of course the consequence of that is that 'the young and reproductive' of other countries are entering and replacing the indigenous population that has stopped reproducing. Darwin would claim that the more productive shall win. I guess we will see.
You missed the point. The global birthrate has peaked and is declining. That includes those young and reproductive. They're still reproducing at more than replacement rate, but they're trending downward, too. And much of the developed world is already well below replacement rate. Some northern European countries have actually started public service advertising campaigns encouraging couples to make babies, because the declining population numbers are playing havoc with their labor market and their economic structure (especially pension systems).
It turns out that birthrate is positively correlated with infant and child mortality and negatively correlated with wealth and female education. Better access to medical care reduces infant and child mortality, which appears to reduce the motivation of parents to make lots of 'em, just in case. Wealth and female education both enable family planning, and while women generally like babies, they also don't want to have more than they can really manage or care for. And given the very low baseline much of the world is at, wealth and education levels are exploding. People are still living in what you and I would consider unbearable poverty, but it's dramatically better than what the last generation had.
These facts also point out exactly how we can take action to reduce population even faster: Work harder to empower and educate more people in the third world. Actually, great progress is being made in the poor areas of Asia. The big opportunities are in Africa. Teach African men to farm more effectively, make education more available to men and women, make medical supplies and facilities more accessible, and provide international oversight to reduce the damage done by their kleptocratic (and in some cases, genocidal) governments, and you'll make peak population happen sooner, and at a lower level.