Notes from researcher Amy Pace, a fellow descendant of Jacob Parker:
My question was whetehr she had seen others trees that indicated Jacob Parker came from the Atwater family of Connecticut.

Hi Steve, 

I have seen many of these trees but they have the wrong Jacob Parker JR attached. I can not definitively prove that Jacob Parker SR's parents are Benjamin or Mary (Atwater) Parker. Typically you named a first son and a daughter after your parents and this doesn't pan out. Also, none of Jacob Parker SR's children used the name Benjamin. It would be great to find the evidence proving this though. I have attempted to research other Parker men in Pennsylvania who could be Jacob's father and haven't had any luck. I have searched through a Parker Family in America book, too. I have other Parkers in my family that married into the Morse family in New England so I have found some of them in that book-available on line.

Still hunting for this branch of the family...
Amy

last name Hodgson is speculative and needs further research