What birds eat?

[TNDemo]

I have a small fenced back yard. The people who owned the house before us were bird lovers and had a lot of birdhouses. That was nice last spring and summer (our first year in this house) except that my cat kept coming through the doggie door with a bird in her mouth. I think only one died but we spent a lot of time catching birds and getting them back outside. She seemed to go after the ones learning to fly the nest (she's too fat to catch the good flyers) so this year we decided to take down all the bird houses and put them on the outside of the fence (she is too fat to ever climb or get over the wood fence).

That has cut down on the bird population in the back yard but for the last few weeks we are having the most ticks we have ever seen. Both pets have Frontline on them. I also have found a couple of centipedes in the house and I have never seen them before. Could the birds have been controlling the population of those before? Or is this just a bad year for ticks or what?