Birds on a Wire

On the taxi ride to the airport, I saw a set of three power lines that were parallel to each other and arrayed vertically.

The bottom one had 1 bird perched on it, the middle one has 3 perched birds, and the top one had a large number of birds on it (too many for me to count).

Any ideas what the mechanism is for this? Is there a preference for height? Does it have a bit of a DLA-like flavor in that a bird lands on the first available wire from something like a random walk or Levy flight such that it's more likely to "stick" on the top one? Does anybody know if somebody has tried to model this?

Also: Mine.