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This work is devoted to the study of an integro-differential system of equations modelling the genetic adaptation of a pathogen by taking into account both mutation and selection processes. First, we study the asymptotic behaviour of the system and prove that it eventually converges to a stationary state. Next, we more closely investigate the behaviour of the system in the presence of multiple EAs. Under suitable assumptions and based on a small mutation variance asymptotic, we describe the existence of a long transient regime during which the pathogen population remains far from its asymptotic behaviour and highly concentrated around some phenotypic value that is different from the one described by its asymptotic behaviour. In that setting, the time needed for the system to reach its large time configuration is very long and multiple evolutionary attractors may act as a barrier of evolution that can be very long to bypass.
The classical historian J. B. Bury (1861–1927) was the author of a history of Greece (also reissued in this series) which served as a standard textbook for over a century. He also wrote on the later history of the Roman empire, and, in this 1911 work, examines the text (of which he provides an edition) of the 'Kletorologion' of Philotheos, an otherwise unknown official at the court of Byzantine Emperor Leo VI in the late ninth century. The work is a guide to precedence and court hierarchy, which at this time were of great political and social importance. Bury uses it to throw light on an administrative process in a period from which few other administrative documents have survived, but also works backwards from it to the far better recorded period of the reign of Justinian, demonstrating the likely developments of the imperial system in the intervening three centuries.