberg, 1984; Hensler and Robert, 1990; Goodman, 1965), horizon orientations ranging from −90 deg to +90 deg gave rise to a clear-cut change in the insects' head orientation, the direction of rotation of which was that imposed by the horizon's inclination. The hoverfly was unexpectedly able to episodically orient its head and keep its orientation almost entirely locked to the horizon when the latter was rotated by ±90 deg. As shown in Fig. 4B,D, no responses to the orientation of the horizon were produced during non-flying periods, as reported by Hengstenberg et al. (1986) and these phases were therefore excluded from our analysis. Fig. 4A,C shows that the flies' responses were often incomplete and included a non-null steady-state orientation error between the head and horizon.

In Fig. 5A,B, similar significant correlations (P<0.001) were obtained with males or females between the orientation of the artificial horizon and the mean orientation of the head recorded during a run. Fig. 5C,D shows the existence of a significant difference in the dispersion of θ_head during a run between sexes: females showed greater head roll stability than males. However, regardless of sex, the head orientation recorded with a 0 deg artificial horizon was also significantly more stable than with any other orientation of the horizon (P<0.001). The inclination of the head frequently showed the occurrence of a steady-state error in response to the inclination of the horizon, despite large rotations of the artificial horizon up to ±90 deg. The median value of ranged between ±25 deg, nevertheless, several males (≈25%) were able to keep their head rotated in average larger than +50 deg during 20 s runs when the artificial horizon was inclined by +90 deg. The correlations between the mean head response and the orientation of the horizon were consistent with the vision-based model (VM, see Fig. 2). However, since the correlation between and θ_horizon was found to be lower than 1, the insects' responses may have been constrained here by a saturation mechanism: this point will be discussed below.

Table 1 shows the great variability of the gain K, which determined the final value of the step response. As expected for a dynamic in a system with no integrator, the higher K was, the less the steady-state error became. In control engineering, at least one integrator is necessary in a closed-loop model to be able to reach a null steady-state error in response to a step. Although the previous finding that locusts' responses featured a zero steady-state error under free-roll conditions (Goodman, 1965) suggested the existence of an integrator, the step responses measured in our tests featured steady-state errors. In view of these findings, no integrator was included in the model, although these errors may be attributable to the tethered condition, which may have induced proprioceptive conflicts (see the Discussion). In addition, males showed higher K than females under all the orientation conditions tested, whereas the term τ, which is the time constant of the response, seems to have been very consistent in females, where it ranged between 0.1 s and 0.2 s. The time constant was again larger in males than females and varied between approximately 0.3 s in the case of negative (clockwise) rolls and 1 s in that of positive (counter-clockwise) ones. This unexpected difference between clockwise and counter-clockwise response dynamics is unexpected and difficult to explain, but it may have been due to uncontrollable airflow heterogeneity in the tube exerting differential forces on the neck. It is worth noting that the head roll induced by the artificial horizon never involved head saccades but always involved a smooth head rotation.

A reversed artificial horizon (with an orientation of 180 deg) was used here in order to saturate the control input signal sent to neck muscles. In these experiments, periodic (0.2 Hz), 60 deg amplitude steps were applied to the body, consisting of a transient 0.05 s phase (1200 deg s⁻¹) and a 4.95 s static phase. The insect's body was initially tilted by an angle of +30 deg in order to avoid having a perfect 180 deg alignment between horizon and head (which could have led to ambiguities) and this made it possible to establish that the head roll occurred in the direction that minimized the difference between the orientation of the head and that of the horizon. We only included in the analyses sequences in which the flies showed head roll amplitudes greater than ±60 deg before the onset of a body perturbation (50% and 27% of males and female sequences, respectively). Fig. 7B shows that hoverflies tried to correct the error between their head and the upside-down artificial horizon.

In the initial closed-loop model presented in Fig. 2, we simply included a measurement of θ_head relative to θ_horizon as a visual output controlling the head. Based on this simple model, the simulated response of the VM model shows that when the horizon is in the upside-down configuration, an angular step applied to the body will modify only the amplitude of the head roll, not its sign (Fig. 7B, red dashed lines). However, contrary to the VM model response, hoverflies quickly rotated their head in the same direction as that imposed by their body roll in the steady state (see Fig. 7B, red lines).

This study focused on the reaction of a visuomotor reflex in charge of controlling the head orientation with respect to the horizon in hoverflies. In this section, a new model for the visuomotor reflex is presented and the possible role of the neck proprioceptor organs combined with visual information is discussed.

