The behavioral data on Eristalis tenax were collected in a previous study (Geurten et al., 2010). The trajectory data were obtained with a pair of high-speed cameras running at 500 fps with a resolution of 1024 × 1024 pixels and analyzed as described in detail in Geurten et al. (2010). For electrophysiological experiments, we collected Eristalis pupae from cow dung. This method was developed by Prof. Dr. K. Lunau (University of Düsseldorf). Calliphora vicina and Eristalis tenax were bread 25°C in 12:12 light–dark cycle in the lab stock.

The trajectory data of Calliphora were obtained from C. Schilstra and J. H. van Hateren (Schilstra and van Hateren, 1999; van Hateren and Schilstra, 1999). Calliphora semi-free flight behavior was recorded in a 40 cm × 40 cm × 40 cm arena surrounded by a Helmholtz coil. Head orientation was recorded via small magnetic coils positioned on the fly’s head (for details see Schilstra and van Hateren, 1998).

Clustering algorithms find density clouds in high dimensional data spaces. We used the translational and rotational velocities corresponding to subsequent recorded video frames (Eristalis) or trajectory positions (Calliphora) as the data on which our algorithms operated. In our case this was a 5D data space for Eristalis with the following velocities: forward, sideways, upward, yaw, and pitch. In the case of Calliphora it was a 6D data space including roll-velocity as well. The k-means algorithm (MacQueen, 1967), which was employed for the final segregation of the data, searches for accumulations of data points that lie closely together (“group”). When all groups were found by clustering we derived the center of each group, which we called the PM (for more detail see Braun et al., 2010; Geurten et al., 2010). Finally, every frame of a given trajectory was assigned to one of the PMs.

Please note that the PMs shown in Figure 1 are from two different data sources. The Calliphora PMs are based on head trajectories, while the Eristalis PMs are based on body trajectories. We were not able to obtain a large enough data-base to cluster Eristalis head trajectories, because these trajectories had to be acquired manually from the video data (see Geurten et al., 2010 for more details). We tested thoroughly, if the important but subtle differences between head and body trajectories have an influence on the resulting PMs of the clustering (data not shown). Because clustering is a rather coarse classification and thus cannot pick up the subtle differences between head and body movements, the resulting PMs are very similar.

For the optic flow analysis we used head trajectories for Calliphora and Eristalis. Eristalis head trajectories were calculated from position and orientation data obtained by manual video analysis. The video material was a subset of the footage used during clustering analysis (see Geurten et al., 2010). The optic flow analysis is based on the calculation of the distances between fly and flight arena for every viewing direction (“sampling points”) and the corresponding change in the position of the fly along the trajectory (Koenderink and Doorn, 1987). For this, we used custom software written at our department. We rebuilt the flight arenas’ walls in virtual reality and set a sample point matrix at the position and in the orientation of the fly’s head. The sample point matrix consists of 36 sample point positions in azimuth times the 12 sample point positions in elevation, covering a field of view from −60° to 60° in elevation and the complete azimuth. The sample points were evenly spaced. For all sample points, we calculated the intersection between a line drawn from the fly’s head through the respective sample point and a wall of the flight arena. The calculations were done for all entries of a given trajectory. By comparing the intersection positions of each sample point through time we calculated the time course of image shifts on the retina. This calculation is independent of contrast, illumination and texture of the walls. An optic flow field was calculated for every single location along a given trajectory. This was done for all trajectories. Since every trajectory entry had been assigned to a given PM (see above), the prototype-specific optic flow was calculated as the mean of all optic flow fields corresponding to the respective PM. Note that in case of Eristalis PM assignment, in contrast to prototype-specific optic flow calculation, was based on body data.

We used two different preparations for the two species.

