# Inbreeding coefficient

### Description

`inbreeding`

calculates inbreeding coefficients of
individuals in the pedigree

### Usage

1 |

### Arguments

`x` |
pedigree object |

`method` |
character, method of calculation "tabular", "meuwissen" or "sargolzaei", see details |

`sort` |
logical, for the computation the pedigree needs to be sorted, but results are sorted back to original sorting (sort=TRUE) or not (sort=FALSE) |

`names` |
logical, should returned vector have names; this can be used to get leaner returned object |

`...` |
arguments for other methods |

### Details

Coefficient of inbreeding (*F*) represents probability that two
alleles on a loci are identical by descent (Wright, 1922; Falconer and
Mackay, 1996). Wright (1922) showed how *F* can be calculated but
his method of paths is not easy to wrap in a program. Calculation of
*F* can also be performed using tabular method for setting the
additive relationship matrix (Henderson, 1976), where *F_i = A_{ii}
- 1*. Meuwissen and Luo (1992) and VanRaden (1992) developed faster
algorithms for *F* calculation. Wiggans et al. (1995) additionally
explains method in VanRaden (1992). Sargolzaei et al. (2005) presented
yet another fast method.

Take care with `sort=FALSE, names=FALSE`

. It is your own
responsibility to assure proper handling in this case.

### Value

A vector of length *n* with inbreeding coefficients, where
*n* is number of subjects in `x`

### Author(s)

Gregor Gorjanc and Dave A. Henderson

### References

Falconer, D. S. and Mackay, T. F. C. (1996) Introduction to Quantitative Genetics. 4th edition. Longman, Essex, U.K. http://www.amazon.com/gp/product/0582243025

Henderson, C. R. (1976) A simple method for computing the inverse of a
numerator relationship matrix used in prediction of breeding
values. *Biometrics* **32**(1):69-83

Meuwissen, T. H. E. and Luo, Z. (1992) Computing inbreeding coefficients
in large populations. *Genetics Selection and Evolution*
**24**:305-313

Sargolzaei, M. and Iwaisaki, H. and Colleau, J.-J. (2005) A fast
algorithm for computing inbreeding coefficients in large
populations. *Journal of Animal Breeding and Genetics*
**122**(5):325–331
http://dx.doi.org/10.1111/j.1439-0388.2005.00538.x

VanRaden, P. M. (1992) Accounting for inbreeding and crossbreeding in
genetic evaluation for large populations. *Journal of Dairy
Science* 75(11):3136-3144
http://jds.fass.org/cgi/content/abstract/75/11/3136

Wiggans, G. R. and VanRaden, P. M. and Zuurbier, J. (1995) Calculation
and use of inbreeding coefficients for genetic evaluation of United
States dairy cattle. *Journal of Dairy Science*
**78**(7):1584-1590
http://jds.fass.org/cgi/content/abstract/75/11/3136

Wright, S. (1922) Coefficients of inbreeding and relationship.
*American Naturalist* 56:330-338

### See Also

`Pedigree`

, `relationshipAdditive`

,
`kinship`

and `geneFlowT`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 | ```
data(Mrode2.1)
Mrode2.1$dtB <- as.Date(Mrode2.1$dtB)
x2.1 <- Pedigree(x=Mrode2.1, subject="sub", ascendant=c("fat", "mot"),
ascendantSex=c("M", "F"), family="fam", sex="sex",
generation="gen", dtBirth="dtB")
fractions(inbreeding(x=x2.1))
## Compare the speed
ped <- generatePedigree(nId=25)
system.time(inbreeding(x=ped))
# system.time(inbreeding(x=ped, method="sargolzaei")) # not yet implemented
system.time(inbreeding(x=ped, method="tabular"))
``` |