SOURCE : Various articles in NYTimes

What is the correct usage for "X's Dominance {of / on / in / over} Y". Some examples I have collected are as follows

1. In a report, the Competition Commission said BAA's dominance of the airport markets in southeast England and central Scotland limited choices for passengers and airlines

2. The move could strengthen Google's dominance over the most lucrative portion of the fast-growing online advertising field.

3. The world's No. 1 player, Tiger Woods, testing his surgically repaired knee, will seek to extend his dominance over No. 2 Phil Mickelson on a grueling course that the two have been playing since childhood

4. Mr. Gates took advantage of both notions and combined them to build Microsoft's dominance in PCs, spreading its influence with computer makers and software developers

5. Nadal's rivalry with Federer has been marked by the Spaniard's dominance of the Swiss on clay at Roland Garros and the reverse on the grass of the All England Club.


Is each of the usages correct and interchangable ???

not completely interchangeable, no. i would say #2 and #5 are unidiomatic, while the other three are unquestionably correct.

it may be easier for you to think about these distinctions if you use the adjective 'dominant', rather than the noun 'dominance', so some of my examples will use that adjective.

dominant / dominance IN
this is used when you're describing dominance in a particular field, specialty or area of influence, as in #4.
in fact, this isn't really an idiomatic construction of "dominant"; it's more properly parsed as just "dominant", coupled with the prepositional phrase "in FIELD X" (which should itself be considered an idiomatic construction).

dominant / dominance OF
in this usage, "dominance" is pretty much the same as "control".
so, #1 uses this construction correctly. note that you can remove "dominance" in that sentence, substitute in "control", and the meaning remains essentially the same.
#2 should use this construction, but it doesn't.

dominant / dominance OVER
this usage basically means that something/someone outperforms something/someone else in some competition or other context.
#3 is correct.
#5 should use this construction, but it doesn't.

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IMPORTANT NOTE:
still, these are subtle differences, and, occasionally, the gmat makes usage decisions that contradict "mainstream" usage conventions. so, while the above are the most common criteria for the use of these constructions, you shouldn't take any of them as gospel without direct evidence from official problems.