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From SNPedia

The genes governing inherited tendencies for taller or shorter stature are just beginning to be known. In an excellent article [1] about his own genome data, psychologist Stephen Pinker puts this in perspective:

"Though health and nutrition can affect stature, height is highly heritable: no one thinks that Kareem Abdul-Jabbar just ate more Wheaties growing up than Danny DeVito. Height should therefore be a target-rich area in the search for genes, and in 2007 a genomewide scan of nearly 16,000 people turned up a dozen of them. But these genes collectively accounted for just 2 percent of the variation in height, and a person who had most of the genes was barely an inch taller, on average, than a person who had few of them. If that’s the best we can do for height, which can be assessed with a tape measure, what can we expect for more elusive traits like intelligence or personality?"

And now back to the details:

nature SNP rs1042725 is associated with height (P = 4E-8) in a study involving over 20,000 individuals. The gene harboring this SNP, HMGA2, is a strong biological candidate for having an influence on height, since rare, severe mutations in this gene are known to alter body size in mice and humans.

Note that this SNP is by no means the whole story; rs1042725 is estimated to explain only 0.3% of population variation in height in both adults and children (approx 0.4 cm increased adult height per C allele), leaving over 99% of the influences on height to be described in the future ...

Science Daily April 7, 2008: 20+ additional regions linked to variance in height based on 3 studies published in Nature Genetics (6 April 2008 Advance Online Publication)

nature 54 snps.

Online Height Prediction Calculator based on heritability of 0.80 and parental height, this (free) Javascript calculator is probably just as good at predicting height as using SNPs, at least until a lot more is learned about roles of both genes and environment on height.

Other SNPs reported to be associated with height include:

[PMID 19343178] Contains a list of 21 SNPs (see bold entries in Table 1 in this publication) replicating as associated with height in this 2009 study of ~20,000 individuals.