Properties of predictive gain modulation in a dragonfly visual neuron

Dragonflies detect and capture small moving prey and pursue conspecifics for mating and territorial defence. During predatory flights, the dragonfly's target rarely spans more than 1 deg of visual space, thus stimulating only two or three ommatidia of the compound eye (Horridge, 1978; Lin and Leonardo, 2017). A population of target-detecting neurons, which we refer to as small target motion detectors (STMDs), have been identified in the optic lobe of several inspect species, including the dragonfly (O'Carroll, 1993; Geurten et al., 2007). These STMDs are responsive to target contrasts as low as 1.3% (Wiederman et al., 2017), matching the sensitivity of fly ‘optic-flow’ neurons that are responsive to large moving patterns (Harris et al., 2000). However, such responses to large objects are the result of many presynaptic units being integrated over space, each viewing different portions of the same feature (Bausenwein et al., 1992). STMDs do not have a similar advantage, as each unit encounters a small and noisy signal which cannot be pooled. Though STMD receptive fields can be similarly large to those of fly optic flow neurons (over 80 deg×80 deg), STMDs respond at any given time only to the presentation of small targets within this larger receptive field. In fact, it is at an individual photoreceptor's signal detection limit where target sizes are able to elicit STMD responses and generate pursuit behaviour (Combes et al., 2013; Rigosi et al., 2017).

We recently described a predictive mechanism employed by STMDs that increases responses to these small targets. Following target onset, spiking activity is initially weak, building in strength over several hundred milliseconds when the target's trajectory is continuous in space and time (Nordström et al., 2011; Dunbier et al., 2012). This property, which we previously termed ‘facilitation’, is matched to a large improvement in contrast gain, with detection thresholds improved 5-fold following the longer target motion (Wiederman et al., 2017). The facilitation results in a local gain increase situated 5–10 deg ahead of a target's current position; however, it is also concomitant with a global suppression within the rest of the surrounding receptive field. Thus, facilitation is more suitably termed ‘predictive gain modulation’ with simultaneous regions of both positive and negative changes in response (gain enhancement and suppression). The predictive gain modulation spreads forward in space following an occlusion, matched to the target's direction of travel. As a result, signal strength is improved for more realistic, continuous target trajectories, whilst background distracters and false positives are suppressed.

Psychophysical experiments reveal that humans use information of prior trajectory to improve their ability to detect and track moving targets (Watamaniuk et al., 1995; Watamaniuk and McKee, 1995). For example, during target occlusions, humans account for target attributes, such as velocity, in their predictions (Bennett and Barnes, 2003). Similarly, observers looking at a scene use specific feature attributes such as their size, direction of movement and colour, to ignore distracters and enhance the saliency of a target of interest (Saenz et al., 2002).

For the dragonfly, the angular size and velocity of a moving target may change dramatically throughout a pursuit. Therefore, robust interception of the target's location should be resilient to a wide range of stimulus properties. Here, we tested attributes of the target and its trajectory that might drive the visual neuron's predictive gain modulation. These results provide insight into how neuronal processing underlies fundamental behavioural tasks, such as predicting the future location of a moving target in the visual environment.

These data are from intracellular recordings in a total of 31 male wild-caught adult Hemicordulia, gathered from the Adelaide Botanic Gardens. Animals were immobilised with a 1:1 bees wax–rosin mixture (Colophony Kolophonium, Fluka Analytical), and fixed to an articulating magnetic stand. The animal's head was tilted forward to expose the posterior surface of the head capsule, before dissecting a small hole in the cuticle directly over the left lobula complex.

We used a Sutter Instruments P-97 electrode puller to taper aluminosilicate electrodes, which were backfilled with 2 mol l⁻¹ KCl solution (AnalaR). We stepped electrodes through the neural sheath and into the proximal lobula complex with a piezoelectric stepper (Marzhauser-Wetzlar PM-10). Electrodes had a typical electrical resistance of between 50 and 150 MΩ.

Animals in which neurons were freshly penetrated were first presented with a series of visual stimuli for neuronal classification, including small targets, bars, gratings and patterns. The centrifugal small target motion detector (CSTMD1) is one specific STMD neuron with a large axon which permits repeated recordings across different animals. Each optic lobe contains an unknown number of unidentified STMDs with similar tuning properties, but only two CSTMD1 neurons (previously identified via intracellular labelling), mirror symmetric on either side of the brain. In this work we performed all of our experiments in CSTMD1, so that effects of receptive field position and physiological tuning were constant across all biological replicates. We identified CSTMD1 by its small target selectivity, characteristic large (80 deg×80 deg) excitatory receptive field in the contralateral visual hemisphere and action potential waveform (Geurten et al., 2007). Intracellular responses were digitized at 5 kHz with a 16-bit A/D converter (National Instruments) for off-line analysis with MATLAB.

