Around the start of the Common Era, the family trees of the gens Julia and the gens Claudia became intertwined into the Julio-Claudian family tree as a result of marriages and adoptions.
Descendancy of the emperors of the Julio-Claudian dynasty
The Julio-Claudian dynasty was the first dynasty of Roman emperors. All emperors of that dynasty descended from Julii Caesares and/or from Claudii. Marriages between descendants of Sextus Julius Caesar and Claudii had occurred from the late stages of the Roman Republic, but the intertwined Julio-Claudian family tree resulted mostly from adoptions and marriages in Imperial Rome's first decades. Note that descendancy of the Julii Caesares before the generation of Julius Caesar's grandfather is in part conjectural, but as presented by scholars.[1]
In the Julio-Claudian dynasty of Roman emperors, the lineage of the Julii Caesares was separated from those of the Claudii up to Augustus' generation. The next generation had both Claudii with a Julia as ancestor, as Claudii adopted into the Julii Caesares family. After Tiberius, the remaining three emperors of the dynasty had, outside adoptions, ancestors in both the Julian and the Claudian families.
The Claudii were a powerful gens with consuls and other high ranking politicians in several of its families across several generations. In this generation the first marriages between Claudii and descendants of the Julii Caesares took place. This however didn't mean yet that the dynastic family trees of both gentes got merged into a single one: that didn't happen until the adoption of Claudii by (adopted) Julii Caesares in the generations to come.
Octavia the Younger's first husband was a Claudius from the Marcelli family. Claudia, descending from Claudii, became the first wife of Octavian, who by then was adopted in the Julii Caesares family by the testament of his uncle Julius Caesar. After her first husband's death, Octavia married Mark Antony, who besides the offspring of his first three marriages had had children by Cleopatra.
Octavianus, becoming Augustus the first Roman emperor, married Scribonia who gave him a daughter (Julia the Elder). His last marriage was with Livia, a Claudia who had been married to a Claudius. Their son Tiberius, by birth a Claudius, was later adopted by Augustus, thus, like his stepfather Augustus, becoming one of the Julii Caesares by adoption.
Without son, Augustus had adopted his grandsons (by his only daughter Julia) Gaius, Lucius and Postumus, and his stepson Tiberius, in order to ensure an heir and successor. Around the time of his death only Tiberius remained and he became the next emperor. Tiberius, a Claudius by birth had become one of the Julii Caesares by adoption: from this moment this first dynasty of Roman emperors was both Julian and Claudian. The further emperors of this dynasty had both Julian and Claudian ancestors.
Caligula was the last emperor adopted into the family of the Julii Caesares. He was a Claudius by descendance, although he had Julii Caesares among his ancestors, from both his mother's and his father's side.
Nero, the last emperor of the dynasty, was by birth a Domitius with as well Julian ancestors (from both his mother's as his father's side), as Claudian (from his mother's side). He became a Claudian himself, by adoption by his stepfather emperor Claudius, a brother to his grandfather from his mother's side, or, from his father's side, a son of his grandmother's sister.