It depends on the degree of regression to the mean, and to which mean the children are regressing to. Due to selection criteria bias of immigrants they are more

It depends on the degree of regression to the mean, and to which mean the children are regressing to. Due to selection criteria bias of immigrants they are more likely to be outliers than non immigrants. While it's very likely that the outliers have a genetic advantage it seems that important combinations of genes are often lost and on average subsequent generations do regress to the mean intelligence of the general population that they come from more. If intelligence was a single gene or the average of multiple genes what would normally be expected would be an average of the parents intelligence. It appears that the actual results are the mix of the two which could be readily explained by important combinations of genes not being lost some of the time. In the future when the important combinations of genes yielding more intelligence are known it'll be possible to select for certain combinations and children selected this way would be expected to have a higher intelligence than either parent. i.e. making multiple draws from a distribution and picking the highest value.