Is smiling a sign of submission?

I read somewhere recently that smiling is a sign of submission among primates. Now, I haven't verified this. However, it seems to me that smiling among some humans may have the same effect. My problem is that I like to smile, but I am not trying to be submissive.

Do our human leaders smile a lot? Most managers I know carry a serious look with them, but can and do smile. How about presidents? Well, Pres. Reagan smiled often, but he could also be serious (e.g. "Mr. Gorbachev, tear down this wall!"). Pres. Obama can smile, but most of his campaign pictures portrait him with a serious expression.

Maybe it is a matter of maturity. That is, mature people understand that being friendly is not a sign of weakness. The less mature a person is, the more they see smiling as a sign of weakness?

Just a thought. As they say in the US Congress, I reserve the right to extend and revise my remarks on this matter.