Sewall Wright on Coefficients of Inbreeding and Relationship (1922)

JayMan continues to misunderstand basic population genetics, and continues to respond to people who point this out to him by sticking his fingers in his ears and reiterating his misunderstandings:

@johan stavers:

coefficient of relationship is flawed, if a man fathers a child with his sister his child is more than 50% related, this extends to niece/nephew mating and therefore logically also to mating within ethnicity or even nation

No, coefficient of relationship is perfectly fine.

I attempt yet again to get across to JayMan that the table of coefficients of relationship he looked up on wikipedia in no way proves that "unrelated" members of a given race share no kinship relative to members of other races (if JayMan were correct, of course, observable racial differences would not exist; JayMan inadvertently assesses his own level of knowledge in an unrelated twitter comment: "according to people who don't know science, there's no such thing as race."). Sewall Wright explicitly noted in the 1922 paper in which he defined coefficients of relationship that values like ".50 for brothers" hold "in a random stock" and that individuals belonging to an "inbred subline" will share relatedness relative to the general population.

JayMan, the fact that the table of "coefficients of relationship" on wikipedia is not valid for the purpose you're attempting to use it is not some subtle issue that's open to debate, but a point that follows directly from the definitions of the relevant terms.

Thus, if we can calculate the percentage of homozygosis which would follow on the average from a given system of mating, we can at once form the most. natural coefficient of inbreeding. The writer3 has recently pointed out a method of calculating this percentage of honmozygosis which is applicable to the irregular systems of mating found in actual pedigrees as well as to regular systems. This method, it may be said. gives results widely different from Pearl's coefficient, in many cases even as regards the relative degree of inbreeding of two animals.

Taking the typical case in which there are an equal number of dominant. and recessive genes (A and a) in the population, the random-bred stock will be composed of 25 per cent. AA, 50 per cent. Aa and 25 per cent. aa. Close inbreeding will tend to convert the proportions to 50 per cent. AA, 50 per cent. aa, a change from 50 per cent. homozygosis to 100 per cent. homozygosis. For a natural coefficient of inbreeding, we want a scale which runs from 0 to 1, while the percentage of homozygosis is running from, 50 per cent. to 100 per cent. The formula. 2h-1, where h is the proportion of complete homozygosis, gives the required value. This can also be written 1-2p where p is the proportion of heterozygosis. In the above-mentioned paper it was shown that the coefficient of correlation between uniting egg and sperm is expressed by this same formula, f 1-2p. We can thus obtain the coefficient of inbreeding fb for a given individual B, by the use of the methods there out- lined.

The symbol r_bc, for the coefficient of the correlation between B and C, may be used as a coefficient of relationship. It has the value 0 in the case of two random individuals, .50 for brothers in a random stock and approaches 1.00 for individuals belonging to a closely inbred subline of the general population. [. . .]

If an individual is inbred, his sire and dam are connected in the pedigree by lines of descent from a common ancestor or ancestors. The coefficient of inbreeding is obtained by a summation of coefficients for every line by which the parents are connected, each line tracing back from the sire to a common ancestor and thence forward to the dam, and passing through no individual more than once. The same ancestor may of course be involved in more than one line.

Coefficients of Inbreeding and Relationship
Sewall Wright
The American Naturalist
Vol. 56, No. 645 (Jul. - Aug., 1922), pp. 330-338
http://www.jstor.org/stable/2456273

Go ask Greg Cochran about this if comprehension continues to elude you.

From Wright's 1943 paper on "Isolation by distance" (pdf):

Study of statistical differences among local populations is an important line of attack on the evolutionary problem. While such differences can only rarely represent first steps toward speciation in the sense of the splitting of the species, they are important for the evolution of the species as a whole. They provide a possible basis for intergroup selection of genetic systems, a process that provides a more effective mechanism for adaptive advance of the species as a whole than does the mass selection which is all that can occur under panmixia. [. . .]

THE INBREEDING COEFFICIENT

Departures from panmixia may be expressed in terms of the average inbreeding coefficient of individuals, relative to the total population under consideration. This coefficient has been defined as the correlation between uniting gametes with respect to the gene complex as an additive system. It has been shown that its value can be found for any pedigree by finding all paths by which one may trace back from the egg to a common ancestor (A) and thence forward to the sperm along a wholly different path. [. . .]

The inbreeding, measured by F, may be of either of two extreme sorts: sporadic mating of close relatives with no tendency to break the population into subgroups, and division into partially isolated subgroups, within each of which there is random mating. The latter is the case in which we are primarily interested here.

Sewall Wright, incidentally, was of New England Puritan stock.