A theory of the pattern induced flight orientation of the fly Musca domestica II

In a preceding paper, Poggio and Reichardt (1973a), a phenomenological theory describing the visual orientation behaviour of fixed flying flies (Musca domestica) towards elementary patterns was presented. Some of the problems raised in this first paper are treated here in more detail. The mapping between the position dependent torque distribution — D(ψ) characteristics — associated with a given pattern and the stationary orientation distribution p(ψ), is studied taking into account that the fluctuation process (generated by the fly) is coloured gaussian noise. Under certain critical conditions this may lead to an “early symmetry breaking” in the mean values of the p(ψ) distribution. The validity of the “superposition principle” has also been examined. Although shift and superposition give the main qualitative features of the “attractiveness profile” D(ψ), associated with a 2-stripe pattern, superposition does not hold quantitatively for stripe separations up to about 80°. Evidence is presented suggesting that such an effect is due to inhibitory interactions between input channels of the fly's eye. Implications of this finding with respect to the problem of spontaneous pattern preference are also discussed.