As for the hereditary factor in longevity it can be said...
As for the hereditary factor in longevity it can be said: firstly from the scientific aspect hereditary has not been established in longevity. Secondly in numerous hereditary factors some are seen in the next generation while others are not. Moreover, the hereditary factor is propounded just as a probability and it is not that all the characteristics of an individual are transferred or transmitted to the next generation, leave alone to all his descendants.
Therefore, even if we assume the proof of hereditary as true for the sake of argument yet under this rule, we cannot claim that all the sons are exactly identical in age to their father. As we see that there have been people who enjoyed long lives but their sons were either still born or die at a very young age. Also there have been people who died in the prime of their youth but their sons enjoyed extremely long lives.
Without prejudice to whatever we have discussed, even if we assume that longevity is hereditary, it will apply only for natural lives. But if in a family, all the ancestors have been poisoned or killed, we cannot submit that the short lives of the ancestors will affect their eleventh generation descendant (particularly where all have been either poisoned or killed).
Imam-e-Zaman (a.t.f.s.) belongs to that family where all his forefathers, till Ameerul Momineen Ali (a.s.) have been martyred and did not die their natural deaths. Thus, even if accept the argument of legacy, it will not be applicable for this particular family. As for establishing longevity, numerous anthropologists have presented and jotted down their investigations. Among the best books on the subject is that of Dr. Paaknejaad and I advise all of you to go through it.
Its title is "Awwalleen Daanishgaah wa Aakhareen Peyaambar" (The First University and the Last Prophet). In the second or third volume, he discusses longevity and mentions the views of various scientists on the subject. The anthropologists mentioned in this book opine that man is like an existent whose structure is such that if all his requirements are provided for and external factors are kept at bay, he will continue to live for an indefinite period.
A comparison will facilitate the understanding of the discussion. Let's say, a watermelon that is kept in the open will become rotten in a week or a month even if none touches it. But this card is unlike the watermelon.