Is it correct to say "a species of moth" or "a species of moths", or are they both correct? Is it the same if I use "family" or "genus" instead of "species"? Does it matter if I continue with another taxon, such as "This is a species of moths in the geometrid family."
As mentioned in Jesse Ivy's answer, "species" is of course a plural form as well as a singular form. In expressions like "many species of moths", "several species of moths", "various species of moths", the plural ("moths") seems at least strongly preferred.
When "species" is used as a singular noun ("a species"), it seems to be preferred to use a singular noun after it. The Google Ngram Viewer indicates that "a species of moth" is more common than "a species of moths":
In fact, according to the Google Ngram Viewer, "a species of mouse" and "a species of louse" also seem to be more common than "a species of mice" and "a species of lice". So irregular plural forms, in and of themselves, don't seem to have that strong an effect on the acceptability of the plural in this context.
However, the word algae is not only an irregular plural, but is often treated as a mass noun, and "a species of algae" does seem to be somewhat more common in the present day than "a species of alga":
Similarly, the mass noun "grain" does not typically seem to be pluralized after "species of", even in contexts where "species" is plural like "five species of grain" or "several species of grain".
Another word with an irregular plural sometimes treated as a mass noun is bacteria, and "a species of bacteria" and "a species of bacterium" seem to be relatively close as well.
To me, "a genus of moth" or "a family of moth" sound completely unacceptable. For "family", I suppose part of it is probably that a "family" is typically used to describe a collection of individuals, in its other uses as well as in its biological use. I can't think of any particular explanation for why the singular sounds bad with "genus". Janus Bahs Jacquet has left a comment saying that the singular does not seem impossible for him after "a genus of".
Good question. The word species is both singular and plural. To complicate things, the singular refers to a group of creatures with similar characteristics. So they are all correct, but mean different things. I like your last example best which has the same meaning as the first, referring to one specific "species of moth". Singular.
In the second example you've given, you are referring to multiple "species of moths". Plural.
In conclusion, a "species of moth" is singular, while several "species of moths" is plural.
Of course the singular form refers to a group, whereas the plural form refers to a group of groups.
For scientific citation use the binomial name, like you listed, only if a genus exist I think that's used in place of family, you've got it reversed in your example, and there is special formatting.
The binomial name consists of a genus name and specific epithet. The scientific names of species are italicized. The genus name is always capitalized and is written first; the species epithet follows the genus name and is not capitalized. There is no exception to this.
Also known as binomial nominclature. http://www2.nau.edu/~bio372-c/class/evolution/binom.htm
i.e Attacus atlas moth