Predominate

In a large forest, there are many kinds of trees: oak, maple, pine, and birch. But after a forest fire, the pine trees regrow faster and taller than the others. Over time, most of the forest becomes pine. The other trees still exist, but the pine trees are clearly the most common and influential. What do the pine trees do? They predominate in the forest.

Sway (to influence or change opinion through persuasion or emotional appeal) contrasts with predominate, which means to be the most common, powerful, or noticeable element within a mix, often in a quantitative or statistical sense. Predominate focuses on majority or dominance, while sway focuses on the act of persuading.