Why are Gaussian distributions everywhere?
colab.research.google.com> The trick is that a normal distribution occurs when you sum independent, symmetric distributions.
It's not neccesary that the distribution is symmetric. You can try for example with 500 genes witn 10% of 0.00 extra height and 90% of 0.01 extra height. You will get again a gaussian but the center will be in 500*(.10*0.00+.90*0.01).
Interesting, will try this. I imagine "symmetric" is not the correct term, but what is? I imagine there are constraints on types of random variables for which this will work, but I haven't looked into it deeply.
It's weird/interesting/ammazing, that there are almost no constrains. The distribution can be as weird as you want. The only condition is that the variance must be finite.
tl;dr: Gaussians show up when you add together enough small random effects. The notebook has some code and prose that shows why that's the case both for human height and for manufacturing wooden doors.