Visual stimuli were presented on high-definition LCD monitors (144–165 Hz) placed 20 cm from the animal, centred on the frontal midline. Stimulus scripts were written using MATLAB's Psychtoolbox and integrated into the data acquisition system. All stimuli consisted of 1.5 deg×1.5 deg dark targets drifting vertically on a white background, with the exception of experiments described in Results, ‘Gain modulation in response to the height of the primer target’, where horizontally drifting targets of a series of heights were used. We used intermediate contrast (Weber contrast of 0.41) in order to prevent neuronal saturation masking changes in response gain. STMD neurons will habituate if salient stimuli are repeatedly presented within the same region of the visual field, over a short period of time. In these experiments, we implemented a minimum rest period (8 s) to minimise the effect. We present randomised stimulus conditions to ensure any remaining habituation cannot skew experimental results. A post hoc examination of the data respective to the order of stimulus conditions verified that any temporal changes co-varied across stimulus conditions. Neuronal responses that exhibited stronger habituation resulted in either experiment cessation or discarding of the dataset.

Data were also excluded as a result of pathological damage, as indicated by drifts in resting membrane potential, decreases in spike amplitude or excessively high spontaneous activity. Each experiment consisted of two stimulus types, ‘probes’ and ‘primers’ (Wiederman et al., 2017). Probes were presented either alone or following a primer. Responses to probe targets are weak when presented alone and changed by varying amounts (gain) when preceded by a primer. In most experiments, we introduced a 50 ms pause between the presentation of the primer and the probe, to ensure that residual primer responses were not detected inside the probe analysis window. We did not use this pause for the experiments presented in Figs 1 and 2, as these experiments replicate and build on data presented in Nordström et al. (2011) where no pause was used. The introduction of short pauses does not affect the amount of gain generated by a primer (Wiederman et al., 2017). These long continuous trajectories are likely to resemble the initial target detection phase of behavioural pursuits, where movement on the retina is dominated by prey or conspecific translation. Once closed-loop, active pursuit starts, the dragonfly's own translation and head rotations will alter this retinal image (Mischiati et al., 2015).

We replicated the experimental paradigm of Nordström et al. (2011) by drifting targets on short (probe-only) and long (primer plus probe) trajectories. The probe consisted of a 1.5 deg×1.5 deg target drifting at 40 deg s⁻¹ for 200 ms, but unlike in previous work we used 16 different combinations of primer duration and distance, each terminating at the same location (n=6 dragonflies). To compare the amount of gain generated for a probe following different primers, the mean probe-only response for a given neuron was subtracted from each primed-probe response. This subtractive normalisation removes the effect of an inhomogeneous receptive field (variation in sensitivity at different spatial locations), leaving only the gain effect of the different priming conditions.

We mapped the receptive field of CSTMD1 in one dimension using a series of six probes drifting vertically through the receptive field (n=12 dragonflies). Each probe drifted at 45 deg s⁻¹ for 135 ms, starting at different elevations separated by 6 deg, such that the end position of one probe was identical to the start position of the next. These probe trials were randomly interleaved with primed trials consisting of one of two primers, drifting at either 30 or 60 deg s⁻¹ (both with a duration of 500 ms). Primers terminated either 100 or 300 ms prior to presentation of the probe to test the spread of the predictive gain modulation.

To be consistent with prior work investigating target height tuning (Geurten et al., 2007; O'Carroll and Wiederman, 2014), we drifted targets horizontally. Target height tuning was measured by drifting probe targets (40 deg s⁻¹) at heights varied logarithmically (orthogonal to the direction of motion) between 0.16 and 20 deg (n=15 dragonflies). Probes were presented alone or following one of two priming targets with a size of either 1.5 deg×0.5 deg or 1.5 deg×5 deg (both drifting at 40 deg s⁻¹ for 500 ms).

Probes were moved vertically through the receptive field for 500 ms at 40 deg s⁻¹, either presented alone or preceded by 500 ms of primer motion (terminating at the probe's start position). An individual dragonfly was presented with both conditions of this experiment 40 times in randomised order, with each trial separated by 146 s to ensure that any neuronal variability observed was not due to local habituation. The same experiment was replicated 5–10 times in a further 8 dragonflies (n=9 dragonflies in total) to analyse the variability of gain (modulation) across different animals.

STMD neurons are probably involved in the visual detection and tracking of prey and conspecifics. Here, previously quantified latencies of a dragonfly's reactions to prey movement (timing of visual signals and behaviour) were complicated by predictive mechanisms (Mischiati et al., 2015). STMD neurons are confined to the optic lobes and midbrain (Geurten et al., 2007), separating their activity from behavioural output by at least one intermediate processing stage, potentially the previously described ‘target selective descending neurons’ (Olberg, 1986). It is not yet clear how the timing of elicited STMD responses to targets relates to observations of specific, pursuit behaviours. Therefore, in the absence of this information, we chose a 100 ms analysis window, beginning 50 ms following the onset of a probe. This analysis duration permits a robust spike rate calculation, whilst minimising the amount of ‘self-priming’ of the probe itself. Introducing a 50 ms offset accounts for CSTMD1's response latency (Nordström et al., 2011). Gain modulation was calculated by subtracting the response to probe-alone trials from the paired primed-probe response (at the corresponding time windows). This measure of change allowed us to compare gain modulation across animals without confounding overall neuronal excitability. To compare height tuning between conditions, we display absolute responses to primed and non-primed probes.

In Results, ‘Gain modulation and neuronal variability’, we present data from an individual CSTMD1 recording, where we computed instantaneous spike rate for 40 trials of a 500 ms probe presented alone, as well as 40 trials with the same probe preceded by a 500 ms primer. Given the receptive field of CSTMD1 is inhomogeneous (Geurten et al., 2007), we normalised responses based on receptive field location. This was performed by dividing the instantaneous spike rate of each individual short path trial by the mean instantaneous spike rate for a primed probe presented at the same location. The same experiment was performed in a total of nine CSTMD1 recordings in subsequent animals (inter-animal variability), with the average probe onset presented for each neuron. In addition, by applying a 100 ms analysis bin, sliding in 1 ms increments, we computed the mean (μ) spike count across each trial, as well as the variance (σ²) for each bin. These two values were also used to calculate the Fano factor (FF=σ²/μ).

All statistical tests are non-parametric, paired, two tailed and corrected for multiple comparisons. The experiments shown here are highly exploratory, characterising complex physiological phenomena for the first time. For this reason, there are no suitable data to estimate effect size or variance, so a sample size estimation could not be performed. Instead, we gathered data until we were confident of the effects in question, and then tested for significance.

Previous studies of STMD facilitation presented priming targets that drifted for similar durations and covered similar distances (Nordström et al., 2011; Dunbier et al., 2012; Wiederman et al., 2017). These experiments demonstrated consistent increases in the frequency of spike generation, which we call gain; however, they did not deconfound the effect of duration with the distance the primer target had traversed. Therefore, it was unclear whether the enhancement component of the predictive gain modulation (i.e. in front of the target trajectory) resulted from a target stimulating a certain number of detectors across space, or whether it simply required constant stimulation over a sufficient duration of time.

To answer this question, we presented target trajectories segmented into two sections: a primer and a probe (Fig. 1A). The primer-only (blue line indicates stimulus duration) and the probe-only (black line indicates stimulus duration) conditions elicited spiking activity. We then analysed the change in response to the probe when preceded by a primer. As illustrated by the space–time plots in Fig. 1B, primer targets were drifted for different combinations of space and time, each terminating at the start position of a probe stimulus. Fig. 1C shows individual, example CSTMD1 responses to primers of varying duration, with the analysis time window (100 ms) indicated by the green shaded region. Across neurons, we calculated the average spike rate in response to the 16 combinations of varying primer duration and distance (Fig. 1D, n=6 dragonflies).

