Consider the following two sentences:
People in North America are predominantly English speakers.
People in North America are dominantly English speakers.
Merriam-Webster defines predominantly as "for the most part; mainly"; and while it doesn't directly define dominantly, the definition for dominant is "commanding, controlling, or prevailing over all others". Therefore, I would take dominantly to mean "in a commanding or controlling manner".
What I don't understand is how adding the prefix pre- changes the meaning of dominantly to the aforementioned definition.
Best Answer
Rather than being a function of its etymology, predominantly sounds to this linguist like an analogical neologism based on the following relationships: dominate : dominant : dominantly : -- where all three refer to POWER -- : predominate : predominant : predominantly -- where all three refer to NUMBER. Of course, there is power in numbers, but not always. For example, Old English was the predominant language of England after the Norman Conquest, but because French became the dominant language, Old English was largely relexified to become Middle English, which can thus be seen as at least in part a French creole.