White noise methods have been well established for analysing linear and nonlinear properties of biological systems (De Boer & Kuyper 1968
; Marmarelis & Naka 1972
). Using a rapid white-noise approach in a visual flight simulator, we measure the sensory-motor impulse response of an intact fly to visual sideslip against the background of simultaneous forwards, backwards or sideways translation. The optomotor impulse response does not imply linearity within those mechanisms. Indeed, visual processing contains nonlinearities at several stages. However, the impulse response does provide a robust predictive model that has no free parameters. The predictions then enable precise quantitative assessment of manipulations to the complexity of optic flow such as that experienced under natural conditions.
In free flight, Drosophila
generally iterates a sequence of straightforward flight punctuated by rapid turns (Tammero & Dickinson 2002
). Therefore, the world continuously translates backwards across the eyes. Fruitflies also orient upwind during flight (Budick & Dickinson 2006
), but in anything but purely laminar wind flow, they probably experience substantial sideslip movements. Visual sideslip evokes powerful visual equilibrium wing kinematics (Duistermars et al. 2007
) and strong reaction forces and moments (Sugiura & Dickinson 2009
Our results indicate that (i) the linear impulse response predicts a large fraction of the explainable variation (the variation linked to optic flow) in yaw kinematics during perturbations to sideslip optic flow, and (ii) there appears to be little or no crosstalk between the optomotor control algorithms operating along different axes (a). This optimal linear filter is highly robust and selective in that it is not influenced at all by superimposed forward velocity (b). This suggests that compound optic flow stimuli are effectively decomposed into their elemental components, and then in this case only sideslip signals are fed into the stability control algorithm. This interpretation is consistent with the result that sideslip velocity dramatically alters the control of sideslip stabilization. Remarkably, added offset in sideslip velocity improves temporal sensitivity by shortening both the response delay and relaxation time (c). This result was surprising, because we expected that the background velocity might be perceived as added noise and render the impulse response more sluggish and less correlated with the input stimuli.
In this study we did not consider the effect of rotational velocities, although these might also alter the responses to sideslip. However, rotational saccades comprise vastly less of a flight trajectory than forward translation. Sustained rotation would be experimentally problematic to test for several reasons. It is periodic, bringing the fly back to its original orientation each full rotation cycle, and it alters the direction of wing generated forces with respect to gravity. These issues make standing rotation a more challenging and less relevant stimulus to analyse.
Patterns of optic flow are encoded by wide-field integration neurons of the third optic ganglion in flies (Borst & Haag 2007
) that synapse with interneurons projecting into the thoracic motor centres (Haag et al. 2007
). Thus, it is probable that these circuits perform critical computations for encoding and decomposing optic flow patterns. Yet, flies exhibit diverse visual behaviours, such as sensitivity to second-order motion, that cannot be readily explained by our current understanding of these circuits (Theobald et al. 2008
), and fascinating crossmodal interactions with motion processing and optomotor behaviour have recently been brought to light (Parsons et al. 2006
; Chow & Frye 2008
We are far from achieving a comprehensive model of the control algorithms by which naturalistic patterns of visual motion are integrated into stabilization flight reflexes in these high performance fliers. The linear filters account for most of the mean responses, but there is substantial variation still unexplained, especially in the case of standing sideslip velocity, which may imply static or dynamic nonlinearities. The analyses presented here provide an entry point for further quantitative behavioural, neurophysiological and genetic analyses of the cellular circuits and computational algorithms that bestow flies with visuo-motor robustness and flexibility that have propelled their evolutionary success.