| Title: | Implementation of the Natural and Orthogonal InterAction (NOIA) Model |
|---|---|
| Description: | The NOIA model, as described extensively in Alvarez-Castro & Carlborg (2007), is a framework facilitating the estimation of genetic effects and genotype-to-phenotype maps. This package provides the basic tools to perform linear and multilinear regressions from real populations (provided the phenotype and the genotype of every individuals), 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 presented in Le Rouzic & Alvarez-Castro (2008). |
| Authors: | Arnaud Le Rouzic (2007-2015), Arne B. Gjuvsland (2010), Olivier Ariste (2010) |
| Maintainer: | Arnaud Le Rouzic <[email protected]> |
| License: | GPL-2 |
| Version: | 0.97.3 |
| Built: | 2024-10-31 22:07:21 UTC |
| Source: | https://github.com/lerouzic/noia |
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).
| Package: | noia |
| Type: | Package |
| Version: | 0.94.1 |
| Date: | 2010-04-20 |
| License: | GPL-2 |
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 (where 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
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.
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") mapsset.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
geneticEffects displays the genetic effects (and their standard
errors) from the result of linearRegression. If a new
reference point is provided, a "change of reference" operation is performed
(Alvarez-Castro and Carlborg 2007).
geneticEffects(obj, reference="P1", ref.genotype = NULL)geneticEffects(obj, reference="P1", ref.genotype = NULL)
obj |
An object of class |
reference |
The new reference point. Can
be |
ref.genotype |
The same as |
Variance decomposition and change of reference operation are not possible from the result of a multilinear regression.
Arnaud Le Rouzic
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.
Le Rouzic A, Alvarez-Castro JM. (2008). Estimation of genetic effects and genotype-phenotype maps. Evolutionary Bioinformatics, 4.
linearRegression, multilinearRegression.
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$Loc2)) geneticEffects(linear, "P1")map <- c(0.25, -0.75, -0.75, -0.75, 2.25, 2.25, -0.75, 2.25, 2.25) pop <- simulatePop(map, N=500, sigmaE=0.2, type="F2") # Regressions linear <- linearRegression(phen=pop$phen, gen=cbind(pop$Loc1, pop$Loc2)) geneticEffects(linear, "P1")
The regression aims at estimating genetic effects from a population in which the genotypes and phenotypes are known.
linearRegression(phen, gen=NULL, genZ=NULL, reference="noia", max.level=NULL, max.dom=NULL, fast=FALSE) multilinearRegression(phen, gen=NULL, genZ=NULL, reference="noia", max.level=NULL, max.dom=NULL, fast=FALSE, e.unique=FALSE, start.algo = "linear", start.values=NULL, robust=FALSE, bilinear.steps=1, ...)linearRegression(phen, gen=NULL, genZ=NULL, reference="noia", max.level=NULL, max.dom=NULL, fast=FALSE) multilinearRegression(phen, gen=NULL, genZ=NULL, reference="noia", max.level=NULL, max.dom=NULL, fast=FALSE, e.unique=FALSE, start.algo = "linear", start.values=NULL, robust=FALSE, bilinear.steps=1, ...)
phen |
The vector of individual phenotypes measured in the population. |
gen |
The matrix of individual genotypes in the population, one column per locus. See |
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 |
reference |
The reference point from which the regression is performed. By default, the |
max.level |
Maximum level of interactions. |
max.dom |
Maximum level for dominance effects. Does not have any effect if >= |
fast |
This "fast" algorithm should be used when (i) the number of loci is high (> 8) and (ii) there are uncertainties in the dataset (missing values or Haley-Knott regression). This algorithm computes the regression matrix directly function, i.e. without computing |
e.unique |
Whether the multilinear term is the same for all pairs. |
start.algo |
Algorithm used to compute the starting values. Can be |
start.values |
Vector of starting values. |
robust |
Tries sequentially all starting values algorithms. |
bilinear.steps |
Number of steps. Ignored if |
... |
Extra parameters to the non-linear regression function |
If a gen data set is provided, it will be turned into a genZ. Missing data (unknown genotypes) are considered as loci for which genotypic probabilities are identical to the 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 a key to ensure convergence, and different 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. "subset" estimate all genetic effects from a random subset (50%) of the population, and "bilinear" estimate alternatively marginal and epistatic effects.
linearRegression and multilinearRegression return an object of class "noia.linear" or "noia.multilinear", both having their own print methods: print.noia.linear and print.noia.multilinear.
Arnaud Le Rouzic
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.
