Accessory gland proteins are a major component of Drosophila seminal fluid. These proteins have a variety of functions and may be subject to sexual selection and/or antagonistic evolution between the sexes. Most population genetic data from these proteins are from D. melanogaster and D. sinulans. Here, we extend the population genetic analysis of Acp genes to the other simulans complex species, D. mauritiana. and D. sechellia. We sequenced population samples of seven Acp's from D. mauritiana, D. sechellia, and D. simulans. We investigated the population genetics of these genes on individual simulans complex lineages and compared Acp polymorphism and divergence to polymorphism and divergence from a set of non-Acp loci in the same species. Polymorphism and divergence data from the simulans complex revealed little evidence for adaptive protein evolution at individual loci. However, we observed a dramatically inflated index of dispersion for amino acid Substitutions in the simulans complex at Acp genes, but not at non-Acp genes. This pattern of episodic bursts of protein evolution in Acp's provides the strongest evidence to date that the Population genetic mechanisms driving Acp divergence are different from the mechanisms driving evolution at most Drosophila genes.
This paper proposes several definitions of "norm-observability" for nonlinear systems and explores relationships among them. These observability properties involve the existence of a bound on the norm of the state in terms of the norms of the output and the input on some time interval. A Lyapunov-like sufficient condition for norm-observability is also obtained. As an application, we prove several variants of LaSalle's stability theorem for switched nonlinear systems. These results are demonstrated to be useful for control design in the presence of switching as well as for developing stability results of Popov type for switched feedback systems.
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