My question is this:

Is it a one to one to one ratio of ammonia converted to nitrite to nitrate, or do differing concentrations of nitrite and nitrate result from a fixed amount of ammonia in beginning the cycle?

The reason I ask is this - my well water typically contains 4 (or maybe slightly more) ppm ammonia. I've been cycling my new system without adding fish or any new water for just 4 days now, relying on the ammonia in the well water to kick off the cycle. I did add some old media and sludge drained from my other systems' biofilters to jump start the nitrification cycle. The system is now showing just a trace (less than 0.25ppm ammonia, zero nitrites, and between 5 and 10 ppm nitrates. Water pH is 8.3. Last night my testing showed 2ppm ammonia and barely a trace of nitrites. I tested for ammonia and nitrites daily, but other than an initial test for nitrates (results 0.0) I have not tested for nitrates until the ammonia drop results this morning. I never saw any sort of spike in nitrites other than the less than 0.25 ppm last night - perhaps there was sufficient bacteria from the old media to convert the nitrites as they developed? I'm a bit puzzled why the nitrate concentration now reads higher than the initial ammonia concentration - hence my original question.

Thanks!