How many PS+ subscriptions do we need to play on a private server over the Internet?

Solution 1:

According to this help page:

In almost all cases, a PlayStation Plus subscription is needed to play online multiplayer on the PS4™.

This seems to be the case for Ark: Survival Evolved, since the game case (for physical copy) and page in the store page say:

Online multiplayer (2-70 players). A paid-for PlayStation Plus membership is required.

So you need one PS+ account per console.