Eristalis was dissected according to Nordström et al. (2008). The head was opened above the lobula plate and tracheal tissue was removed. In contrast to Nordström et al. (2008) the head orientation was aligned with the stimulus setup using the deep pseudopupil. Without any Ringer solution or removal of the neuronal sheath, the target tissue was approached with aluminum silicate (AlSi) electrodes. The electrodes were pulled in a two-step heating program on a P-97 Sutter Instruments Puller. When filled with 1 M KCl recording electrodes had a typical tip resistance of 85 MΩ. The reference electrode was placed in the contralateral head hemisphere. For morphological identification we filled the electrode tips with 15 mM Oregon Green 4888 (BAPTA)-1 hexapotassium salt (Molecular Probes, OR, USA) in 1.7 mM KOH/33 mM (4-(2-hydroxyethyl)-1-piperazineethanesulfonic) acid/3.3 mM KCL. The dye was iontophoretically injected (0.5–1 nA) for 5–30 min. During dye injection no electrophysiological experiments were done. Dye-filled neurons were visualized with a fluorescence microscope in the living animal without further histological processing. We assembled a depth projection which was then copied by hand into a vector graphic.

Calliphora was dissected differently. The animal was fixed with wax ventral side up to a glass holder and its head tilted forward in order to give access to the head capsule’s back plate. The legs and antennae were removed and the amputation holes closed with beeswax. The proboscis was immobilized with wax. In this case we used a Ringer solution, as described in Kurtz et al. (2006). We used borosilicate electrodes, pulled on a P1000 Sutter Instruments puller. These electrodes had a typical tip resistance of 35 MΩ when filled 1 M KCl.

For both species the pre-amplified signal was fed into a custom-designed amplifier (TK 88, Max-Planck-Institute for Biological Cybernetics, Tübingen, Germany). The signal was low pass filtered with a cut-off frequency of 2.4 kHz and then sampled at 8.192 kHz by a DT3001 I/O-card (Data Translation, Marlboro, MA, USA). A thermometer recorded the temperature next to the animal for each single trial. The data was stored via the MATLAB data acquisition toolbox (The MathWorks Inc., Natick, MA, USA) for offline data analysis.

As stimulus device we used an updated version of the high-speed panoramic LED stimulus device FliMax described in Lindemann et al. (2003). The FliMax2 has the same icosahedric shape as its precursor model, covering more than 200° in azimuth and more than 150° in elevation. It’s 7168 ultra bright LEDs (WU-14-752GC, 525 nm, 5 mm diameter, Vossloh-Wustlich Opto, Kamp-Lintfort, Germany; ∼12,000 cd·m⁻² maximum brightness) are arranged in rhomboids containing 32 × 32 LEDs each. All LEDs are bent to the center of the icosahedron, which results in a spatial resolution of 2.3°. The number of brightness steps was increased in comparison to the FliMax1 (eight steps) to 256. Presentation rate of FliMax2 is 354 fps, i.e., sufficiently high to account for the temporal resolution of the fly’s visual system.

The data presented in this article was recorded with four different stimuli. Each stimulus trial starts with a contrast ramp bringing each LED from 50% intensity to the first pixel value of the first stimulus image. After the stimulus trial again a contrast ramp fades the pixels from the last stimuli image to 50% intensity (500 ms duration). This is done to avoid transient on- and offset response. Between stimuli trials the LEDs were left at 50% intensity for at least 7 s.

The vCH neuron responds with a change in its graded membrane potential to stimuli. In all cases we subtracted the resting potential from the vCH response. The responses of each cell were averaged over repetitive presentations of the same stimulus. Then the mean and standard deviation (SD) of the responses across cells were calculated.

For calculation of PM-triggered response averages we used the change of PMs or the occurrence of a PM as a trigger for the analysis. First, every data point in the trajectories was assigned to a PM. Next, we defined a time window of 50 ms symmetrically around transitions between certain PMs. Finally, we calculated the triggered response averages within the time window. In a similar way, we calculated the saccade-triggered averages in a time window of 200 ms located symmetrically around the peak velocity of each saccade.

In Figure 2 we describe how we collected data and categorized the resulting measurements. We used the PMs to reduce the complexity of naturalistic time-dependent flight patterns. In this way, we reduced the trajectories’ complexity originally given by their time-dependent rotational and translational velocity values to a series of just nine states, i.e., the PMs. The PMs are plotted in Figure 1 to allow for easy comparison and are discussed in detail in Braun et al. (2010) and Geurten et al. (2010).

The different flight styles of hoverflies and blowflies manifest themselves in partly large differences of the optic flow evoked by the different PMs (Figure 3). These PM-triggered flow fields were obtained by the following procedure: The optic flow for all positions and trajectories was acquired by using the Koenderink algorithm (Koenderink, 1986). The Koenderink algorithm uses the 3D structure of the world and calculates geometrically the optic flow vectors. We projected these vectors onto a cylindrical coordinate system, as can be seen in Figure 3. We then used the PM assignment for each trajectory position to calculate the mean optic flow over all flow fields elicited by one PM (see Figure 3).

