We have terrific fluctuations in the cottontail population here, without any other change in the area. Last year we had cottontails all over the place; this year there are very few.
I assume that when the population goes way up, bunnies are closer together and communicate disease more readily. With the reduction in food supply per bunny, their immune systems get weakened and they die off even more readily. Always seem to come back, tho. We'll see.
