it's well known that a great many human characteristics are extremely heritableMethinks you are not completely familiar with what "extremely heritable" really implies in studies of human behavioral genetics. (I attribute this to a knowledge gap, as I have generally found your other comments about natural science to be highly reliable, if they are close to the field you work in.) I am blessed with the opportunity to attend the weekly behavioral genetics seminar ("journal club") at my alma mater university each week during the school year, and from the seminar I have learned about professional articles that dispel common misconceptions about human behavioral genetics.
Turkheimer, E. (2012). Genome wide association studies of behavior are social science. In K. S. Plaisance & T.A.C. Reydon (Eds.) Philosophy of Behavioral Biology (pp. 43-64). New York, NY: Springer.
http://people.virginia.edu/~ent3c/papers2/Turkheimer%20GWAS%...
"If the history of empirical psychology has taught researchers anything, it is that correlations between causally distant variables cannot be counted on to lead to coherent etiological models."
Johnson, W., Turkheimer, E., Gottesman, I. I., & Bouchard, T. J. (2009). Beyond heritability: Twin studies in behavioral research. Current Directions in Psychological Science, 18, 217-220. [I am personally acquainted with three of the four co-authors of this paper, one of whom regularly exchanges links with me by email.]
http://people.virginia.edu/~ent3c/papers2/Articles%20for%20O...
"Moreover, even highly heritable traits can be strongly manipulated by the environment, so heritability has little if anything to do with controllability. For example, height is on the order of 90% heritable, yet North and South Koreans, who come from the same genetic background, presently differ in average height by a full 6 inches (Pak, 2004; Schwekendiek, 2008)."
Turkheimer, E. (2008, Spring). A better way to use twins for developmental research. LIFE Newsletter, 2, 1-5.
http://people.virginia.edu/~ent3c/papers2/Articles%20for%20O...
"Unfortunately, that fundamental intuition is wrong. Heritability isn’t an index of how genetic a trait is. A great deal of time has been wasted in the effort of measuring the heritability of traits in the false expectation that somehow the genetic nature of psychological phenomena would be revealed. There are many reasons for making this strong statement, but the most important of them harkens back to the description of heritability as an effect size."
To sum up, individual human differences in poverty (on a relative basis, within any one society) probably have something to do with individual human differences in the genes shuffled into each person at conception, but those differences neither fix an absolute level of poverty nor fix a stable rank-ordering of relative poverty. Other factors that are properly called "environmental," both at the societal and individual level of analysis, can and do overcome the odds influenced by individual genomes.
A link I just discovered yesterday
http://www.economics.harvard.edu/faculty/fryer/files/Fryer_R...
leads to a LONG, detailed article about reasonable social policies that may do much to alleviate poverty in the United States.