evolution - Height and natural selection in humans?

@kate has what is probably the more correct answer for the observed pattern.

But as an experiment, I set up a basic simulation to approximate the conditions that you lay out:

1. Starting mean heights of 5'8" (172.72 cm) and 5'4" (162.56 cm) with standard deviations of 2.8" (7.112 cm). I used cm, because it's easier than dealing with inches.


2. Males will not mate with females that are taller than themselves.


3. Females will not mate with males more than 8" taller.


4. Males will not mate with females more then 8" shorter (follows from #3 above).

The problem that I quickly ran into was that, by truncating part of the normal distribution, the variance in height at each generation gradually decreased. After about 20 generations, the means weren't evolving because there was so little variation in height.

Human height is one of the most studied quantitative traits, going back over 100 years to some of the very first statisticians (Fisher, Galton). Height is a polygenic trait with very high heritability (h² = 0.8)¹. Genome-wide association studies have reported 54 genes involved in determination of human height².

Imagine that each of these 54 genes has just two alleles: a and b. a gives a +1 to height. b gives a -1 to height. So aa would be +2, ab or ba 0, and bb -2. The sum of all those alleles is correlated to height. So if all 54 were aa, then the height would be +108.

The problem comes in when people only mate with taller people. Over time, the proportion of b's will decrease, and the proportion of a's will increase, but only to a point. Once all the alleles are fixed at a, there won't be any room left. The genetic variation will be exhausted. Without the input of new alleles, height will cease to evolve.

1 Lettre, G. 2011. Recent progress in the study of the genetics of height. Hum Genet 129:465–472.

2 Visscher, PM. 2008. Sizing up human height variation. Nat Genet 40(5):489-90.