Cyclopia is the presence of one eye. It turns out that not all that many organisms on earth are Cyclopean/Cyclopic or in popular parlance, "Cyclops". There are a number of "cartoon" cyclops organisms that have gained prominence in pop-culture (see at right). But, most of the cyclopean organisms known to humans (that are viable) are aquatic invertebrates.
If one wants to study a biological phenomenon such as cyclopia I would argue that the best approach is to study an actual cyclopean organisms. Better yet, why not study a whole class of cylops! The class Branchiopoda houses a large number of these organisms including Daphnia magna our pet model organism. But the really interesting thing about Branchiopoda is that within this class there are organisms with two eyes and one eye.
In Branchiopoda we find these evolultionary "gifts" that can be leveraged to better understand the developmental genetics of cyclopia. At least one or two versions of it. We really cannot know if cyclopia as we see in the Branchiopods or other aquatic invertebrates like those called Cyclops will explain midline developmental anomalies in vertebrates but it seems like a reasonable place to explore this phenomenon.