It could be as simple as this:
FK1 and FK2 that denote FOREIGN KEYs (FATHER_ID references PERSON_ID and MOTHER_ID also references PERSON_ID). FATHER_ID and/or MOTHER_ID can be left NULL if unknown.
This model is not perfect. For example, it doesn't enforce parents' gender (the father is male and mother female) and it only represents biological parents, but not other kinds of relationships such as adoption (all of which can be done, but with certain complications in the model).
However it's very simple and can be naturally traversed (in recursive fashion), analyzed or exported.
For example Parent A has a Children B and C. So, what if Children C produce a Children too in the future. How does it add to the tree by using database?
A child D
of C
could be represented like this:
PERSON_ID FATHER_ID MOTHER_ID
A
B A
C A
D C
Or like this if C
is a mother:
PERSON_ID FATHER_ID MOTHER_ID
A
B A
C A
D C