The idea that the Roman Empire had grown too large to efficiently be managed by one emperor, and was more appropriately governed by two co-ruling emperors, had become established by the time of emperor Diocletian (284–305) in the late 3rd century. Throughout the fourth century, various different divisions were made, until the empire was firmly and permanently divided into western and eastern spheres of imperial administration from the death of emperor Theodosius I (379–395) in 395 onwards. Though modern historians typically use the terms Western Roman Empire and Eastern Roman Empire to describe the new political situation, the Romans themselves never considered the empire to have been formally divided, still viewing it as a single unit, although most often having two rulers rather than one. The Western Roman Empire, more rural than the east, with less people and a less stable economy, and prone to an increasing number of Germanic barbarian invasions and settlements, experienced catastrophic decline throughout the 5th century. In 410, the Visigoths under Alaric I had sacked Rome and in 455, the last western emperor of the Theodosian dynasty, Valentinian III (425–455), was deposed and murdered. That same year, Rome was sacked again for the second time in less than fifty years, this time by the Vandals under Gaiseric, who captured Valentinian's widow, Licinia Eudoxia, and two of his daughters, Eudocia and Placidia. The Western Roman army gradually became increasingly reliant on barbarian mercenaries. After Valentinian's murder, the most powerful barbarian generals, such as Ricimer, became politically dominant, ruling through proclaiming puppet emperors. In the time between the death of Valentinian and the accession of Julius Nepos, a period of less than twenty years, seven different emperors ruled the west and effective imperial control was only exercised in Italy, Raetia and some regions of Gaul.