The saccadic PMs lead to the strongest optic flow (see Figure 3, dark shading). Optic flow vectors evoked by the saccadic PMs are pointing uniformly against the direction of rotation. The saccadic optic flow is quite similar for both species, which is due to the fact that both animals show similar fast rotations of short duration. Likewise, there is also translational optic flow which is similar for Eristalis and Calliphora. These similar flow fields (Figure 3, intermediate shading) belong to combined forward and sideways movements (Eristalis PMs 3 and 4 | Calliphora PMs 5–8). Not all flow fields attributed to translational PMs of Eristalis and Calliphora are similar though (Figure 3, light shading). Rather, they may differ strongly from each other. For further information, e.g., the focus of expansion, see Appendix.

To assess whether these different PM-driven inputs are reflected by the properties of neurons that are sensitive to optic flow, we focused on the vCH neuron from which we recorded repeatedly in both animals (Calliphora N = 8; Eristalis N = 8). Evidence that the presumed vCH cell of Eristalis is homolog to its Calliphora counterpart is based on the cell’s receptive field properties and preferred direction of motion (see Figure A2 in Appendix) as well as its anatomy. Since the anatomy of vCH of Eristalis was not known before, we dye-injected it as well as other tangential cells with Oregon green (see Materials and Methods for details). We used a dorso-ventral projection of the fill to draw a reconstruction of the cell’s main arborizations (see Figure 4). The main arborization of the Eristalis vCH does branch in a similar fashion to that of Calliphora (Hausen, 1993), and its position relative to the HS-cells, another type of identified tangential cells (Hausen, 1982a,b), is similar.

In a preceding study Eristalis tangential cells were shown to be more sensitive to slower temporal frequencies under steady-state conditions than blowfly tangential cells (O’Carroll et al., 1996). Therefore and because of the differences in flight dynamics between blowflies and hoverflies we asked whether vCH cells in both species are differently tuned to motion transients. To assess the cells’ dynamical response properties, they were exposed to instantaneous velocity changes. We presented a spinning drum covered with a stripe-pattern, which drives the cell to very large graded membrane potential changes. The pattern moved horizontally at a temporal frequency of 2 Hz, instantaneously switching direction after 1080 ms. Although both species’ vCH cells (Calliphora N = 5, n = 3–7 | Eristalis N = 8, n = 2–10) signals are similar with respect to amplitude and shape (see Figure 5), they differ in the timing. The Eristalis vCH responds faster to the direction change than does the Calliphora vCH. For a change from preferred to anti-preferred direction, the time shift between the responses of the two species – determined at half-maximal response – is 6.8 ms, and for the opposite directional change the time shift is 4.3 ms. Our further analysis concentrates on the properties of this difference.

To ensure that these large time shifts are not artifacts of the data analysis, we conducted several controls. Since response latencies have been found to be temperature sensitive (Tatler et al., 2000; Warzecha and Egelhaaf, 2000; Egelhaaf et al., 2001), we controlled the temperature in all experiments. The mean temperature during the Eristalis experiments was 29.7 ± 1.8°C, the mean temperature during all Calliphora experiments was 28.9 ± 1.8°C. In all tests, only one Calliphora vCH was faster than the three slowest Eristalis vCH cells. All other Calliphora vCH were slower than any of the eight Eristalis cells. We only used female freshly emerged flies (1–3 days old) to ensure that the time shift was not biased by gender or age differences.

We reconstructed the image sequences seen by both fly species during real flight trajectories and analyzed the responses of each vCH (see Figure 6) cell to the image sequences induced by the flight of its own and the other species (Calliphora N = 5, n = 3–23 | Eristalis N = 8, n = 3–11). The complete response to a 3.5-s flight sequence (see Figure 6) is extremely complex because of the many factors that influence the visual input perceived by the animal. The responses of vCH cells are influenced by the motion of the fly, the distance to the walls and the apparent texture of the walls, as well as the history of stimulation. This makes deciphering which of the parameters elicited which component of the cellular response a very complex task. The PMs aid our analysis by reducing this complexity, as they did when we analyzed differences in the overall optic flow experienced by the two species as a consequence of their different flight styles.

