Sorry for the delay.
Wagner uses dates sparingly, assuming the reader needs only a skeletal summary. No dates here. He has Herod the Great, son of Antipater, procurator of Judaea, son of Antipater, governor of Idumaea. No father for the first Antipater.
I have a note that Antipater's father was Herodes (Herod), born, say 178 BCE. That should be enough to answer this specific question, but I wanted to track down a real source.
There are four versions of Herod the Great's ancestry.
1. Nicolaus of Damascus said Herod's father Antipater belonged to one of the leading Jewish families returned from Babylon. Josephus discounted this story because Nicholaus of Damascus was a friend of Herod's and the story seems designed to please him (Antiquities 14.9).
2. Justin Martyr said it was reported among Jews that Herod's father Antipater was an Ascalonite (Dialogue with Trypho, 52.3). Julius Africanus said Antipater's [presumably Antipater the governor] father was Herodes, a slave in the temple of Apollo. Antipater was taken prisoner by Idumaean robbers and raised by them because his father was too poor to ransom him. Africanus said he received this story from the kinsmen of Jesus (Epistola ad Aristidem).
3. Josephus said Herod was son of Antipater, procurator of Judaea, son of Antipater, governor of Idumaea, from an Idumaean family forcibly converted to Judaism (Antiquities 14.9). His is the standard version today.
4. The Talmud says Herod the Great was a Hasmonean slave. No genealogy (Baba Bathra 3b).
So, the short answer is that Herod's father and grandfather are from Josephus, and his great grandfather is from Julius Africanus.