When in graduate school, I learned a convention from Dr. Roger Morse for insect names (I have since learned the idea originated with Robert E. Snodgrass). The insect names that are taxonomically correct, such as honey bees are actually bees, should be written as two words. Insect names that are not accurate in identification are given as one word. For example, whiteflies are not really flies, but are relatives of aphids, and thus should be one word.
Quiz (answers at the bottom of this post):
Pick the correct common name according to this convention:
1. Butter fly or butterfly?
2. Crane fly or cranefly?
3. Dragon fly or dragonfly?
4. Lady bug or ladybug?
5. Leaf-footed bug or leaf-footedbug?
Photo from Wikimedia
6. Bumble bee or bumblebee?
The convention is only a rule of thumb, however, because there are definitely exceptions:
Photograph by Craig Pemberton. Wikimedia
Although this creature is really a wasp, it’s common name is velvet ant (2 words).
B. Mantis or mantid?
This distinction is more difficult. I had learned that either is correct, that is the two terms are interchangeable. There is, however, a growing convention that mantis only be used for the insects of the genus Mantis, and that all others be called mantids. (Whitney Cranshaw, Colorado State University).
I personally like to use mantids for the plural, it is just easier.