Coefficient of relationship
Encyclopedia
In population genetics
, Sewall Wright
's coefficient of relationship or coefficient of relatedness or relatedness or r is defined as 2 times the Coefficient of Inbreeding. The 'Coefficient of Relatedness' (or: coefficient of kinship) is defined as the probability
that the allele
s at a particular locus
chosen at random from two individuals are identical by descent.
).
There is a notable difference between exact and average relatedness. The former describes the inheritance of an exact and consistent fraction of identical alleles whereas the latter is an average of variable relatedness. For example, one might share exactly half of one's alleles from a parent. On the other hand, a sibling does not receive exactly half of the same alleles as oneself, but can theoretically receive any fraction from all to none of the same alleles. In this case, genetic relatedness merely dictates the expected fraction of shared alleles.
Some other relatedness examples: (assuming no consanguinity
of the parents, for diploid species unless noted otherwise)
Some of these definitions of r are tricky to calculate. For example, consider that you are one of a family of half brothers with the same mother but different fathers. Call rm the coefficient of matrilineal relatedness and call rp the coefficient of patrilineal relatedness. What is the coefficient of relatedness to each of your half brothers?
rm=0.5 as it does for normal siblings, since there is a 1 in 2 chance that you and your half brother developed from eggs harboring the same haploid genome selected during maternal meiosis. But rp=0 since there is no chance that any two half-brothers inherited the same allele from different fathers by descent. The average of these rs equals 0.25, as we see above. You and your half brother are one quarter genetically identical by descent.
The following images demonstrates the effect of gene distribution through 16 generations.
To illustrate how an imprinting turns normal siblings into half siblings, consider that you are one of a cadre of full siblings. What is your coefficient of relatedness to one of your siblings at an imprinted locus in a maternally inherited allele? (Maternally inherited alleles are called "madumnal," and paternally inherited alleles are called "padumnal".)
The value of r at this imprinted locus is equal to the value of r for the entire genome of the half brothers. For the brothers above, rm=0.5 and rp=0. For the madumnal locus in the family of full siblings rm=0.5 too, since all expression is from the mother's allele. Normally, rp=0.5 for full siblings with the same father, but the effect of imprinting is to negate paternal expression, hence rp=0. Therefore you and your full siblings resemble half-siblings at imprinted loci.
Population genetics
Population genetics is the study of allele frequency distribution and change under the influence of the four main evolutionary processes: natural selection, genetic drift, mutation and gene flow. It also takes into account the factors of recombination, population subdivision and population...
, Sewall Wright
Sewall Wright
Sewall Green Wright was an American geneticist known for his influential work on evolutionary theory and also for his work on path analysis. With R. A. Fisher and J.B.S. Haldane, he was a founder of theoretical population genetics. He is the discoverer of the inbreeding coefficient and of...
's coefficient of relationship or coefficient of relatedness or relatedness or r is defined as 2 times the Coefficient of Inbreeding. The 'Coefficient of Relatedness' (or: coefficient of kinship) is defined as the probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
that the allele
Allele
An allele is one of two or more forms of a gene or a genetic locus . "Allel" is an abbreviation of allelomorph. Sometimes, different alleles can result in different observable phenotypic traits, such as different pigmentation...
s at a particular locus
Locus (genetics)
In the fields of genetics and genetic computation, a locus is the specific location of a gene or DNA sequence on a chromosome. A variant of the DNA sequence at a given locus is called an allele. The ordered list of loci known for a particular genome is called a genetic map...
chosen at random from two individuals are identical by descent.
Calculation
The coefficient of relationship between parent and offspring is 0.5, meaning half of the offspring's genome comes from that parent. Or, more precisely said, half the genes are identical by descent (i.e. not accounting for genomic imprinting and other non-Mendelian inheritanceNon-mendelian inheritance
Non-Mendelian inheritance is a general term that refers to any pattern of inheritance in which traits do not segregate in accordance with Mendel’s laws. These laws describe the inheritance of traits linked to single genes on chromosomes in the nucleus. In Mendelian inheritance, each parent...
