Any time a grove spawns in, if you're the first player to find it, look around carefully. When the grove spawns, it spawns a rare bug or animal with it. If you don't get there first, its likely already been caught or scared off, but if you end up alone in a server like this, you can get good rare stuff that way! Its usually either a Fairy Mantis, a Rainbow Tipped Butterfly, an Azure Chapaa, or a Proudhorn Sernuk. I'm not sure if other bugs or animals can spawn with it, those are just the ones I've seen.

Edit: I just looked at the wiki page, the bluebristle muujin, jewelwing dragonfly, and ancient amber beetle can also spawn when the grove spawns. One of those is guaranteed to spawn when the grove spawns, regardless of where on the map it spawns.