Let's start with a simpler sentence:
The tiger moths are one example.
We can split this clause into its subject "the tiger moths" and its predicate "are one example". This predicate can be split into the verb "are" and the subject complement "one example".
The "are" is a copular verb or linking verb. It associates some additional description with its subject. There are two common types of subject complement, predicate adjectives and predicate nouns. This "one example" is a predicate noun subject complement.
Predicate adjective subject complements are easier to identify. Adjectives don't function well as the subjects of clauses. In a sentence like "Happy is the man who finds a true friend," we are not likely to mistake "happy" as the subject of anything. It remains an additional description of the man who finds a true friend, even though it occurs first in the sentence.
Predicate noun subject complements can be tricky. They could function well as the subjects of clauses. When we invert a sentence like "knowledge is power", the "power" of "power is knowledge" may well be the subject of the new clause.
If knowledge is power, then a god am I. -- The Riddler, Batman Forever
Here, we have to assume that "knowledge is power" is in canonical order. "Power" is an additional description of "knowledge".
"A god am I" is inverted. The additional description is "a god", even though it appears first in its clause and even though "a god" can easily be the subject of some other clause. Here, we can be certain that that was the speaker's intent. The pronoun "I" is a subjective form. The form "am" agrees with its first-person singular subject. It doesn't agree with the third-person "a god".
Let's return to the original sentence:
One of the most beautiful of the more than 100,000 known species in the order Lepidoptera are the tiger moths, moths known for the striking appeal of their distinctive coloration.
Here, that they are one of the most beautiful species in their extensive order is an additional description of the tiger moths. We can be confident that this is the author's intent because the verb "are" must agree with its subject. "Are" cannot agree with "one", but it does agree with "the tiger moths".
The subject is easy to find, despite the fact that a predicate nominative subject complement begins the clause.