Mayflower Families Vol. 15 p. 89 states that he was a son of Isaac and Abigail (Leavitt) (Lazell) Johnson.
Sources
Mayflower Families Vol. 15 p. 89-90
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DNA Connections
It may be possible to confirm family relationships with Daniel by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA test-takers in his direct paternal line.
Mitochondrial DNA test-takers in the direct maternal line:
Frank Gill :
Mitochondrial DNA Test HVR1, haplogroup H
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Daniel: