Yeah Chris. I can't comment on bird populations, but when I lived on a ranch in NV the jack rabbits were a good example. Some years were overrun with rabbits. So much so that they would eat large sections out of our hay fields. The hay that we depended on to feed our cattle in the winters. Then other years you hardly saw any of them around. This was 30 miles from the nearest town (180 population), 30 miles away, nearest neighbors 7 miles, so there definitely wasn't any encroachment on their habitat.
Some years, when the population was low it would be because of disease (we would see lots of carcasses). Some years due to an extremely rough winter and they would starve. Some years due to a late spring and they wouldn't reproduce or the babies would die. They coyote population would fluctuate in sync with the rabbit population, as would the deer population.