There has been quite a lot of research on a similar problem – heritability of intelligence – in the past (now this area is a bit suppressed because it can be applied to interracial differences). Simply google for ‘heritability coefficient’ and IQ/intelligence or go to WIKI . A classical name in this area is Arthur R. Jensen.
Most studies put that coefficient between 0.5-0.6. This means that 50-60% of intelligence (often measured as IQ) variation in offspring is explained by genetics, 40-50% by other factors (environment). This environmental component explains why IQ can grown from generation to generation (this growth is used by some PC people with limited background in genetics to explain the shift by pure non-genetics factors). If I remember correctly, the coefficient is even higher for very high IQs.
Disclaimer: I don’t follow this area much (since it is more politics than science).
