The most common and most likely answer to this crossword clue is the 9 letter word SQUIRRELS
I've seen this crossword clue in Independent
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More clues leading to the result SQUIRRELS
Buddy explains!

The straight part
We know that "rodent populaiton" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case rodent populaiton = squirrels.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SQUIRRELS mean?
SQUIRRELS noun- Any of the rodents of the family Sciuridae distinguished by their large bushy tail.
- A person, usually a freezoner, who applies L. Ron Hubbard's technology in a heterodox manner.
- One of the small rollers of a carding machine which work with the large cylinder.
- To store in a secretive manner, to hide something for future use