Horn E
Biol Cybern. 1978 Dec 5;31(3):145-58. doi: 10.1007/BF00337000.
The orientation behavior of walking flies, Drosophila melanogaster, towards a single 6 degrees wide black vertical stripe (elementary stripe) can be explained by use of the turning tendency function H(beta). This function is characterized by maximal values at an angular distance of beta = 25 degrees from the stable zero position (= orienting direction), a sharp decline from this maximum to beta = 60 degrees, and a very slow approach to the unstable zero position (Horn and Wehner, 1975). The shape of this function is influenced by both translatory and rotatory components of movement. If the translatory component is minimized by measuring the turning function W(beta) (see 2.3) at a distance of 10 mm (C1) from the center of the arena, a change in the strength of this decline is caused. But with increasing translatory component, i.e. at a greater distance from the center of the arena, W(beta) approximates the heuristical function H(beta) (Fig. 12). The turning functions W(beta) are pattern-specific; the angular positions of the maximum responses shift to greater angles with increasing width of the patterns (Fig. 2). In the two-pattern configuration with double or single stripes, there is always a coincidence between the stable zero positions of Wsigma(beta), the mean of the frequency distributions P(beta) of the flies' positions and ng(beta) of the straight courses, and the stable zero positions of Hsigma(beta) obtained from an additive superposition of two or more angular shifted turning tendency functions H(beta) (Fig. 5, 7). Therefore, the mean positions of the flies in a multi-stripe experiment composed of elementary stripes can be predicted from the addition of many angular shifted turning tendency functions H(beta). Between H(beta) and the frequency distribution P(beta) of the flies' positions beta, the following formula holds: P(beta) = C.intregal of H(beta)dbeta (Fig. 13). With this equation, the spontaneous preference of the broader of two double stripes can be explained presuming lateral interactions between the components of the patterns (Fig. 8, 10). The strength chii of this lateral interaction depends on the width delta of the double stripes. The greater delta, the smaller is chii. chii is a pattern-specific value (Table 1, 2).