As is known from previous studies, the vCH cell of blowflies reacts to yaw saccades with strong depolarizations and hyperpolarizations, depending on the turning direction (van Hateren et al., 2005). When stimulated with the optic flow generated by Calliphora flights (Figure 6B) the saccadic turns and the peak depolarizations of the membrane potential are strongly correlated with the vCH cell responses of both species. Note that response amplitude is not linearly related to saccade peak velocity. This can be observed in Figure 8B for the saccades between 1.75 and 2.5 s. Saccades in this part of the stimulus have very different peak velocities, but the vCH cells respond with similar depolarization levels. In intersaccadic intervals that are dominated by translations, the vCH cells are much less activated. The cells from both fly species respond differently to the optic flow generated during Eristalis flights (Figure 6A). Here, not all depolarizing response peaks correlate with yaw saccades but instead correlate with translational PMs, for example the depolarizations marked with an asterisk in Figure 6A. Hence, the response profiles of vCH cells in Calliphora and Eristalis seem to mainly depend on the characteristics of the flight used for stimulus reconstruction. The translational movements of Eristalis (in our arena) are slower than those of Calliphora, which leads to a different stimulation history.

The average responses of Calliphora and Eristalis vCH cells (Calliphora N = 5, n = 3–23 | Eristalis N = 8, n = 3–11) triggered by yaw saccades are shifted in time with respect to each other (Figure 7). Again, we calculated the time shift at half-maximal response. The Eristalis vCH is always faster than its blowfly counterpart. The time shift between responses of both species’ vCH amounts to 12 ms for blowfly preferred-direction saccades (Calliphora; Figure 7B) and to ∼10 ms for hoverfly preferred-direction saccades (Eristalis, Figure 7A). For the anti-preferred direction, the values seem to differ considerably but cannot be quantified, because the responses have no distinct peaks, which are necessary to accurately assess time-shifts.

Hoverflies and blowflies do not only change rotational velocities rather abruptly, but also translational ones, for example during zig-zagging. In this case forward flight is superimposed by alternating sideways components (Schilstra and van Hateren, 1999; van Hateren and Schilstra, 1999; Geurten et al., 2010). Components of the zig-zagging can also be found in the PMs of both species (see Figure 1, blowfly: PMs 5–8, hoverfly: PMs 3 and 4). Therefore we analyzed the responses of blowfly and hoverfly vCH cells (Calliphora N = 5, n = 3–23 | Eristalis N = 8, n = 3–11) to transitions from forward-left PMs to forward-right PMs and vice versa (Figure 8). The translational direction changes lead to smaller changes in optic flow than do saccades. The corresponding time shifts in the neural responses (Figure 8) are also smaller than those corresponding to saccades (Figure 7).

We hypothesized that the values of time shift depend on the transience of change in the optic flow. Although the fastest change in optic flow is elicited by the instantaneous direction reversal in the spinning drum experiment (Figure 9, left column, and Figure 5), it does not produce the largest time shift. The second fastest change as evoked by saccades led to the largest time shifts (Figures 7 and 9). Eristalis yaw saccades in our setup have a mean peak at ∼1000°·s⁻¹ and have a slightly broader shape than their Calliphora counterparts (∼2000°·s⁻¹; Schilstra and van Hateren, 1999; van Hateren and Schilstra, 1999; Geurten et al., 2010). Hence, the change in the corresponding optic flow is less transient in Eristalis than in Calliphora. This difference in optic flow dynamics might be reflected in the somewhat larger response time shift duration for blowfly than hoverfly saccades. We stress here that the gradual change in the magnitude of the time shift duration is not merely due to the amplitude of the cell’s membrane potential change. In all three situations (spinning drum, Calliphora saccade, Eristalis saccade) the cell membrane potentials peak in the saturation region of the cells’ response range. The smallest time shifts were observed for the side-to-side PM combinations (Figure 8). Again, within this subgroup of stimuli, the stimulus corresponding to the largest sideways component (the largest change in optic flow) elicits the largest time shift.

In summary, Eristalis vCH cells respond the faster to optic flow, the more transient the change in optic flow is. This holds true for naturalistic situations, but not for the instantaneous direction reversal.