"a number of X" means "a lot of X" and takes a plural verb, as in "Recently a number of violent crimes have been reported"

"the number of X" merely means the mass or the group of X and takes a singular verb as in "Recently the number of foreign cars is on the increase"

I saw the following sentence in Nature. I am fine with what the sentence means, but is it possible to say "the continent's dwindling number of wild elephants is being...."?

The continent's dwindling numbers of wild elephants are being forced into contact and conflict with man.

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Yes, "the number....is" would be fine here. This meaning would fit this definition from the American Heritage Dictionary*:

"¢ number: An indefinite quantity of units or individuals: The crowd was small in number. A number of people complained.

The original sentence from Nature is also correct, and has a similar meaning, as in a separate entry in the American Heritage:

"¢ numbers: A large quantity; a multitude: Numbers of people visited the fair.

The meanings of the two sentences are very close.
In your sentence – the continent's dwindling number of elephants is being forced – the reference is to the total number of elephants in the continent, no matter where they are.

In the original sentence – the continent's dwindling numbers of elephants are being forced – the reference seems to be to groups of elephants in different areas of the continent.

*The American Heritage Dictionary of the English Language, Fourth Edition. Houghton Mifflin Company. 2003

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