high rank or high power

A term borrowed from Biology and used in Human Ecology to denote a social structure in which a ranking exists with each animal dominant over those below it and submissive to those above it in the hierarchy.

The higher status position when social rank is organized according to a dominance-submission hierarchy; commonly found in human societies and in certain animal groups.

to be higher ranked (as in the bull is dominant over the cow) or to be more common (as in grasses are the dominant species)

Dominance in the context of biology and anthropology is the state of having high social status relative to other individuals, who react submissively to dominant individuals. The opposite of dominance is submissiveness.