PEMBA, Tanzania — It's springtime on this green, hilly island, and the pungent, sweet smell of cloves spices the air. Zaharan Salim's father, who crossed the turquoise water from Oman to settle here nearly 100 years ago, taught him as a boy that the annual bouquet signaled harvest time. His father planted a small grove of clove trees to support the family, and Salim expanded the plantation into one of Pemba's largest, with more than 2,000 of the tall evergreens sprouting from the fertile soil. But it's unclear whether the family business will last into a third generation. The groves...