Some data is available on the effect alleles have on height. For example Common DNA Variants Accurately Rank an Individual of Extreme Height

However after browsing the literature I was not able to easily answer the following.

If we take a genome and allow only one gene to change there is going to be an allele maximizing the genetic potential for height. If we take two different genomes and allow one gene to vary are the optimal alleles going to be the same?

If this can happen then linear polygenic scores cannot fully capture the genotype–phenotype map.

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    $\begingroup$ Linearity is an assumption of convenience established by Fisher 1918 (ncbi.nlm.nih.gov/pmc/articles/PMC6456325) to make the math easier. There really isn't any biological reason to believe it's true; even the existence of dominance is sufficient to make it obvious that linearity isn't complete. I recommend reading about epistasis (nature.com/articles/nrg2452). That said, linear predictions yield pretty good predictions under the assumption that most pairs of loci don't interact (also shown by Fisher I believe). $\endgroup$ Oct 6 '21 at 0:52
  • $\begingroup$ See also e.g. pubmed.ncbi.nlm.nih.gov/31761530. Even if polygenic scores can be used for prediction, they're honestly not doing a very good job! They suck even for highly "heritable" traits, showing the weaknesses of the concept of heritability (but that's a different conversation). $\endgroup$ Oct 6 '21 at 0:58

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