Some of Francis & Hester Cooke's descendants ended up in Nova Scotia.
When tracing the COOK surname from Yarmouth, Nova Scotia, I found myself at coming to Francis Cooke of the Mayflower.
The surname with the "E" or without, is the same. I found brothers who spelled their names, one as Cooke and the other as Cook.
I assume it had to do with the education of the person who wrote the name in a newspaper or a document.
My web site: http:wmanser.com has a link to the Yarmouth Genealogies by George Brown who documented the lines from Yarmouth to the Mayflower.