This question is related to the plural of "octopus" (yet another ancient Greek loanword animal):
What is the plural of "mantis"?
Oxford Dictionaries suggests "mantis" or "mantises".
This page from the Iowa State University Entomology Department suggests "mantids" (emphasis mine).
Praying mantids (preferred plural form of mantis) have never been numerous in Iowa and historically they were only common in the far southeastern corner of the state.
Personally, I use a mixture of "mantises" and "mantes" and find the usage of "mantids" strange, but what is the most etymologically correct / most recommended plural for the animal?