I don't watch Pat Robertson but let me try to put in perspective what I know.
First, there were so many wars and deaths in the 1900's that the West lost many future generations which could be felt today. You add to that the changing roles and attitudes in the family for smaller families and the estimated 50 million children lost to abortions in the US alone for Roe vs Wade and other events it should begin to become clear that the West is losing population overall, not gaining it.
Other populations, such as the Middle East populations including the Muslims, did not suffer from this and today the world is on the move between the receiver nations, such as the USA, and the emigration nations, such as Mexico for example.
It is a fact the Europe alone will lose over 75 million of it's population due to it's low birth rate. Even Russia has a negative birth rate. European nations are happy to take in Muslims to raise or replace their future populations because of this just as our Government is happy to do so with Mexico and South America.
Now what we have have are historical outcomes that no one cared to consider when this began. There are Mexicans that don't want to be American, they want to stay Mexican as well as Muslims in Europe who don't want to be European they want to stay Muslim. Moving large populations at a time has produced this same outcome over and over again in history and it is well documented.
Today France is expected to become a fully Muslim nation in about twenty years, the same time China may become the financial leaders of the world. At least 40% of the British population in a recent survey said they wanted to do away with the Monarchy and place her under Sharia Law. Even here in the USA I read once in a while that some border towns don't celebrate Christmas vacation in their school year as it's been replaced with either Cinco De Mayo or is offensive to Muslims.
In short, the West is decreasing and the Third World is increasing and everyone's way of life is in the balance. This may be the defining issue of the century. This century is supposed to bring forth wars over resources like water and such.
At least that's how the UN describes it.