If gain modulation only requires the stimulation of several adjacent motion detectors (∼5 deg and larger), we should observe strong facilitation irrespective of the target's duration traversing that space. Conversely, if gain is modulated only by the time of stimulation, primers of equal duration (over varying distance) should produce equal facilitation. As the primer's duration or span approach zero, we know that no facilitation will occur (i.e. the probe-only response). We therefore limited the range of test durations and spans to elicit responses from an STMD neuron. Priming targets that drifted over different combinations of space and time generated different response time courses and elicited different effects on the probe (Fig. 1D). Plotting the change in response magnitude as a function of both primer length and primer duration revealed an oriented pattern, suggesting that the dependent property may be a combination of both primer trajectory length and duration (Fig. 2A). To investigate this, we pooled datasets by trials with equal length, duration or their combination, velocity (Fig. 2B). This revealed that all of the tested primers produced a mean gain increase. When trials were sorted by their length or duration, we observed no net difference on the amount of facilitation generated. However, when we sorted trials by primer velocity (primer length divided by primer duration), we observed responses similar to a velocity tuning function. Primers that drifted at 80 deg s⁻¹ produced the strongest increase in gain, irrespective of their duration or length. This velocity dependence suggests a motion-input pathway underlying the facilitation (gain increase), on a scale less than 5 deg and elicited in under 125 ms. Therefore, although the establishment of the facilitation is motion dependent utilising small spatial scales, the effects are elicited over long distances and time courses (Wiederman et al., 2017).

A distinguishing property of predictive gain modulation is that when a moving target is temporarily occluded, the ‘focus’ of gain modulation spreads forward in space (Wiederman et al., 2017). The extent of the forward spread matched the distance the target would have travelled had it continued at the same velocity during the two tested occlusion periods (150 and 300 ms). However, this experiment was conducted at a single primer velocity. It was therefore unclear whether the focus spread forward at a target-matched velocity, or whether it was set at a ‘hardwired’ velocity that by coincidence matched that of the target in those previous experiments. To investigate further, we presented two primers of equal duration, one drifting at 30 deg s⁻¹ and the other at 60 deg s⁻¹ (Fig. 3A). The faster primer covered twice the distance of the slow primer; however, it terminated at the same position. Following termination of the primer, we introduced a pause of either 100 or 300 ms to allow gain to spread, before presenting probes at different locations ahead and behind the primer's final position. If the predictive focus spread at a primer-matched velocity, then over the same time period the gain elicited by the faster primer should spread twice as far as the gain elicited by the slower primer. Fig. 3B shows example traces of the stimulus paradigm, both to the probe alone and also following two pause durations. The probe response was determined by counting the spike rate in the 100 ms analysis window (green shaded region).

As described in the above results (Fig. 2), primer velocity has a large effect on the size of the gain modulation (Fig. 3C). That is, a 60 deg s⁻¹ primer lies closer to the velocity optimum and will evoke stronger facilitatory effects across all spatial locations compared with the slower 30 deg s⁻¹ primer. This dependence on primer velocity induces a vertical offset in neuronal activity (Fig. 3D,E, dashed red line), presumably with an important effect on the functional system. However, in addition to this offset, there may also be changes in gain at varying spatial locations accounting for the primer target's velocity (i.e. the predictive ‘spotlight’). To test this, we corrected for the motion-dependent offset by subtracting the mean difference in priming strength across the two primers (30 and 60 deg s⁻¹) from the 60 deg s⁻¹ primed trials at all spatial locations (Fig. 3D,E). In agreement with our previous work (Wiederman et al., 2017), a primer followed by a 100 ms pause increased gain ahead of the primer's final position and reduced it behind (Fig. 3D). However, after accounting for the vertical offset in the curves (red dashed line), the modulation in space was similar for all points across both velocity primers. Following a 300 ms pause, the spatial location of gain shifted forward; however, we did not observe any statistically significant effect of primer velocity on the distance of this predictive spreading spotlight (Fig. 3E).

Dragonflies are highly selective for the angular size of prey, with pursuit rarely initiated for targets spanning >1 deg on the retina (Combes et al., 2013; Lin and Leonardo, 2017). The tuning range of STMD neurons is usually much broader, with CSTMD1 producing optimal responses to targets spanning 2–3 deg (Geurten et al., 2007). In the past, target height tuning has been measured with targets that drift across the entire visual display and are therefore ‘self-facilitated’. This means that these tuning curves represent not only the underlying size tuning of CSTMD1 but also any potential size tuning of the gain modulation itself. During pursuit of prey or conspecifics, the size of a target will fluctuate, gradually increasing in angular size as the distance to the target is reduced. Given that predictive gain modulation shifts CSTMD1's direction tuning to match the direction of the target being tracked (Wiederman et al., 2017), is it possible that a target's angular size could also shift an STMD neuron's optimal target height? Such an effect would be similar to that observed in feature-based attention studied in the human visual cortex (Saenz et al., 2002).

