Strictly speaking, both the biological term Quantitative Trait Locus and its plural Quantitative Trait Loci can be abbreviated as QTL. However, one often reads the abbreviations QTL and QTLs. Is the -s behind QTL wrong or correct? After all, it's not "Locuses".
For a given abbreviation XYZ (doesn't mean anything, I'm making up an abbreviation so I can generalise), the plural is XYZs if the plural can be meaningfully and usefully distinguished from the singular, and XYZ if it cannot.
An example of the latter, is if XYZ abbreviates an abstract noun, or is already plural (that is, there is no such thing as a single XYZ).
It would once have been XYZ's but that style is now so old-fashioned as to be obsolete and a risk of being perceived as a mistake.
There are two overlapping exceptions.
- If there's a separate abbreviation for the plural.
- If the abbreviation is a traditional one, particularly those that come from Latin abbreviations.
An example in the overlap would be that where the abbreviation for "page" is p. (borrowing the abbreviation of pagina), the abbreviation for "pages" is pp. (borrowing the abbreviation of paginae).
From all the above, we would expect the plural to be QTLs unless there was a good reason for those who particularly care about Quantitative Trait Loci to not particularly care about an individual Quantitative Trait Locus.