Conclusion
The frequency response decomposition employed in this study allowed us to reveal for the first time the quantitative relationship between the higher-order statistical properties of environmental stimuli and processing of these stimuli in fly photoreceptors. In light of the results, we argue that the goal of early sensory coding is to maximize sensitivity to higher-order statistical features of the stimuli that are behaviorally relevant to the animal whilst minimizing sensitivity to non-informative signals, to encode efficiently these features and increase their salience to facilitate further processing. Our framework elegantly explains the differences in coding of naturalistic and white noise signals and how this is achieved efficiently without a change in the response transfer function of the photoreceptor when the mean light intensity is constant. It also explains why and how naturalistic stimuli increase the rate and efficiency of information transmission.