I own that book but don't agree with the conclusion.I think that Sam Walter Allerton's has got the Isaac III Allerton family line correct.The Isaac in New Haven is Isaac III Allerton.This book doesn't prove the relationship but the Mayflower Descendant book doesn't disprove it either.
I don't follow the logic in the Mayflower Descendant book that because he wasn't in the will that it must be assumed that this unamed individual must be dead and didn't have any children.I find it as likely or more likely that he received his portion of the estate early just as the will states his sister did and because he wasn't living in the area, there would be no need to leave a memorial for Isaac's children as he did his daughter's.This, the the link to Mrs. Allerton of New Haven and the Harriman chest, combined with the the fact that Isaac III's grandson Isaac Allerton via son John claimed to be a descendant of the Mayflower pilgrim as well as many of today's descendants of the Isaac Allerton of New Haven convince me that this Isaac Allerton was Isaac III Allerton.
Note C: p. 122 The Allerton Family by Samuel Walter
All authorities concede that Isaac Allerton, of the Mayflower, was the only Allerton known to have emigrated to New england, at an early day, except one John Allerton, a sailor on the Mayflower, who died before the return of the vessel to England, and who had no descendants.
Isaac II resided at New Haven Conn. Isaac III was born 6/11/1655 in New Haven.
In 1682, the stepmother of Issac II died in New Haven, and he returned from Virginia, to have the original deed confirmed and properly witnessed, in order to be sure that the homestead might come into the possession of his daughter Elizabeth, who had married, in New Haven, Benjamin Starr, as her first husband; and at this time, was living with her second husband, Simon Eyres.
At just about this time, and Isaac Allerton, is found in New Haven.He could not have been other than Isaac III, the brother of Elizabeth, and who had returned from Virginia, with his father - for in no other way could an Isaac Allerton have been there at that date.
It is claimed by one or two genealogists that Isaac III, son of Isaac II,died before 1702, because he is not mentioned in his father's will.Granting that he was dead, (which is very improbable, from other circumstances), it does not necessarily follow that he left no children.
In the will of Isaac II, he states that his daughter Frances Travers had received her full portion of his estate, at the time of her marriage, and consequently wills her nothing, but for memorial sake, he gives each of her three daughters one thousand pounds of tobacco, and as they were living in Virginia, and where constantly in his company, it was very natural that he should leave them a memorial.No doubt Isaac III, had also received his full portion, at the time of his marriage, or, as is most probable, when he became of age, and therefore is not spoken of in his father's will.
In an abstract of Colony Records, made by my great uncle, (E.C. Bacon, Esq.), in 1835, I note:
"Allerton, Isaac, New Haven, October, 1643." "His afflicted state, noted, 1652.""His son, Isaac II married, as early as 1655 or 1656.""Inventory of Isaac I, February, 1658-9.""Eldest, and only son, noted, 1659" "Mrs. Allerton sent in 1684, for a chest, at Mr. John Harriman's""At this time, John Harriman, Senior, lived at Elizabethtown NJ, and his son, John Harriman, Junior, at New Haven."My great uncle, therefore, apparently found evidence that Isaac III, born 1655, was the same man as Isaac Allerton, who was in New Haven, 1684.The "Mrs. Allerton," who sent for the chest, in 1684, at John Harriman's was evidently the wife of Isaac III, for the widow of Isaac I died in 1682, and Isaac II was then living in Virginia, married, and his family there, except his daughter Elizabeth, and Isaac, as above.It will be noted, also, that John Harriman, Senior, swore to the will of Isaac I Allerton, in October 1659, showing an intimacy between the families, and carrying with it the probability of the identity of Isaac III.