We investigated whether gain modulation produced by primers of different height affects CSTMD1's height tuning. We presented a series of probes of varying height, either alone or following the presentation of primers of two heights, either 0.5 deg×1.5 deg or 5 deg×1.5 deg (Fig. 4A,B). These sizes lay either side of CSTMD1's optimal height tuning and were expected to elicit responses of similar magnitude (Geurten et al., 2007).

Our results show that CSTMD1's optimum target height remained at 2–3 deg, irrespective of whether or not the target was primed, or the size of the primer itself (Fig. 4C). The two primers produced responses of equal strength, potentially explaining the equal amount of gain generated (Fig. 4D, 123.4±16.9 for 0.5 deg, 123.7±15.6 for 5 deg, P=0.84). However, the strength of the response gain was not equal across all probe sizes. Rather, the gain produced by a given primer was greatest when the probe was also at an optimal size and weaker when probes were either too small or too large (39.6±6.8 for weak probe sizes, 84.8±13.5 for strong, P=0.007). This result suggests that it is the interaction between properties of both the primer and probe that determines the overall strength of the gain.

Following our description of the effect of primer attributes (e.g. length, duration, velocity and height) on mean predictive gain modulation, we turned to an investigation of the response variance (both inter-trial and inter-animal). That is, what variability is observed in this response gain, when such primer parameters are kept constant? Nordström et al. (2011) reported that gain in CSTMD1 builds with a mean time to 50% of maximum response (t₅₀) of 180 ms, and this value justifies our time window for analysis in all subsequent work. However, the question arises as to whether this value is consistent across multiple animals or stable within the same neuron over extended periods of time.

We measured variability in the onset time course of response gain, with the presentation of a series of targets drifting on either short or long paths (Fig. 5A). We determined the time onset of gain modulation, by normalising the short path responses by their corresponding long path counterparts (the spatial location of the short path covers the long path's second half). This approach provides a temporal signature (onset time course), that accounts for inhomogeneity of the spatial receptive field. We repeated this experiment 40 times in a single CSTMD1 recording at regular intervals over 90 min (Fig. 5A,B), and across nine CSTMD1 recordings in 9 different animals (Fig. 5C). In both cases, we observed variability in the response time course, even though the underlying stimuli and neuronal architecture were identical. This raises the intriguing possibility that the strength of the predictive gain modulation is itself modulated by an internal stimulus-independent factor. Variations in the response onset time course will result in variance in the number of spikes in our standard analysis time window (50–150 ms following stimulus onset). A degree of STMD variability may be due to neuronal habituation, resulting from the presentation of repeated stimuli. Even though each stimulus was separated by a 146 s rest period, the responses show a slight downward trend due to some habituation (Fig. 5D). This decrease in responsiveness to our typical long path stimuli was accounted for in our experiments by randomisation of stimulus conditions. However, there was an additional variation in response over time, evident in responses to short path targets (black line). To quantify the variability of responses over time, we plotted the response variance as a function of mean spike count for the repeated presentation of a target trajectory in a single CSTMD1 neuron (Fig. 5E, same data as in Fig. 5A). These data were generated by sliding a short analysis window across the 1 s peristimulus time window in 1 ms increments. The relationship between response variance and mean spike count varies dependent on the length of analysis window (Warzecha and Egelhaaf, 1999); therefore, we analysed our data across a broad range of bin sizes (100 ms bin data shown). We observed that the ratio between variance and mean spike count, also known as the Fano factor, was strongly dependent on the time following stimulus onset, with very large values (FF>4) shortly after stimulus onset, dropping to FF<0.5 after several hundred milliseconds of motion (Fig. 5F). The time course of this Fano factor drop was closely aligned with the build-up of gain modulation following the onset of both the short and the long paths (Fig. 5G). A higher Fano factor indicates that the signal is encoded with more variability. Given that the short path and the second half of the long path covered the exact same space on the retina, this difference in neuronal variability cannot be explained by input noise. Instead, this variation arises from changes in the strength of modulatory signals throughout the visual pathway.

Our previous description of STMD gain modulation proposed that during continuous target motion, neuronal activity increased (i.e. facilitation) over hundreds of milliseconds (Nordström et al., 2011). Subsequently, we showed that this gain was not due to local ‘elementary motion detectors’ (Wiederman et al., 2017), as it exhibited a long-lasting time course and a large spatial extent that spread in front of the target's trajectory over time (including excitatory and inhibitory regions, i.e. the predictive ‘spotlight’). Here, we show that changes of CSTMD1's response to the probe target is dependent on the velocity of the primer target. Priming targets themselves elicit responses that vary across the different spatial and temporal conditions and it is these velocity-dependent combinations that generate differing amounts of gain for the probe response. The parsimonious explanation for this result is that velocity-tuned elements serve as inputs to the mechanism underlying predictive gain modulation. Such local velocity tuning could be derived from either ‘elementary motion detectors’ (Hassenstein and Reichardt, 1956) or our previously proposed ‘elementary small target motion detectors’ (Wiederman et al., 2008; Wiederman and O'Carroll, 2013).

