Genetic regression {noia}R Documentation

Linear and Multilinear Genetic Regression

Description

The regression aims at estimating geneticEffects from a population (genotypes and phenotypes).

Usage

linearRegression(phen, gen = NULL, genZ = NULL, 
        reference = "noia", max.level = NULL, max.dom = NULL)
multilinearRegression(phen, gen = NULL, reference = "noia", 
        genZ = NULL, max.level = NULL, max.dom = NULL, e.unique=FALSE, 
        start.algo="linear", start.values=NULL, ...)

Arguments

phen The vector of individual phenotypes measured in the population.
gen The matrix of individual genotypes in the population, one column per locus. See genNames for the genotype coding. Not necessary if GenZ is provided.
genZ The matrix of individual genotypic probabilities in the population, 3 columns per locus, corresponding of the probability of each of the 3 genotypes (the sum must be 1). Not necessary if gen is provided.
reference The reference point from which the regression is performed. By default, the "noia" reference point is used, since it provides a fairly good orthogonality. Other possibilities are "G2A", "F2", "F1", "Finf", "UWR", "P1" and "P2".
max.level Maximum level of interactions.
max.dom Maximum level for dominance effects. Does not have any effect if >= max.level. In the multilinearRegressions, the maximum level for dominance effects cannot be > 1.
e.unique Whether the multilinear term is the same for all pairs.
start.algo Algorithm used to compute the starting values. Can be "linear" or "multilinear".
start.values Vector of starting values.
... Extra parameters to the non-linear regression function nls.

Details

If a gen data set is provided, it will be turned into a genZ through the gen2genZ function. Missing data (unknown genotypes) will be turned into genotypic probabilities identical to genotypic frequencies in the population.

The algebraic framework is described extensively in Alvarez-Castro & Carlborg 2007. The default reference point ("noia") provides an orthogonal decomposition of genetic effects in the 1-locus case, whatever the genotypic frequencies. It remains a good approximation of orthogonality in the multi-locus case if linkage disequilibrium is small. Other optional reference points are those of the "G2A" model (Zeng et al. 2005), and the unweighted regression model "UWR" (Cheverud & Routman, 1995). Several key populations can be taken as reference as well: "F2", "F1", "Finf" (F infinity), and the two "parental" homozygous populations "P1" and "P2".

The multilinear model for genetic interactions is an alternative way to model epistatic interactions between at least two loci (see Hansen & Wagner 2001). The computation of multilinear estimates requires a non-linear regression step that relies on the nls function. Providing good starting values for the non-linear regression is an important step, and two different (and complementary) algorithms are provided, that can be specified by the "start.algo" option. "linear" performs a linear regression and approximates the genetic effects from it, while "multilinear" performs a simpler multilinear regression (without dominance) to initialize the genetic effects. See startingValues for more information.

Value

Returns an object of class "noia.linear" or "noia.multilinear", both having their own print methods: print.noia.linear and print.noia.multilinear.

Author(s)

Arnaud Le Rouzic <a.p.s.lerouzic@bio.uio.no>

References

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, in press.

Cheverud JM, Routman, EJ. (1995). Epistasis and its contribution to genetic variance components. Genetics 139:1455-1461.

Hansen TF, Wagner G. (2001) Modeling genetic architecture: A multilinear theory of gene interactions. Theoretical Population Biology 59:61-86.

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

Zeng ZB, Wang T, Zou W. (2005). Modelling quantitative trait loci and interpretation of models. Genetics 169: 1711-1725.

See Also

geneticEffects, GPmap, varianceDecomposition.

Examples

set.seed(123456789)

map <- c(0.25, -0.75, -0.75, -0.75, 2.25, 2.25, -0.75, 2.25, 2.25)
pop <- simulatePop(map, N=500, sigmaE=0.2, type="F2")

# Regressions

linear <- linearRegression(phen=pop$phen, gen=cbind(pop$Loc1, pop$Loc2))

multilinear <- multilinearRegression(phen=pop$phen, 
        gen=cbind(pop$Loc1, pop$Loc2))

# Linear effects, associated variances and stderr
linear

# Multilinear effects
multilinear

[Package noia version 0.91 Index]