There exist many methods to detect recombination or mosaic structure in a sample of DNA sequences. But how reliable are they? Four methods were investigated with respect to their power to detect recombination in simulated samples with different amounts of recombination and mutation. In addition, we investigated the impact of the shape of the underlying genealogy on their performances. We found that the methods detected far fewer recombinations than were theoretically possible and that methods based on the principle of incompatibility in general had more power than methods that did not make use of this principle explicitly. This seemed, in particular, to be the case for phylogenies generated under population expansion scenarios which result in long branches at the tips and small deep branches. In addition to the results obtained through simulations, a series of new theoretical results on recombination is presented.
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Cosima describes a most agreeable picture. Richard is in splendid spirits.Dinner conversation is more animated than usual. Progress on the duet between Klingsor and Kundry is proceeding apace, and there is a provocative new article on the Jews from the Deutsche Reichspost to discuss. After the dinner plates have been cleared, our couple retires to the parlor for their regular evening reading-this week, Walter Scott's Waverly. But Richard is in a mood for some four-hand music. Seidl and the other copyists are invited to join them. Richard takes out his worn copy of Haydn symphonies and sits down at his new Steinway with Cosima. Together they read through Symphony No. 82 in C Major (the "Bear"). Everyone is enchanted. "In him," he observes, "one clearly sees how the popular genius finds its way. The form is more compact than in Mozart; he always went after the melody, had no time to spare for the work (with the exception of the four great symphonies). This is why these Haydn works are also much more interesting." Playing through a Mozart symphony with Seidl confirms his reservations about Mozart, whom he pronounces "a great chromaticist," but adds, "he rarely gave expression to his nature."1 I owe to numerous colleagues thanks and gratitude for their bibliographic suggestions and constructive responses to several earlier incarnations of this paper. In particular, I would like to acknowledge the thoughtful readings I received from . While I have not been able to incorporate all of their many valuable suggestions, this paper is immeasurably better on account of their collective wisdom. Finally, I must mention several former colleagues at the University of Iowa-in particular, David Gompper, Daniel Shapiro, Rene Lecuona, Kevin Kopelson, and Uriel Tsachor-with whom I have shared innumerable pleasant evenings of four-hand and eight-hand music making over the past six years and with whom I have been able to test some of the ideas presented in this essay.
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