Final answer:
Joan, Shakespeare's sister, is the only sibling with documented descendants, and thus provides the only genetic link to William Shakespeare. The correct answer is option a.
Step-by-step explanation:
The only sibling of William Shakespeare who provides a genetic link to him is Joan. Out of Shakespeare's siblings, Joan is the one who has documented descendants. Shakespeare had three brothers: Gilbert, Richard, and Edmund, and two sisters: Anne, who died at the age of seven, and Joan. As Anne died young and Shakespeare's male siblings did not leave any recorded offspring, Joan remains the sole sibling through whom Shakespeare's family line continued.
Shakespeare himself had three children: Susanna, Judith, and Hamnet. Unfortunately, Hamnet died at the age of 11, and while both Susanna and Judith had marriages, Shakespeare's direct bloodline ended as those branches did not produce any surviving descendants to continue his genetic legacy.