the.com/alpha dog

means The dominant figure in a group, whose authority is assumed rather than argued for — others fall in line before anyone says why.

from From wolf-pack biology: wildlife researchers in the mid-20th century labeled the top-ranking wolf the 'alpha,' using the first letter of the Greek alphabet to mark first rank. The term jumped into human slang by the late 20th century to describe the dominant one in any room, though biologists later walked back the 'alpha wolf' model itself — wild packs turned out to be family units, not hierarchies won by force. The science got more modest; the metaphor, stubbornly, did not.