Currently, we have tested three individuals with paper descents from Jacob II.  These individuals are all Haplogroup J2, and they are a tight genetic match with each other, consistent with them having a near common ancestor.  Each descends from a different son of Jacob II, so, logically, Jacob II must also have been J2.  The other tested descendants of Jacob STROUP I — and his great-grandfather, Martin STRAUB (1616-1676), of Großgartach, Württemberg — are Haplogroup I1, which means these individuals cannot have shared a common ancestor with the descendants of Jacob II for tens of thousands of years.

There is strong paper evidence that Jacob II was a son of Adam (in a deed, Jacob II gives his father's name as Adam), which leads us to a possible scenario that, as Adam's eldest son on paper, he is probably the child of a former marriage of Adam's wife, Catherine ALEXANDER.  In other words, Jacob II may be Adam's stepson.  The fact that these three J2 individuals have a strong DNA match (35/37) with an individual surnamed BIDDLE suggests that Catherine's prior husband was a man surnamed BIDDLE.  With the goal of identifying this man, or at least of identifying his family, I've started a BIDDLE Y-DNA Surname Project.