Sewall Wright’s Coefficient of Relationship

Repost

At the bottom is Sewall Wright’s Coefficient of Relationship and it touches on human genealogy.

  • Coefficient of inbreeding – The probability that two alleles at a given locus are identical by descent. i.e. The extent to which an individual is more likely to be homozygous rather than heterozygous because of related parents.
  • Coefficient of relationship – Denotes the proportion of genes that are held in common by two individuals as a result of direct or Collateral relationship.

As breeder cockfighters, we can use this tool to know more about inbreeding chickens. The more inbred an individual the more it manifests its characteristics on its offsprings.

I also want to mention that cousin marriage is legal to most of the world except China and Philippines. Cousin marriage is legal in 26 states of the United States.

– Gameness til the End

Coefficient of relationship

In population geneticsSewall Wright‘s coefficient of relationship or coefficient of relatedness or relatedness or r is a measure for the level of consanguinity between two given individuals.

The coefficient of inbreeding is calculated for a single individual, and is a measure for the amount of pedigree collapse within that individual’s genealogy.

Roughly speaking, the coefficient of relationship approaches a value of 1 for individuals from a completely inbred population, and approaches a value of 0 for individuals with arbitrarily remote common ancestors.

Definition

The coefficient of correlation as defined by Wright (1922) is derived from the definition of the coefficient of inbreeding f as defined in Wright (1921).

Inbreeding coefficient

The purpose of such a coefficient is to express the likelihood of effects due to inbreeding to be expected based on a known pedigree (i.e. a fully documented genealogy e.g. due to a fixed system of breeding). The coefficient introduced by Wright (1921) expresses the expected percentage of homozygosity arising from a given system of breeding.

For a given gene with dominant and recessive variants A and a, a random-bred stock will be 50% homozygous (25% AA and 25% aa), while a closely inbred population will be 100% homozygous (100% AA or 100% aa). The coefficient of inbreeding f is thus designed to run from 0 for an expected 50% homozygosis to 1 for an expected 100% homozygosis, f=2h-1, where h is the chance of finding homozygosis in this gene.

Note that f is an expectation value for an unspecified, hypothetical, perfectly Mendelian gene. Its definition holds regardless of whether the organism’s genome actually contains such a gene. Therefore, the coefficient of inbreeding is a statistical value derived from the individual’s pedigree and cannot be verified or “measured” exactly by looking at the individual’s genome.

Coefficient of relationship

The coefficient of relationship rBC between two individuals B and C is obtained by a summation of coefficients calculated for every line by which they are connected to their common ancestors. Each such line connects the two individuals via a common ancestor, passing through no individual which is not a common ancestor more than once. A path coefficient between a ancestor A and an offspring O separated by n generations is given as:

pAO= 2-n⋅((1+fA)/(1+fO))½

where fA and fO are the coefficients of inbreeding for A and O, respectively.

The coefficient of correlation rBC is now obtained by summing over all path coefficients:

rBC = Σ pABpAC.

By assuming that the pedigree can be traced back to a sufficiently remote population of perfectly random-bred stock (fA=0) the definition of r may be simplified to

rBC = Σp 2L(p),

where p enumerates all paths connecting B and C with unique common ancestors (i.e. all paths terminate at a common ancestor and may not pass through a common ancestor to a common ancestor’s ancestor), and L(p) is the length of the path p.

To given an (artificial) example: Assuming that two individuals share the same 32 ancestors of n=5 generations ago, but do not have any common ancestors at four or less generations ago, their coefficient of relationship would be

r = 2n⋅2-2n = 2n = 3%.

Individuals for which the same situation applies for their 1024 ancestors of ten generations ago would have a coefficient of r = 2-10 = 0.1%. If follows that the value of r can be given to an accuracy of a few percent if the family tree of both individuals is known for a depth of five generations, and to an accuracy of a tenth of a percent if the known depth is at least ten generations. The contribution to r from common ancestors of 20 generations ago (corresponding to roughly 500 years in human genealogy, or the contribution from common descent from a medieval population) falls below one part-per-million.

Human genealogy

The coefficient of relationship is sometimes used to express degrees of kinship in numerical terms in human genealogy.