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 4.
Zeng ZB, Wang T, Zou W. (2005). Modelling quantitative trait loci and interpretation of models. Genetics 169: 1711-1725.
geneticEffects, GPmap, varianceDecomposition.
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 multilinearset.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
The Genotype-to-Phenotype map is a vector providing the estimate of
the genotypic value for any multi-locus genotype. The estimates may
be computed from linearRegression or
multilinearRegression.
GPmap(obj)GPmap(obj)
obj |
An object of class |
Returns a matrix with two columns: the first one is the estimate of genotypic effects, the second one the standard error of this estimate.
Arnaud Le Rouzic
Le Rouzic A, Alvarez-Castro JM. (2008). Estimation of genetic effects and genotype-phenotype maps. Evolutionary Bioinformatics, 4.
linearRegression, multilinearRegression,
genNames.
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") # Regression linear <- linearRegression(phen=pop$phen, gen=cbind(pop$Loc1, pop$Loc2)) # GP map GPmap(linear)set.seed(123456789) map <- c(0.25, -0.75, -0.75, -0.75, 2.25, 2.25, -0.75, 2.25, 2.25) pop <- simulatePop(map, N=500, sigmaE=0.2, type="F2") # Regression linear <- linearRegression(phen=pop$phen, gen=cbind(pop$Loc1, pop$Loc2)) # GP map GPmap(linear)
Functions for doing a NOIA analysis of a GP map for loci in a population where the loci are in complete linkage equilibrium.
linearGPmapanalysis(gmap, reference="F2", freqmat=NULL, max.level=NULL , S_full=NULL)linearGPmapanalysis(gmap, reference="F2", freqmat=NULL, max.level=NULL , S_full=NULL)
gmap |
Vector of length |
reference |
The reference population in which the analysis is done. By default, the |
freqmat |
For For |
max.level |
Maximum level of interactions. |
S_full |
Boolean argument indicating whether to keep full |
The algebraic framework is described extensively in Alvarez-Castro & Carlborg 2007. When analysing GP maps in ideal populations
we can work directly with the S matrix and do not have to consider the X and Z matrices used in linearRegression.
When it comes to the S_full argument keeping the multilocus S matrix in memory is generally fastest for computing all
genetic effects. However it does not allow for computing only a subset of the effects and also runs out of memory for on a typical desktop machine.
For S_full=NULL in linearGPmapanalysis a full S matrix is used if and max.level=NULL, while single locus S matrices are used otherwise.
linearGPmapanalysis returns an object of class "noia.linear.gpmap" , with its own print method: print.noia.linear.gpmap.
Arne B. Gjuvsland
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.
Cheverud JM, Routman, EJ. (1995). Epistasis and its contribution to genetic variance components. Genetics 139:1455-1461.
Le Rouzic A, Alvarez-Castro JM. (2008). Estimation of genetic effects and genotype-phenotype maps. Evolutionary Bioinformatics 4.
Zeng ZB, Wang T, Zou W. (2005). Modelling quantitative trait loci and interpretation of models. Genetics 169: 1711-1725.
map <- c(0.25, -0.75, -0.75, -0.75, 2.25, 2.25, -0.75, 2.25, 2.25) # Genotype-to-phenotype map analysis linearGP <- linearGPmapanalysis(map, reference="F2") # Linear effects in ideal F2 population linearGPmap <- c(0.25, -0.75, -0.75, -0.75, 2.25, 2.25, -0.75, 2.25, 2.25) # Genotype-to-phenotype map analysis linearGP <- linearGPmapanalysis(map, reference="F2") # Linear effects in ideal F2 population linearGP
This function computes some parameters of interest (mean phenotype, genetic variance, additive variance, and evolutionary change in additive variance) for a combination of allele frequencies, based on a genotype-phenotype map.
marginallocus(gmap, freq=NULL, what="mean", definition=11, mc.cores=1, ...) ## S3 method for class 'noia.marloc' plot(x, xlab=NULL, ylim=NULL, ylab=attr(x, "what"), ...) ## S3 method for class 'noia.marloc' image(x, xlab=NULL, ylab=NULL, zlim=NULL, main=attr(x, "what"), col.max="red", col.min="blue", col.zero="white", n.cols=1000, zeropart=0.01, contour.levels=10, contour.options=list(), ...)marginallocus(gmap, freq=NULL, what="mean", definition=11, mc.cores=1, ...) ## S3 method for class 'noia.marloc' plot(x, xlab=NULL, ylim=NULL, ylab=attr(x, "what"), ...) ## S3 method for class 'noia.marloc' image(x, xlab=NULL, ylab=NULL, zlim=NULL, main=attr(x, "what"), col.max="red", col.min="blue", col.zero="white", n.cols=1000, zeropart=0.01, contour.levels=10, contour.options=list(), ...)
