# inverseA

##### Inverse Relatedness Matrix and Phylogenetic Covariance Matrix

Henderson (1976) and Meuwissen and Luo (1992) algorithm for inverting relatedness matrices, and Hadfield and Nakagawa (2010) algorithm for inverting phylogenetic covariance matrices.

- Keywords
- array

##### Usage

```
inverseA(pedigree=NULL, nodes="ALL", scale=TRUE, reduced=FALSE,
tol = .Machine$double.eps^0.5)
```

##### Arguments

- pedigree
ordered pedigree with 3 columns: id, dam and sire, or a

`phylo`

object.- nodes
`"ALL"`

calculates the inverse for all individuals/nodes. For phylogenies`"TIPS"`

calculates the inverse for the species tips only, and for pedigrees a vector of id's can be passed which inverts the relatedness matrix for that subset.- scale
logical: should a phylogeny (needs to be ultrametric) be scaled to unit length (distance from root to tip)?

- reduced
logical: should childless nodes be dropped from the inverse and the pedigree/phylogeny representation be reduced?

- tol
numeric: differences in branch length smaller than this are ignored when assessing whether a tree is ultrametric.

##### Value

inverse as `sparseMatrix`

inbreeding coefficients/branch lengths

pedigree/pedigree representation of phylogeny

##### References

Henderson, C.R. (1976) Biometrics 32 (1) 69:83

Quaas, R. L. and Pollak, E. J. (1980) Journal of Animal Science 51:1277-1287.

Meuwissen, T.H.E and Luo, Z. (1992) Genetic Selection Evolution 24 (4) 305:313

Hadfield, J.D. and Nakagawa, S. (2010) Journal of Evolutionary Biology 23 494-508

##### Examples

```
# NOT RUN {
data(bird.families)
Ainv<-inverseA(bird.families)
# }
```

*Documentation reproduced from package MCMCglmm, version 2.29, License: GPL (>= 2)*