NOTES: I now have what looks like much better information from The Underwood Families of Massachusetts. It does not identify Mary Wilder with certainty, but it does make clear that Joseph had a daughter Mary who married Isaac Ong, so the chart is at least correct to that extent.
Joseph probably emigrated from London to Virginia in 1635. His brother Thomas ("sometimes woolen draper in London") moved to Hingham, Mass. in 1637, and he probably went with him then; in any event he was admitted freeman at Watertown, Mass. in 1645. His first wife Mary (mother of all the children named above) died in 1658, and he married Mary How of Dorchester 4/29/1665. His brother Thomas died in 1668, apparently childless, as he left his estate first to his widow Magdalen and after her death to his nephew Thomas (Joseph's son) who was living with them. It is possible that the younger Thomas actually married the widow afterward.