Surely the DRK/BTC price will keep the same ratio as the BTC/USD price in relation to the DRK/USD price.
Meaning you wouldn't get BTC/USD and DRK/USD dropping and DRK/BTC rising. They are all in sync with one another.
I'd say the DRK / BTC ratio drives the DRK dollar price, not the other way around. That's because the BTC / USD market volume far outwighs the DRK / USD volume.
So:
DRK($) = BTC($) x (DRK/BTC ratio)