# inbreeding: Inbreeding coefficient In GeneticsPed: Pedigree and genetic relationship functions

## Description

`inbreeding` calculates inbreeding coefficients of individuals in the pedigree

## Usage

 `1` ```inbreeding(x, method="meuwissen", sort=TRUE, names=TRUE, ...) ```

## 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

`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")) ```

### Example output

```Loading required package: MASS

Attaching package: 'GeneticsPed'

The following object is masked from 'package:stats':

family

S1  S2  S3  S4  S5  S6
0   0   0   0 1/8 1/8
user  system elapsed
0.014   0.004   0.019
user  system elapsed
0.001   0.000   0.002
```

GeneticsPed documentation built on Nov. 8, 2020, 5:54 p.m.