# Regression to the mean and evolution

I don't have a strong biological background but, in studying statistics, I met the idea of regression to the mean. e.g. children of tall parents tend to be shorter than their parents, and so on.

Does this interact with evolution ?

• Interestingly, statistics have evolved quite significantly in parallel of evolutionary biology. Galton, Pearson and R. Fisher are important names that contributed to both biology and statistics. Jan 3, 2016 at 17:01
• Have a look at Wikipedia > Heritability > Parent-offspring_regression. Jan 3, 2016 at 18:33
• When you talk about "regression toward the mean", do you refer to the modelling of data (linear regressions) or do you refer to the natural tendency for extreme values to be less extreme in a future measurement (origin of the term regression but rarely used with this meaning today)? Jan 3, 2016 at 18:35
• answers to this question are related: Is it possible for a child to grow taller than their tallest parent? Jan 4, 2016 at 13:17
• Actually i was referring to the tendency of values to be around the mean on the normal distribution curve. Jan 4, 2016 at 13:34

TL;DR answer: Regression to the mean doesn't always occur (children can be taller than either parent, as can be easily observed at any high-school basketball game), so it doesn't affect the theory of evolution through natural selection.

The observation of regression to the mean was of great concern to Darwin and early thoughts on natural selection (don't confuse "evolution", which is the observed phenomenon, and "natural selection", which is one of the theories proposed to explain evolution). The problem has been effectively resolved since the rediscovery of Mendel's genetic work at the end of the 19th century.

"Regression to the mean" is inevitable if inheritance works through blending of features. That was how everyone believed inheritance to work in the mid-1800s, and Darwin understood that it presented an insuperable obstacle to his theory. That is, if blending inheritance was true, then natural selection could not be true. Darwin puzzled over this quite a bit, and came up with some unsatisfying suggestions to overcome it, but at the end of the day, one of the predictions that his theory of evolution through natural selection made, was that blending inheritance could not be true.

Of course, blending inheritance is not true. Mendel showed that in fact inheritance is quantal, not blending. We now know that many traits of interest look, superficially, as if they're blending (which leads to regression to the mean), but are actually the result of multiple traits interacting.

With blending inheritance, the variation that is required for natural selection to work is lost, generation after generation; regression to the mean in an inevitable consequence. With gene-based inheritance, variation (can be) preserved generation after generation; regression to the mean is a common but not inevitable consequence, because the variation in the original population is still present and can be re-created given appropriate selection pressure.

• Interesting read on how Mendel was mostly wrong. Jan 3, 2016 at 19:08
• Mendel wasn't wrong on the key point that inheritance is not blended, which is what's relevant here. Jan 3, 2016 at 19:57
• That's true, I should have been more specific. I was just mentioning the article as possible interesting reading for those whose understanding of Mendel's work didn't go beyond high school biology. Your answer is actually pretty decent. Jan 3, 2016 at 20:02

There is a concept known as "heritability" which essentially is a measure of how much of the variability in a certain trait that is due to genetic factors. This is closely related to regression to the mean. Now for length the heritability sometimes is estimated, by measuring the lengths of many parents and their offspring, to be around 0.7. This means that if your father is ten centimeters taller than the average man in your population and your mother is ten centimeter taller than the average woman in your population you are expected to be around three centimeters shorter than your same sex parent but still seven centimeters taller than the average for your sex in your population.

A heritability of 0.7 is very high so if it were a clear evolutionary advantage for an individual to be taller or shorter than the current average height the length of the population will be expected to change rather fast.

There are other traits, for instance the tendency to have one-egg twins, where the heritability is believed to be basically zero. This means that even if you are a one-egg twin and being a one-egg twin constitutes a clear evolutionary advantage the relative amounts of one-egg twins will not increase in the population because there is no heritability.

You could say that the higher the heritability, and thus the lower the regression to the mean, the faster a trait will change in a population in a certain direction if there is evolutionary pressure for it to do so.