Is "may or may not" a correct way of negation of "may"?

Solution 1:

'May not' is indeed the negation of 'may', but 'may' has several meanings. The two that interest us here are "is permitted"...

You may enter here if you wish

...or 'is possible'

There may be rain tomorrow

In the second case, the 'not' is not negating the possibility, but negating the clause after it. "There may not be rain tomorrow" means that it is possible there there is not rain tomorrow.

In your sentence 'may' is expressing possibility.

Individual fitness may project into the demography rates.

It is possible that individual fitness projects into the demography rates.

Individual fitness may not project into the demography rates.

It is possible that individual fitness does not project into the demography rates.

The sentence states both cases to emphasize that both are possible.

Individual fitness may or may not project into the demography rates.

It is possible that individual fitness projects into the demography rates and possible that it does not.

'May or may not' is correct and has the meaning above.

Note that it is not always possible to determine which meaning of 'may' is intended in a sentence. Grammatically they are often identical, and you have to determine the meaning from context. In this case it makes no sense that 'individual fitness' is prohibited from doing anything.