Interesting analysis:
The automatic succession of sons does not seem to be the norm. There have been over 38 cases on the continent where the leader passed away in office, and sons have succeeded their fathers in only three. Over the last two years there have, however, been two contested elections that involved the son and brother of a former president—Kenyatta in 2013 and Mutharika in 2014. Increasingly, countries have put in place constitutional provisions to handle the passing of the president or are respecting constitutional provisions from earlier constitutions such as in Nigeria, Ghana, Zambia, and Ethiopia, all countries who have seen their presidents pass away and whose transitions have been handled in a smooth and constitutional way. It seems that the passing of presidents has not generated prolonged political instability on the continent.
Her recommendations are sensible:
However, to guard against the creation of birth-right dynasties as opposed to merit-based family political dynasties, recent events suggest that countries should and must have clear constitutional processes for succession as well as open transparent freely contested elections.
Source: From father to son: Africa's leadership transitions and lessons | Brookings Institution