Periodic orbit analysis demonstrates genetic constraints, variability, and switching in Drosophila courtship behavior

Abstract

Ruedi Stoop and Benjamin I. Arthur, Jr. Institute for Neuroinformatics ETHZ/UNIZH, Winterthurerstr. We use symbolic dynamics to describe Drosophila courtship communication. We posit that behavior should be defined in terms of irreducible periodic orbits of fundamental acts. This leads to a first operational definition of behavior, which allows for a fine grained quantitative analysis of behavior. We obtain evidence that during Drosophila courtship, individual characteristics of the protagonists are exchanged (predominantly from the male to the female) and that males in the presence of fruitless males perform a behavioral switch from male to female behavior

Mesocopic comparison of complex networks based on periodic orbits

“…We found that despite an extremely large variability of individual behaviors, to the vast majority of the individuals, the classes are distinguishable. 6 This supports the hypothesis that PC conveys mating suitability, including individual profiles. On the class level, the areas of greatest dissimilar behavior (dark bands and dark subdiagonal parts) indicate a maximally spread communication code between normal males and females, which we believe cannot be accidental.…”

“…After characterizing each file by means of its behavioral vectorb, we calculated the scalar product between the different vectors, and, in order to compare class behavior, we also considered class behavior by averaging over the protagonists of each class (this pooling can be justified 6 ). We found that despite an extremely large variability of individual behaviors, to the vast majority of the individuals, the classes are distinguishable.…”

“…The recorded courtship behaviors were analyzed and each one separated into 37 fundamental (on neuronal time scales irreducible and mutually independent) acts. 6 These are the nodes of the courtship graph that emerges from connecting sequential acts. We now look at DPC as a dynamical system, where the PC fundamental acts correspond to the symbols used in the symbolic dynamics.…”

“…In the past, IUPO have been used to extract salient, essentially macroscopic, properties from dynamical systems. [1][2][3][4][5][6][7] We will show that a similar approach allows one to extract mesoscopic properties from general complex networks, where the dynamical notion of "instability" is generally replaced by a corresponding probabilistic branching property. We will finally demonstrate how, upon a specification of the general method, we can cope with the presence of noise.…”

“…Irreducible unstable periodic orbits (IUPO) have been shown to capture the complexity of chaotic systems in a condensed manner. [1][2][3][4][5][6][7] As IUPO are generally composed of a number of network elements, and since the whole network can be exhausted by IUPO in an efficient and well-controlled manner, they are highly suitable for a mesoscopic description of complex networks. In the past, IUPO have been used to extract salient, essentially macroscopic, properties from dynamical systems.…”