The large carriers, created through mergers that should never have been allowed, have the most popular routes locked up through ownership of landing/takeoff slots and similar. On those routes, fares have substantially increased due to a lack of competition.

The low cost carriers business model is to fly new routes (to secondary airports if required) at low prices, often creating new demand (Breeze is a classic example of this).

The math is very straight forward if you consider what each group is doing in the market.