You posted.
"One thing that research shows is that poverty acts as a stimulant for reproduction in humans. We are wired for it, and it makes sense: as our immediate social group is threatened, the more there are, the more will survive. This is a mechanism polished by the ages, where the surviving carry with them the genetic recipes for the future. It may not seem to work to you, yet it does. Where overpopulation will takes us? To the next burst of evolution, which is not predictable. We may disappear, replaced for something more adaptable to the new environment. It's the law of nature and no amount of social engineering will change it much."
By your own hand you acknowledged the need to allow the weaker to die off thereby allowing the strong and more adaptable to survive. By helping those who are incapable of surviving on their own you are defeating the very concept you have outlined by your own hand. You must allow for nature to take it's course. That's why poverty acts as a stimulant for reproduction. The strong will survive while the weaker will be left behind.
In the US we subsidize those that can't survive on their own. All that does is add to reversing the 'survival of the fittest' law that makes up this world and will lead to a weaker not stronger more adaptable human species.
My way of sharing my good fortune is to donate to a scholarship fund for 'Children of Merit'. Any child that excels against tremendous odds but needs a helping hand for further growth and studies is a human being that I feel deserves my support. Those are the children that as you said,, "have the genetic recipes for the future".