Interestingly, the same primer target can generate different amounts of gain across a range of values for a single parameter of the probe target (i.e. angular target height). This result reveals that gain modulation is not simply an additive operation. Instead, the magnitude of gain modulation is dependent on both the salience of the priming target and the salience of the probe that follows. This is in agreement with our previous work, where the same priming target generated different strengths of gain modulation for probe targets of different contrast and direction (Wiederman et al., 2017). Such a result could be due to a second-order correlation between the velocity-tuned inputs at a larger spatial and temporal scale (Zanker, 1994). Here, primers at an optimal velocity would supra-linearly interact with probes, maximally facilitating CSTMD1 responses. However, CSTMD1 is overall only weakly direction selective. Moreover, we previously showed that targets that ‘leapt’ forward before traversing back in the opposing direction were also strongly facilitated (Wiederman et al., 2017). This would suggest that it is the spatial location, irrespective of directionality, that is facilitated at this second-order stage. Behaviourally, targets will vary across an extensive range of velocities, particularly in closed-loop pursuit; thus, the proposed second-order interaction would be an essential component of the target-detection encoding.

When all conditions were kept constant, we found that the magnitude and time course of response onset varied considerably, both within the same animal and across animals. Dragonflies in this study were caught in the wild, meaning that their age and feeding state were not controlled. These extraneous factors could contribute to the intra-animal variability, though they would not account for the intra-trial variability within the same animal.

As targets moving on short paths stimulate identical presynaptic visual pathways to those for targets moving on the second half of the long path, this large increase in variability must be the result of variability in internal modulatory signals over time. This finding is consistent with prior work that concluded that most response variability in higher-order processing areas is generated by variability of modulatory signals rather than input noise (Goris et al., 2014). Currently, the neuronal circuits responsible for modulating this neuronal sensitivity and gain magnitude are unknown. Target tracking and pursuit simulations that implemented a dragonfly-inspired predictive gain modulation mechanism found that the optimal facilitation time constant should be variable, depending on the spatial statistics of a scene (Bagheri et al., 2015). In cluttered scenes, a longer time constant increases performance because of the high likelihood of temporary target occlusions; however, in more sparse scenery, a rapid facilitation time course is beneficial, as the target remains highly discriminable. While the spatial statistics of our visual stimulus were identical across each trial, these simulations suggest that the ability to dynamically tune the time course of gain modulation via an unknown pathway could be a useful tool for a target-detecting system.

The downside of a dynamically modulated gain mechanism is that neuronal signals to repeated stimuli are significantly more variable. In most sensory neurons, variance increases with mean spike count, with a slope that varies depending on a system’s intrinsic noise (Aldo Faisal et al., 2008). In the H1 neuron of the fly, the ratio between variance and mean spike count (i.e. Fano factor) was reported as ∼0.16 for 10 ms analysis windows, and ∼0.07 for 100 ms windows, a result which highlights that repeated stimuli in H1 are encoded with relatively low variability (Warzecha and Egelhaaf, 1999). In comparison, CSTMD1's target responses were extremely variable until several hundred milliseconds had passed, imposing a challenge to the target-tracking control system. However, whilst the variable magnitude of gain (neuronal variability) was evident in an early time window, at late time windows, neuronal variability decreased, as responses were driven into the saturation region of CSTMD1's firing range.

The key advantage of such a non-linear stimulus–stimulus interaction is that robust tracking of targets can be obtained amidst dynamically changing conditions. A target that temporarily drops out of an optimal range in size, contrast or velocity will still elicit strong responses as a result of enhanced local gain generated during its prior path. Additionally, a target that abruptly enters the visual field can be detected in a reasonably short time if it already accurately matches the system’s tuning parameters. Such a stimulus–stimulus interaction is favourable for improving signal-to-noise ratio when extracting small moving targets from cluttered backgrounds.

We thank the manager of the Adelaide Botanic Gardens for allowing insect collection. We thank the Australian and Swedish Governments for providing funding for this research.