There are decades of studies of the heritability of IQ. Some of them measure H², which is full heritability and some of them measure h², "narrow sense heritability"; and some measure both. Narrow sense heritability is the linear part, a lower bound for the full broad sense heritability. A typical estimate of the nonlinear contribution is H²-h²=10%. In neither case do they make any assumptions about the genetic structure. Often they make assumptions about the relation between genes and environment, but they never assume linear genetics. Measuring h² is not assuming linearity, but measuring linearity.
This paper finds a lower bound for h² of 0.4 and 0.5 for crystallized and fluid intelligence, respectively, in childhood. I say lower bound because it only uses SNP data, not full genomes. It mentions earlier work giving a narrow sense heritability of 0.6 at that age. That earlier work probably has more problems disentangling genes from environment, but is unbiased given its assumptions.
The linked paper says:
We fitted a linear mixed model
y = µ + g + e, whereyis the phenotype,mis the mean term,gis the aggregate additive genetic effect of all the SNPs and e is the residual effect.
If you have 3511 individuals and 549692 SNPs you won't find any nonlinear effects. 3511 observations of 549692 SNPs is already overfitted 3511 observations of 549692 * 549691 gene interactions is even more overfitted and I wouldn't expect that the four four principal components they calculate to find an existing needle in that haystack.
Apart from that i...
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