To be the Yokon in the New World, we have to trust that Big Moam own the power same as Shirohige(Whitebeard). So after the dead of Shirohige, Big mam become the new protector of Fishman island.
What the difference is she make a deal with the island: There have to provide more and more delicious candy to Big man so that she can protect the island.
At the latest manga we can guess the power of this ubique female in Yokon: she can destory a country just because of the candy. Actually I never fell afraid about this sentence but think that this special lady must ne a very interesting guy in the yonko. She love candy than everything. Most of us can remember the onein the Thriller bark called Rora, yes, I think Big Mam must be the mother of this lady. Because Rora ever said that his mom is a totally strong lady in the New World, as far as I know, the unique famous pairte is Big Mam. So in my opinion, she is defintenation is the mother of Rora. Maybe we will know the answer in the next chapter matbe not, but I still believe in my answer!
So I also think that Luffy will have a fight with This Yokon. Eat all of the candy at the party, it means Luffy already have a special relationship with Big Mam. The forcast of fishman island will come true in the future. No matter it was destoryed by Luffy or not, I have to said that it was caused by him!