Regardless of whether people are able to find a way to beat the odds and get out of poverty, humans are, according to scientists, animals who adapt to their environments. One of the often drawn parallels between often seen reproduction strategies in other animals as compared to humans, involves the hostility of the environment.
Among non-human animals we see that the more hostile the environment is to the animal, the more babies the animal is likely to have and the less hostile it is, the fewer they are likely to have. For example, sea turtles lay enormous amounts of eggs as their babies must run the gauntlet of preying birds before they get to the ocean; additionally, they are very small compared to mature turtles when they hatch and their average life expectancy is low because they still have to grow into full sized adults without becoming prey to other predators in the sea all without the assistance of the mother.
On the other hand, bears, for example, have one (or two if they have twins) bay at a time as their environment is no where near as hostile as that of the sea turtle. There are no predators that target bears other than humans and the mother bear stays with the cub until it is an adult. So as you can see the more hostile the environment, the more children are birthed; the less hostile the environment the less children are birthed.
Some argue that among other things, the reason why humans have more babies when in poverty is due to a lack of education or access to birth control. However, in the U.S., where birth control is free and so is public education up to the 12th grade, we still see more babies born per woman in poverty than we do in wealth.
See the graph/links below showing the relationship between wealth and births:
http://www.freakonomics.com/wp-content/uploads/2011/06/wolfersimage012.png
Freakonomics » The Rich vs Poor Debate: Are Kids Normal or Inferior Goods?
What's the solution you may ask ... to me it seems relatively clear ... force the poor to keep their births low or make our environment less hostile, i.e. distribute the wealth in a more even fashion, making it possible for a lower class to be paid a living wage, re-establishing the middle class, while still allowing an upper class