## Law of regression to the mean

Francis Galton, a cousin of Charles Darwin, studied the heritability of body height by the determination of the correlation between the mean value of a height of both parents and the mean height of their progeny. Galton and found two important facts. To begin with, he demonstrated that heritability in a given trait does actually exist, as tall parents actually tend to have tall children and short parents tend to have short children. Secondly, he formulated the *law of regression to the mean*. The further the mean height of the parents from the population mean, the greater was the probability that the height of their children would return back towards the population mean, rather than deviating even further from this mean than the deviation of the mean height of their parents. This return towards the mean can be explained by the existence of non-additive components of genetically determined variability. In a stabilized population, the population mean of the value of a quantitative characteristic should correspond to the optimal value of this trait from the standpoint of the biological fitness of its carriers. As individuals with larger or smaller values of the given trait are constantly removed from the population by normalized selection, a frequency of the individual alleles of the genes affecting the given trait is established in the gene pool of the population that leads to the optimal value of the given trait in the largest possible number of random combinations. If the heights of the mother and of the father deviate substantially from the mean, they most probably have some rare combination of the relevant alleles. This combination will disappear in their progeny either immediately or in the subsequent generations. If only genes with additive effect were relevant for the given trait, the progeny should not return to the population mean.

Galton could, of course, not correctly interpret the results of his study under the conditions at that time. He explained the existence of regression to the population mean as an indication that the characteristics of an individual are determined 50% by predispositions obtained from their parents, 25% by predispositions obtained from their grandparents, 12.5% from their great-grandparents, etc. If predispositions are interpreted as genes in the sense of cistrons, then this would be a quite erroneous explanation, as an individual obtains all his genes from his parents. However, if we realize that a predisposition can also be the effect of certain interactions of a combination of several alleles at various loci, a combination that an individual inherits from his predecessors but that can fall apart or, to the contrary, be formed with a certain probability in each generation, then this, at first glance erroneous explanation, can be basically correct. The probability that an individual inherited a certain combination of alleles from one of his great grandparents is less than the probability that he inherited it from his grandparents and this is again less than the probability that he would inherit it from one of his parents. See also the theory of frozen plasticity.