In a non-modded pre-configured dedicated server with a world with all default settings except map size is Huge, I hunted down all of my buzzards close to my base in the desert biome which has dragonfly at about Day 100. It is about Day 600 now, and the Buzzard icons are still visible on the map, but not a single buzzard has spawned every since in any season, nor their shadow on the ground while they circle around. So, buzzards are extinct from my world.
1. Start a dedicated server with caves using the pre-configured settings through steam tools 2. Create a Huge world with all default settings 3. locate desert biome that has dragonfly 4. kill all buzzards 5. after 20 days, no buzzards re-spawn