The comma is correct. It signals a parenthetical (nonessential or nonrestrictive) element.
That means you can leave off either positive or negative without affecting the meaning of the sentence; while the phrase drives home the point, it doesn't need to be there:
Finally, the populations of Russia and Turkey did not show any alterations.
These alterations, had they happened, would have been positive or negative, and we can presumably infer this from context without the aid of the phrase.
If it helps your understanding, you can consider the phrase to be (in traditional grammar terms) a reduced relative clause. The full relative clause would be reduced from something like:
Finally, the populations of Russia and Turkey did not show any alterations (which would have been either positive or negative).*
It is reduced by omitting the relative pronoun (which) and the to be verb (would have been), leaving the adjectives behind:
Finally, the populations of Russia and Turkey did not show any alterations (either positive or negative).
At What is a noun modifying clause? English and Language Usage's "resident" authority, linguist John Lawler, applies the linguistics term whiz-deletion to describe the concept:
The rule called Whiz-Deletion by linguists (from the fact that
it deletes a Wh-word plus a form of be, quite often is; a
monosyllabic variant of "Wh-is deletion"), when applied to a
relative clause, creates a bare verb phrase without a tensed verb, but
with whatever is left after the deletion. Any phrase of more than one
word simply goes after the noun it modifies. . . . It has long been
suspected that all attributive adjectives . . . are the result of
reduction of relative clauses.
* Note that this whole exercise would be easier with an example in the positive (e.g. The populations showed alterations, either positive or negative reduced from The populations showed alterations, which were either positive or negative).