This is based solely on the information in WikiTree profiles
There are two John Birdseyes from the same generation: B-5 and B-51
B-51 married first Alice Poss and had daughter Margaret (B-58) in 1611, who married William Wilcoxson
He married 2nd Elizabeth Andrews, with whom he had Sarah (B-86) in 1616 and Edward (B-85) in 1618
B-5 married Elizabeth Andrews and had John (B-7) in 1616
But Elizabeth Andrews can not have married two John Birdseyes, as they both died in the same year and the same place.
B-5 also had son Edward Joseph (B-10) in 1597, but B-10's profile does not list a mother and is probably not Elizabeth Andrews. It lists John B-7 as a half brother.
Elizabeth Andrews' profile lists 3 children: John B-7, Sarah B-86, Edward B-85
I'm inclined to believe that B-5 and B-51 are the same person who married Alice Poss (1 child) and then Elizabeth Andrews (3 children). This would involve reconciling birthdates and birthplaces - the merge was once before rejected.
This also leaves Edward Joseph B-10 out in the cold unless the merged John 5/51 had an earlier wife, or if he's an unrecorded brother. I also note that the current profile is the result of merging.
But I think the evidence is pointing to John B-7 being the son of B-51, as the son of Elizabeth Andrews, his wife.
Then there is also the complication of Sarah( Birdseye) Stiles Birdseye-56, who doesn't seem to be the same Sarah BIrdseye as B-86, but who seems to be without parents.
More research appears necessary