).
There is a notable difference between exact and average relatedness. The former describes the inheritance of an exact and consistent fraction of identical alleles whereas the latter is an average of variable relatedness. For example, one might share exactly half of one's alleles from a parent. On the other hand, a sibling does not receive exactly half of the same alleles as oneself, but can theoretically receive any fraction from all to none of the same alleles. In this case, genetic relatedness merely dictates the expected fraction of shared alleles.
Some other relatedness examples: (assuming no consanguinity
Consanguinity
Consanguinity refers to the property of being from the same kinship as another person. In that respect, consanguinity is the quality of being descended from the same ancestor as another person...
of the parents, for diploid species unless noted otherwise)
| r | relationship | exact or average |
|---|---|---|
| 0.5 (½) | parent-offspring | exact |
| 0.25 (¼) | grandparent-grandchild | exact |
| 0.125 (⅛) | great grandparent-great grandchild | exact |
| 1 | identical twins; clones | exact |
| 0.5 (½) | full siblings | average |
| 0.25 (¼) | half siblings | average |
| 0.125 (⅛) | first cousins | average |
| 0.03125 (1/32) | second cousins | average |
| 0.75 (¾) | full hymenopteran sisters | average |
Some of these definitions of r are tricky to calculate. For example, consider that you are one of a family of half brothers with the same mother but different fathers. Call rm the coefficient of matrilineal relatedness and call rp the coefficient of patrilineal relatedness. What is the coefficient of relatedness to each of your half brothers?
rm=0.5 as it does for normal siblings, since there is a 1 in 2 chance that you and your half brother developed from eggs harboring the same haploid genome selected during maternal meiosis. But rp=0 since there is no chance that any two half-brothers inherited the same allele from different fathers by descent. The average of these rs equals 0.25, as we see above. You and your half brother are one quarter genetically identical by descent.
The following images demonstrates the effect of gene distribution through 16 generations.
Coefficient is relative to a base population
It might be objected that all copies of all genes are identical by descent, in that they are all descended from a single ancestral gene. Shouldn't all these numbers be 1? However these calculations implicitly rely on a base population, in which all copies are assumed to not be identical by descent. For example, for a pair of siblings the base population is the one from which their parents are drawn, and only identity by descent that occurred since then is counted. This gives the above numbers.Effect of imprinting
In the example above, the differentiation between maternal and paternal coefficients of relatedness was made in order to introduce the phenomenon of imprinting, or parent-specific gene expression into the calculation of r.To illustrate how an imprinting turns normal siblings into half siblings, consider that you are one of a cadre of full siblings. What is your coefficient of relatedness to one of your siblings at an imprinted locus in a maternally inherited allele? (Maternally inherited alleles are called "madumnal," and paternally inherited alleles are called "padumnal".)
The value of r at this imprinted locus is equal to the value of r for the entire genome of the half brothers. For the brothers above, rm=0.5 and rp=0. For the madumnal locus in the family of full siblings rm=0.5 too, since all expression is from the mother's allele. Normally, rp=0.5 for full siblings with the same father, but the effect of imprinting is to negate paternal expression, hence rp=0. Therefore you and your full siblings resemble half-siblings at imprinted loci.
See also
- HeritabilityHeritabilityThe Heritability of a population is the proportion of observable differences between individuals that is due to genetic differences. Factors including genetics, environment and random chance can all contribute to the variation between individuals in their observable characteristics...
- Inclusive fitnessInclusive fitnessIn evolutionary biology and evolutionary psychology, the inclusive fitness of an organism is the sum of its classical fitness and the number of equivalents of its own offspring it can add to the population by supporting others...
- Kin selectionKin selectionKin selection refers to apparent strategies in evolution that favor the reproductive success of an organism's relatives, even at a cost to the organism's own survival and reproduction. Charles Darwin was the first to discuss the concept of group/kin selection...
- Semantic relatedness
- Coefficient of inbreeding at Wikilectures