Unlike estrogen, androgen levels don't suddenly drop when you reach natural menopause. Instead, androgen production begins slowly falling in your twenties. By the time you reach menopause, you're producing about half as much as you made at puberty. However, your ovaries may still continue to produce small amounts of androgens even after menopause. Some studies show menopausal ovaries continue to produce testosterone; other studies show they do not. One thing is for sure: if your ovaries are removed or damaged, you will go into surgical or early menopause. Some women who experience surgical menopause report a drop in sexual desire and drive.
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.