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

Abstract

The theory presented here describes the visual orientation behavior of fixed flying insects (the fly Musca domestica) in the presence of elementary patterns. The theory, which is based on a number of experimental results, Reichardt (1973), is a phenomenological one whose main purpose is to provide an organizational framework for treating a complex phenomenon without the need of detailed assumptions about the neural mechanisms actually involved.

A simple hypothesis concerning the basic structure of the pattern fixation process leads to an equivalent stochastic equation of the Langevin type, which can be linearized for simple single-stripe panoramas. A critical experiment supports these theoretical assumptions. In addition, the effect on pattern fixation behavior of adding contrast noise to the background of the panorama, is quantitatively predicted by the theory.

In the more general case of a panorama consisting of many vertical stripes, the Fokker-Planck equation associated with the Langevin equation, no longer linear, is solved. Making use of an experimentally proven “superposition principle”, the stationary pattern fixation behavior of the fly in an arbitrary panorama consisting of a collection of vertical stripes is predicted. In this context, concepts like pseudo-invariance and phase-transition can be applied to the insects orientation behavior. The theory presented here seems to contain rich classification properties, which might provide the foundations for an understanding of more complex pattern discrimination processes.

Possible extensions of the theory, as well as some similarities to human eye fixation, are also discussed.