Your family tree as posted on here is pretty limited (the earliest date seems to be in the early 1800s). So, you need to do the research to extend it back about 200 years, and see where it ends up. The list of Mayflower passengers who left descendants is well known. A simple google search will give their names.
If you have an interest in joining the Mayflower society take a look at their website for requirements. The standard of proof is high: internet genealogies are not acceptable as proof.
The Massachusetts Mayflower Society has this posted in their website:
The only officially sanctioned source for approved lineages published is the Mayflower Families Through Five Generations "silver" books and the associated Mayflower Families in Process "pink" pamphlets. Older applications from family members that used secondary sources or any of the Mayflower Index books will need to be redocumented for any new application for membership.