Orientation selective or not? - Measuring significance of tuning to a circular parameter

Orientation and direction tuning are among the most studied features of the visual system and are routinely measured during experiments to estimate the quality of neuronal responses. However, standard approaches to report orientation selectivity are only narrowly quantitative and strongly depend on the signal quality, while the more sophisticated ones are computationally exhaustive, making them difficult to use during ongoing experiments. We propose a fast and efficient method for reporting the reliability of coding applicable to any circular parameter. Similar to standard deviation in the linear statistics, reproducibility measures trial-to-trial variability of a circular response parameter. Reproducibility is a normalized measure easily transformed to p-values, which provide explicit information about significance of the estimated orientation preference. The proposed approach is applicable to a wide range of signal types. Here, we discuss examples from optical imaging and electrophysiological recordings, and provide a more thorough examination based on tuning curves modeled in silico.