The results obtained here show the importance of head locking to an artificial horizon in hoverflies. In particular, they show that the key feature of this response was the white/black polarity of the horizon rather than the contrast edge (Hengstenberg, 1984). The presence of an artificial horizon during flight enables the flies to control their angular head position more accurately. This is a complementary way of adjusting the head's angular speed to that based on optic flow measurements, which has been described as a head roll stabilization process in wasps (Viollet and Zeil, 2013). In addition, stabilizing the head with respect to the horizon greatly simplifies the visual processing by providing a steady reference frame (Taylor and Krapp, 2007). In his studies on blowflies, Hengstenberg (1984) observed that starting at wingbeat initiation, flies took several seconds to turn their heads toward a previously tilted horizon. Contrary to these findings, we did not observe any delay in the hoverflies' responses during the phases when they stopped and started flying again (see Fig. 4). With a horizon tilted by ±90 deg, only a few males were able to turn their head more than 50 deg. One possible explanation for this finding might be the existence of a mismatch between the sensorimotor feedback loops and the insects' visually guided behavioural command under tethered conditions (Zeil et al., 2008). This explanation is coherent with the fully compensatory responses recorded in locusts under free body roll conditions, where the head and body could be perfectly aligned with a light source (Goodman, 1965). However, we consistently observed here that the head of the flying hoverflies compensated for tilted horizons and the extent of their responses to the upside-down configuration certainly shows the importance of the horizon as a zero reference for head control. This finding rules out the hypothesis that these responses may be based purely on local edge detection mechanism, as observed in previous studies (Hengstenberg, 1984), or on differences in lighting between the two sides (Neumann and Bülthoff, 2001), regardless of the contrast. By contrast, the head responses measured here, especially those obtained with the upside-down horizon and the ±90 deg tilted horizon, show indeed that the polarity of the horizon contributes to these responses. The large head rolls measured in the presence of the reversed horizon suggested that a large-field integration has been mediated by the compound eye rather than the ocelli, which have rather narrow visual fields (Schuppe and Hengstenberg, 1993). The ocelli have been found to drive some compensatory head reflexes (J. van Kleef, T. Massey and M. M. Maharbiz, personal communication) and seem to play a role in the initiation of DLR, decreasing the response latency (Stange, 1981; Taylor, 1981a; Parsons et al., 2006). It has been established that the ocelli are characterized by faster visual processing than the compound eye (Hengstenberg, 1993; Taylor and Krapp, 2007) and motion direction sensitivity (Berry et al., 2007; Hung and Ibbotson, 2014). In dragonflies, fast alternating optical stimulation of the lateral ocelli triggered strong compensatory head roll movements (Stange, 1981). The procedure used in the latter study also showed the occurrence of phasic responses to light changes triggered by ocellar inputs. To summarize, the reversed horizon paradigm might be a useful means of elucidating the respective contributions of the ocelli and the compound eyes.

Simulations were conducted directly by using the first-order transfer function with mean time constant for males and females averaged from the closed-loop identification presented in Table 1, whereas the gain K was adjusted in line with the head dynamics. This new VPM model based on visual and proprioceptive information responds in line with behavioural observations to sudden change of body attitude in the upside-down horizon configuration (see Fig. 9).

An objection to our model could be that it is only useful, in comparison with the VM model, under specific conditions where the animal is in an upside-down position, which does not occur very frequently under natural conditions. In any case, the performances of the new model are similar to the VM model's step responses (see Fig. 9). Unlike the VM model, however, the enhanced model presented in Fig. 8 not only accounts for the head roll measured in response to various orientations of the horizon, but also sheds new light on the hoverfly's ability to estimate its own body orientation relative to the horizon (⁠⁠) using neck-proprioceptor organs (Eqn 5).

