I think an 'Alpha' male is generally a cool, calm and collected guy. He behaves in this way even in the most challenging and intense of situations which makes him a natural leader of men without needing to dictate his 'leadership'. Being an alpha male is just about being a man. It is surprising really how few men posses the maturity to be a true man.
The qualities required to be an 'Alpha' male or more simply just a 'man' are outlined so eloquently in Rudyard Kipling's poem - 'If'.
Poems - If--