What is the correct plural of "mantis"?
Mantids is not plural for mantis, but for mantid, which is another term for mantis:
mantis
man·tis (mănʹtĭs)
n. pl. man·tis·es or man·tes (-tēz) Any of various predatory insects of the family Mantidae, primarily tropical but including a few Temperate Zone species, usually pale green and having two pairs of walking legs and powerful grasping forelimbs. The mantis feeds on live insects, including others of its own kind. Also called mantid.
(American Heritage Dictionary)
Evidently, mantid can also have another, more specific meaning:
- See mantis.
- A mantis in the family Mantidae.
In summation: the correct plural for mantis is mantes or mantises, which is what you use. The correct plural for mantid is mantids.
As a practical matter, you may be interested in this Ngram chart tracking the relative frequency of praying mantises (blue line), praying mantes (red line), and praying mantids (green line) in publications contained in the Google Books database, from the years 1820 through 2005:
The chart suggests that mantes was originally the preferred plural—but that it is now the least common of the three plural forms, by a considerable margin. I looked at a number of the Google Books matches for "praying mantes" that are associated with this chart and couldn't spot anything obvious that the texts using "praying mantes" have in common, other than their choice of plural.
Until I read this question, I was not aware that mantes was a plural option at all. My personal experience, living in various parts of the United States and Canada, roughly corroborates the data in the Ngram chart above: I have heard and read "praying mantises" frequently and "praying mantids" occasionally—but "praying mantes" never (until now).