This is actually interesting in terms of GWAS - there used to be a large difference between "heritability" (~the measurable variance offspring shares with their parents, like height in cm, which can be influenced by a ton of parameters if you don't know about them/don't control them [like nutrition]). In the age of genome-wide association studies the linked SNPs often correlate much weaker than the heritability predicts (example: you could explain 10% of variance with SNPs, but heritability says it should be 70%) - this was called the problem of "missing heritability".
>We estimate that 40% of the variation in crystallized-type intelligence and 51% of the variation in fluid-type intelligence between individuals is accounted for by linkage disequilibrium between genotyped common SNP markers and unknown causal variants.
However, look at that "unknown", because the same abstract says:
>Finally, using just SNP data we predicted ~1% of the variance of crystallized and fluid cognitive phenotypes in an independent sample.
Using their SNPs alone it's only 1%. I assume the "true" genetic variability (~~~heritability) is somewhere in between those two values, since the 40/50% number seems to assume that these unknown variants will be discovered (they haven't yet AFAIK, maybe they don't exist, maybe they do).
Many of the studies showing this have some serious flaws, because of the types of people they tended to use. The twins used in the studies where disproportionately from higher income families. You don't find many low SES families who adopt, so for this and other reasons it's very difficult to find twins raised apart in low SES families.
The summary is that it's pretty clear that among higher SES families IQ is more than 50% genetic (but environment still plays a very large role).
However, many studies indicate that among lower SES families, environment is the dominant factor.
There's still conflicting evidence here though, because there are some studies that indicate that SES has little impact on IQ heritability. The argument is that SES has a much greater on the heritability of IQ in children than on that of adults.