Several factors really. Generally when a station makes a format change, promotions dollars follow which drive cume through sampling. A recent example of that in the Seattle area was when 92.5 changed to the 'movin' format. Sandusky spent some promotions dollars on TV with some poorly produced spots (typical for radio). So the station is sampled by listeners, with eventually 75% or greater going back to their usual station listening line-up, or perhaps (if the station is lucky) 25% being added to their car presets.
In all cases however, the ratings for the new station level-off to a flanking position with the hope that someday the new format or station will continue to chip away at the heritage stations numbers, or in very rare instances, the heritage station makes a dumb move, allowing the new upstart to pass. 100.7 in Seattle is also another recent example of this effect.
Regarding your interest in alternative rock, the format struggles due to the narrow demo (males 17-32) who's tastes seem to shift rapidly, especially when the music industry isn't producing a good flow of new content. KROQ has adapted toward more of a classic/active rock format when needed, protecting it's alternative label by throwing in some 80's and 90's when alternative was doing well.
LA has a MUCH larger population base combined with KROQ being a solid legacy alternative station. Whereas I would argue that "The End" has developed multiple personalities over the years, and shed audience through the changes that translate into listeners that don't return. Remember, it's never just the music selections that make a station but the whole package; tenure of personalities, creative promotions, positioning, and continuing to research and stay within the bounds of what your core audience wants.