What does ‘alpha’ mean in the phrase, “A plea came for the President to be more alpha.”

I find the articles of New York Times’ columnist, Maureen Dowd, a treasure house of English expressions unfamiliar to non-native English learners. It’s stud with knotty expressions and new words to me. In her article titled Dystopia and Alpha (August 2), I stumbled on the word alpha in the beginning line

President Obama was on the way to Alpha when a plea came for him to be, well, more alpha.

The first Alpha is obviously the name of a town in Illinois, but what does the second alpha mean? Is it used as a noun, or adjective?

I checked the Cambridge Dictionary to find the meaning of alpha and simply found its definition as ‘the first letter of the Greek alphabet.’ Aside the same definition, Merriam-Webster provides the meanings as adjectives:
(1) closed in the structure of an organic molecule to a particular group of atom
(2) socially dominant, especially in a group of animals.

Solution 1:

The plea is for him to be more dominant. Social animals tend to form hierarchic communities in which each individual has a social rank; the highest ranking individual or pair is referred to as the alpha individual, usually male, or pair. The alpha is typically physically or psychologically dominant. The concept is especially associated with wolves and other canids, though it now appears that the pack leader is generally just the breeder, the common parent, and not an ‘alpha wolf’ that won the position by fighting for it. See this Wikipedia article and some of the articles linked from it. This one may also be of some interest.

Solution 2:

Alpha is used in a number of contexts in the article by Maureen Dowd.

As previously answered, alpha is used:

• As the name of the town: Alpha.

• As the reference to "alpha's " - dominant members of a group.

Also, it has a third sense. Later in the article alpha is used again in this sentence "He was seen in the Bunch of Grapes bookstore on Friday holding Brave New World. Maybe he was brushing up on dystopias and alphas."
In Aldous Huxley's Brave New World the people are divided up into classes known as the Alpha's, Beta's and Gamma's. The Alpha's are the rulers, and Beta's, Gamma's, Delta's, and Epsilon's are the lower classes, each with different status. Brave New World is a strict class society; no one can rise out of their class, or fall from it.