In human genealogy, the value of the coefficient of relationship is usually calculated based on the knowledge of a full family tree extending to a comparatively small number of generations, perhaps of the order of three or four. As explained above, the value for the coefficient of relationship so calculated is thus a lower bound, with an actual value that may be up to a few percent higher. The value is accurate to within 1% if the full family tree of both individuals is known to a depth of seven generations.

r relationship degree of relationship
100% identical twins; clones 0
50% (2-1) parent-offspring
1
50% (2-2+2-2) full siblings 2
37.5% (2-2+2⋅2-4) 3/4 siblings or sibling cousins 2
25% (2-2) grandparent-grandchild 2
25% (2-2) half siblings 2
25% (2⋅2-3) aunt/uncle-nephew/niece 3
25% (2-3+2-3) double first cousins 4
12.5% (2-3) great grandparent-great grandchild 3
12.5% (2⋅2-4) first cousins 4
12.5% (8⋅2-6) quadruple second cousins  6
9.38% (6⋅2-6) triple second cousins  6
6.25% (2-4) half-first cousins 4
6.25% (2⋅2-5) first cousins once removed 5
6.25% (4⋅2-6) double second cousins  6
3.13% (2-6+2-6) second cousins 6
0.78% (2⋅2-8) third cousins  8
0.20% (2⋅2-10) fourth cousins  10

From the above table, it can be seen that most legislation regarding incestuous unions concern relations of r=25% or higher, while most permit unions of individuals with r=12.5% or lower. An exception are certain US states where cousin marriage is prohibited. Also, most legislations make no provision for the rare case of marriage between double first cousins. It should also be noted that incest laws also include prohibitions of unions between unrelated individuals if there is a close legal relationship such as adoption.

Related Standard of Perfection Discussion

Line Breeding: It is fair to say that linebreeding is a form of inbreeding. However, it is done more selectively and with an eye to keeping the inbreeding coefficient (see below for chart) at or below 12.5%. Like inbreeding, linebreeding is an attempt by the breeder to secure, fix or maintain desirable traits within the strain or line.

In Breeding: Is the process of mating parent to offspring and offspring back to parent in an endeavor to retain or improve particular traits or to fix desirable traits within a strain or line. The inbreeding coefficient is often high in inbreeding which is where it differs from linebreeding.

Out Breeding: Is the process whereby unrelated parent stock of the same breed are brought together in an attempt to introduce new traits to a line or strain or to introduce new vitality and vigor into a line or strain that is too inbred.

Cross Breeding: Is the process of mating unrelated parents of unrelated breeds in an effort to achieve completely new offspring possessing the best qualities of each parent often with an eye to creating a new breed or better production stock.

Selective Breeding: Is the process of mating parent stock of the same breed, possessing the best desired traits (usually leading to some standard uniformity) and then culling the offspring to eventually yield the strongest and best examples of the original traits.

Compound Breeding: Using two or more breeding techniques outlined above jointly. Example: Selective Linebreeding, Double Linebreeding, Cross Linebreeding, etc.

Inbreeding Coefficient:

  • Father/daughter, mother/son or brother/sister → 25%
  • Grandfather/granddaughter or grandmother/grandson → 12.5%
  • Half-brother/half-sister → 12.5%
  • Uncle/niece or aunt/nephew → 12.5%
  • Great-grandfather/great-granddaughter or great-grandmother/great-grandson → 6.25%
  • Half-uncle/niece or half-aunt/nephew → 6.25%
  • First cousins → 6.25%
  • First cousins once removed or half-first cousins → 3.125%
  • Second cousins or first cousins twice removed → 1.5625%
  • Second cousins once removed or half-second cousins → 0.78125%
  • Third cousins or second cousins twice removed → 0.390625%
  • Third cousins once removed or half-third cousins → 0.195%

Mendelian Inheritance: States that both dominant and recessive qualities of the parent stock are inherited by their offspring pre-dominately through sex chromosomes and sub-dominately through autosomes (or non sex related chromosomes).

Sex-Linked Inheritance: With chickens, the cock carries two chromosomes for sex while the hen carries only one. So any gene located on the cock chromosome will be passed to both his sons and daughters; while any gene on the hen’s sex chromosome will only be passed on to her sons. Thus as exampled by feather coloring and marking being carried on the sex chromosome results of breeding as follows:

Barred Plymouth Rock Cock to Rhode Island Hen results in all barred offspring.

Rhode Island Red Cock to Barred Plymouth Rock Hen results in barred sons only and black daughters.

(This was the first understanding of auto sexing chicks.)

Record Keeping: I know this may seem redundant to mention record keeping but with breeding records must be kept and be clear and concise on how the line or strain is being developed.




poultry gamefowl chicken gamecock

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