Although we have described and modelled the gaze stabilization process with respect to the horizon in hoverflies, it still remains to be determined how visual information contributes to controlling the body's attitude. Previous studies have focused on the linear relationships between head and body control input signals during yaw rotations, body movements copying head movements in the controversial delayed responses observed by Land (1973) and the simultaneous responses observed in flies (Geiger and Poggio, 1977), bees (Boeddeker et al., 2010) and wasps (Viollet and Zeil, 2013). Even on the roll axis, Goodman (1965) attributed the inability of locusts to realign their head and body without having any prothoracic hair and hair plate to the disappearance of the neck realignment reflex. Yaw and roll gaze-stabilization strategies are known to differ (Schilstra and van Hateren, 1998). Since the roll attitude control system is directly involved in fly stability (Hengstenberg, 1984), it seems unlikely that a strategy based only on an automatic realignment of the body with respect to the head will suffice to stabilize the body during roll movements. As observed by Collett and Land (1975), translational flight in hoverflies requires a tilted orientation of the thorax, while the head remains horizontal. The predictions of the present model suggest that the estimated body roll might be compared with a reference input signal allowing the fly to initiate an arbitrary body roll movement. On similar lines, Boeddeker and Hemmi (2010) have observed that bees in a rotating drum swayed and rolled their body around 0 deg while keeping their head in a stable orientation of either 0 deg or ±35 deg, which suggests the possible existence of different head and thorax control laws. For example, the model developed by Viollet and Zeil (2013) to account for head stabilization in wasps involves two different control pathways for the body and head, which are linked by an internal feedforward control system. In addition, Hensler and Robert (1990) have reported that different body and head control processes are at work in locusts and discussed the possibility that non-linear proprioceptive inputs may be involved in the coordination between head and body roll control. The latter authors suggested that the observed linear relationship between head and body may be due to weaknesses of the experimental procedures used, and that in nature, flying insects must use coupled or uncoupled head/body control processes depending on the task (feeding, chasing, avoiding predation) they are performing. Likewise, in dragonflies, despite the differences between the head, which serves to track prey, and the body, which serves to intercept the trajectory of prey, prey-capture flight must be efficiently guided thanks to the integration of the signals generated by ‘head in body’ measurements (Olberg et al., 2007; Olberg, 2012; Mischiati et al., 2015). These studies suggest that the neck proprioceptor organs may serve as a gateway between two reference frames: the visual frame associated with the head, which serves as a reference frame during visually guided behaviour (Boeddeker and Hemmi, 2010) and the body frame associated with the thorax, on which locomotion is based. In addition to the idea that the head orientation may serve as a zero reference for controlling body roll movements (which are therefore based on ‘head in body’ inputs only), as proposed by Boeddeker and Hemmi (2010), the existence of an internal ‘body in horizon’ estimation suggested by our improved model would mean that the body control process based on the ‘head in body’ is liable to compensate for some visual errors by taking a reference body orientation with respect to the horizon. Body control in insects may therefore be enhanced by using the relative positions of the visual system, as established theoretically (Manecy et al., 2014) and this may account for the near-perfect hovering performances observed in some flying insects, including the hoverfly. In addition, a command based on an internal body roll estimation with respect to the horizon would give an arbitrary head command without any conflict with the two-nested feedback loop of the VPM (see Fig. 10). This configuration would therefore obviously have the advantage of making both the VPM and any other head control loop fully compatible. In other words, head control could be achieved by multiple channels without any need for identifying and switching between channels. It is of great importance to note that visually controlled stabilization of the head and body based on the orientation of the horizon does not require any gravity sense, which has never been observed in flies during flight so far (Hengstenberg, 1984). This hypothesis will now have to be tested experimentally using free roll procedures to study the head/body coordination triggered in response to body roll disturbances and dynamic rotations of the horizon.

One quite unexpected result obtained in this study focuses on the sex-related differences observed in the insects' head roll responses: the males feature slower but smaller steady-state errors in response to tilted horizons, but showed less head stability (see Fig. 3B). The main sex-related differences observed in hoverflies so far is the presence in the male compound eye of enlarged facets between the clypeus and ocellar triangle, which are absent in females (Collett and Land, 1975). This anatomical difference is associated with neural processing differences and the presence of a more accurate receptive field in males (Nordström et al., 2008) although female STMD neurons respond to the presence of small objects in the frontal visual field (Nordström and O'Carroll, 2006). The differences in head roll stabilization still remain to be explained, but they may be linked to behavioural differences such as mate chasing in males, which certainly requires specific stabilization abilities.

In conclusion, we have brought to light the existence in hoverflies of a horizon realignment reflex, which cannot be accounted for by a purely visual feedback under certain conditions. The improved model therefore developed to account for this behaviour was based on a multisensory integration pathway controlling the insects' head roll movements. On the basis of the responses obtained with this model, we have put forward a new hypothesis on the combination of visual and proprioceptive information involved and the possibility that hoverflies may control their body roll orientation with respect to the horizon via proprioceptive sensors located in the neck joint.

We are greatly thankful to Julien Diperi for his work building the experimental device, to Marc Boyron developing the software and electronics on which all the work presented in this paper was based and to Jessica Blanc for correcting and improving the English manuscript. We are grateful to the reviewers for their useful comments.