Reposting from the stats stackexchange.
John Cook, in his blog https://www.johndcook.com/blog/2015/03/09/why-isnt-everything-normally-distributed/, writes that many aren't:
Adult heights follow a Gaussian, a.k.a. normal, distribution . The usual explanation is that many factors go into determining one’s height, and the net effect of many separate causes is approximately normal because of the central limit theorem.
If that’s the case, why aren’t more phenomena normally distributed? Someone asked me this morning specifically about phenotypes with many genetic inputs.
The central limit theorem says that the sum of many independent, additive effects is approximately normally distributed . Genes are more digital than analog, and do not produce independent, additive effects. For example, the effects of dominant and recessive genes act more like max and min than addition. Genes do not appear independently—if you have some genes, you’re more likely to have certain other genes—nor do they act independently—some genes determine how other genes are expressed.
Height is influenced by environmental effects as well as genetic effects, such as nutrition, and these environmental effects may be more additive or independent than genetic effects.
I have two questions regarding this. First, I can't come up with any obvious example of phenotypes that don't follow a normal distribution. Could anyone help me? And second, his claims seem to contradict this other paper: https://www.uvm.edu/~dstratto/bcor102/readings/4_Evol_of_Phenotypes.pdf
To understand the genetic basis of quantitative traits, it is important to think about the effect of a particular allele, not simply its presence or absence. A single locus can produce three discrete phenotypes, but as more and more loci contribute to a trait the phenotypic distribution comes closer and closer to a normal (bell shaped) distribution
Who is right here? Does the fact that genes are digital rather than analog really make a difference? And what about the second argument that they aren't independent. Is that really necessary (second paper seems to indicate otherwise if I am understanding properly).