The NOIA model, as described extensively in Alvarez-Castro & Carlborg (2007), is a framework facilitating the estimation of geneticEffects and genotype-to-phenotype maps. This package provides the basic tools to perform linear and multilinear regressions from real populations, analyse pure genotype-to-phenotype (GP) maps in ideal populations, estimating the genetic effects from different reference points, the genotypic values, and the decomposition of genetic variances in a multi-locus, 2 alleles system. This package is extensively described in Le Rouzic & Alvarez-Castro (2008).

*Regression data set*: The user must provide (i) The vector of
phenotypes of all individuals measured in the population, and (ii) The
matrix of the genotypes. There are two input formats for the genotype,
see ‘linearRegression’.

*Regression functions*: ‘linearRegression’ and
‘multilinearRegression’.

*GP map data set*: The user must provide (i) The 3^L (where L
is the number of loci) vector of genotypic values (*G* in
Alvarez-Castro & Carlborg (2007)) (ii) Allele or genotype
frequencies in the reference population.

*GP map analysis function*: ‘linearGPmapanalysis’.

*Change of reference*: ‘geneticEffects’.

*Genotype-to-phenotype map*: ‘GPmap’.

*Decomposition of genetic variance*:
‘varianceDecomposition’.

Arnaud Le Rouzic, Arne B. Gjuvsland

Maintainer: Arnaud Le Rouzic arnaud.le-rouzic@universite-paris-saclay.fr

Alvarez-Castro JM, Carlborg O. (2007). A unified model for functional and statistical epistasis and its application in quantitative trait loci analysis. Genetics 176(2):1151-1167.

Alvarez-Castro JM, Le Rouzic A, Carlborg O. (2008). How to perform meaningful estimates of genetic effects. PLoS Genetics 4(5):e1000062.

Le Rouzic A, Alvarez-Castro JM. (2008). Estimation of genetic effects and genotype-phenotype maps. Evolutionary Bioinformatics 4.

Examples:

```
set.seed(123456789)
map <- c(0.25, -0.75, -0.75, -0.75, 2.25, 2.25, -0.75, 2.25, 2.25)
names(map) <- genNames(2)
pop <- simulatePop(map, N=500, sigmaE=0.2, type="F2")
# Regressions
linear <- linearRegression(phen=pop$phen, gen=pop[2:3])
multilinear <- multilinearRegression(phen=pop$phen, gen=cbind(pop$Loc1,
pop$Loc2))
# Linear effects, associated variances and stderr
linear
# Multilinear effects
multilinear
# Genotype-to-phenotype map analysis
linearGP <- linearGPmapanalysis(map, reference="F2")
# Linear effects in ideal F2 population
linearGP
# Change of reference: geneticEffects in the "11" genotype (parental 1)
geneticEffects(linear, ref.genotype="P1")
# Variance decomposition
varianceDecomposition(linear)
varianceDecomposition(linearGP)
# GP maps
maps <- cbind(map, GPmap(linear)[,1], GPmap(multilinear)[,1])
colnames(maps) <- c("Actual", "Linear", "Multilinear")
maps
```