# Estimate R square of individual QTLs and QTL interactions

### Description

Estimates the R square (phenotypic contribution) for individual QTLs and their significant interactions for each trait from cross and peak objects.

### Usage

1 |

### Arguments

`cross` |
An object of class |

`peak` |
An object of class |

`th` |
A numeric vector of length 1 with value between 0 and 1. The R square significance threshold to keep the R square values. |

`round` |
An optional integer indicating the precision to be used for the R square value and it significance. The function 'round' is used for R square value |

### Details

Estimates the proportion of the phenotypic variation explained by the segregation of an individual QTL or significant QTL interactions (also called R square). Compute R square i.e. to compare the phenotypic variation explained by the presence of a genetic determinant (an individual QTL or a QTL's interaction) with the total phenotypic variation. Here we use an AnOVa with a linear model including all possible epistatic interactions.

Let a trait be affected by 3 QTLs localised at 3 markers **M1**, **M2** and **M3** respectively.
The AnOVa is computed for the linear model:

*M1 + M2 + M3 + M1:M2 + M1:M3 + M2:M3 + M1:M2:M3*

The R square for each genotypic group is the comparison of the variance due to the between- groups variability (called Mean Square Effect, or MSeffect) with the within- group variability (called Mean Square Error, or Mserror).

The significance of an epistatic interaction is the significance of the group effect of each interaction computed by the AnOVa. If one wants to store the results within a QTL database, it might be useful to compute all genetic determinants by setting `th=1`

and then to extract the significant results by SQL queries.

### Value

Return an object of class `rsq`

which is a simple data frame with columns:

`qtl` |
The name of the genetic determinant. If the genetic determinant is an individual QTL, the name is formated as |

`rsq` |
The R square value (set to |

`pF` |
The significance (set to |

### Author(s)

Hamid A. Khalili

### See Also

`read.cross`

, `define.peak`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
data(seed10);
# Genotype probabilities
## Not run: seed10 <- calc.genoprob( cross=seed10, step=2, off.end=0, error.prob=0,
map.function='kosambi', stepwidth='fixed');
seed10 <- sim.geno( cross=seed10, step=2, off.end=0, error.prob=0,
map.function='kosambi', stepwidth='fixed');
## End(Not run)
# Genome scan and QTL detection
out.em <- scanone( seed10, pheno.col=1:50, model='normal', method='hk');
out.peak <- define.peak(out.em, 'all');
# R square computing
out.rsq <- calc.Rsq(seed10,out.peak);
# R square computing without taking account of any significance
out.rsq <- calc.Rsq(seed10,out.peak,th=1);
``` |