Conclusion: these studies found that castrated rats lived slightly longer than a similar group of intact rats. Castration is not, of course, a guarantee of longer life for an individual rat. Rather, considered as a group, castrated rats have a moderately longer average lifespan than a similar group of intact rats. However, other factors, such as exercise, mating, and restricted food can prolong life even more than castration when compared to similar groups of control rats. Longevity is subject to a wide variety of factors, and hormonal state is just one of the many variables that plays a role in determining how long an individual might live.
The second theory is similar and is known as "evolutionary neuroandrogenic (ENA) theory of male aggression".   Testosterone and other androgens have evolved to masculinize a brain in order to be competitive even to the point of risking harm to the person and others. By doing so, individuals with masculinized brains as a result of pre-natal and adult life testosterone and androgens enhance their resource acquiring abilities in order to survive, attract and copulate with mates as much as possible.  The masculinization of the brain is not just mediated by testosterone levels at the adult stage, but also testosterone exposure in the womb as a fetus. Higher pre-natal testosterone indicated by a low digit ratio as well as adult testosterone levels increased risk of fouls or aggression among male players in a soccer game.  Studies have also found higher pre-natal testosterone or lower digit ratio to be correlated with higher aggression in males.     
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