Anne - Since I posted the message I have found: Isaac's (c.1586) parents = Edward Allerton (b.1553/55, St. Dionis, Backchurch, London, ENGLAND; d. 1589/1590 England) married 14 Feb 1579 -same info as his birth place- Rose Davis (b. 1559 St. Peter, Cornhill, London, England, d. Jun 1596 St. Dionis, Backchurch, London, England). No further info re her parents. Edward's parents= William Allerton (b. c1529, England d. ??) married ???? to ???? That's it.
More info on children of Edward and Rose Davis if you would like to have it.
Also, if you are descended from Isaac, through Mary Allerton & Thomas Cushman, through Eleazar Cushman and Elizabeth Coombs you are also descended from Mayflower pilgrim Degory Priest.Ask me!