gmap |
Either an object of class |
.
freq |
A vector indicating the loci that should be analysed. See Details. |
what |
A character string among "mean", "varA", "varG", or "dvarA.dt". |
definition |
The number of allele frequencies to try for each locus. |
mc.cores |
If more than 1, the calculation is run on |
x |
An object of class |
col.max, col.min, col.zero
|
Colors standing for the maximal, minimal, and nil values, respectively. Setting |
n.cols |
Number of colors in the gradient. |
zeropart |
Width (relative to the full amplitude) of the region around zero which will be colored as |
contour.levels |
Number of contour lines. Setting this to 0 leads to no contour lines. |
contour.options |
List of additional options to the |
xlab, ylab, ylim, zlim, main
|
|
... |
Additional parameters to internal functions. |
marginallocus computes a population parameter for a series of allele frequencies. The loci under investigation are provided through the freq vector, which need to have as many elements as loci in the system. Values of the freq vector indicate fixed allele frequencies, while NA indicate loci under investigation. For instance, freq=c(NA, 1, NA, 0.5), will investigate the effect of varying loci 1 and 3, while keeping loci 2 and 4 at constant allele frequencies. The population is assumed to be at Hardy-Weinberg frequencies. If freq is not provided, all loci will be investigated.
marginallocus returns an array with as many dimensions as loci under investigation. This array is an object of class "noia.marloc" which can be graphically illustrated through the provided plot (for 1-dimensional data) and image (for 2-dimensional data). Arrays of higher dimensionality cannot be represented graphically.
Arnaud Le Rouzic
map <- c(0.25, -0.75, -0.75, -0.75, 2.25, 2.25, -0.75, 2.25, 2.25) mrg2D <- marginallocus(map) mrg1D <- marginallocus(map, freq=c(NA, 0)) # the second locus is fixed for allele 1 image(mrg2D) plot(mrg1D)map <- c(0.25, -0.75, -0.75, -0.75, 2.25, 2.25, -0.75, 2.25, 2.25) mrg2D <- marginallocus(map) mrg1D <- marginallocus(map, freq=c(NA, 0)) # the second locus is fixed for allele 1 image(mrg2D) plot(mrg1D)
These functions allow a graphic representation of the
result of genetic regressions from linearRegression
and GPmap.
## S3 method for class 'noia.linear' plot(x, loc = 1:x$nloc, effect=TRUE, epistasis = TRUE, ylim=range(GPmap(x)[,1]) + c(-1,1)*max(GPmap(x)[,2]), ...) ## S3 method for class 'noia.gpmap' barplot(height, GPcol = c("indianred", "palegreen", "royalblue"), arrowscol = "purple", stderr = TRUE , main=NA, ylab=NA, ...)## S3 method for class 'noia.linear' plot(x, loc = 1:x$nloc, effect=TRUE, epistasis = TRUE, ylim=range(GPmap(x)[,1]) + c(-1,1)*max(GPmap(x)[,2]), ...) ## S3 method for class 'noia.gpmap' barplot(height, GPcol = c("indianred", "palegreen", "royalblue"), arrowscol = "purple", stderr = TRUE , main=NA, ylab=NA, ...)
x |
An object of class |
loc |
The vector loci to plot (by default, all of them are displayed). |
effect |
Whether genetic effects have to be plotted for each locus. |
epistasis |
Whether pairwise effects have to be plotted. |
height |
An object of class |
GPcol |
Colors for each of the three genotypes. |
arrowscol |
Color of the error bars. |
stderr |
If |
main |
The same as in |
ylab |
The same as in |
ylim |
The same as in |
... |
Olivier Ariste, Arnaud Le Rouzic
Display the output of functions linearRegression,
multilinearRegression and linearGPmapanalysis
## S3 method for class 'noia.linear' print(x, ...) ## S3 method for class 'noia.multilinear' print(x, ...) ## S3 method for class 'noia.common' print(x, ...) ## S3 method for class 'noia.linear.gpmap' print(x, ...)## S3 method for class 'noia.linear' print(x, ...) ## S3 method for class 'noia.multilinear' print(x, ...) ## S3 method for class 'noia.common' print(x, ...) ## S3 method for class 'noia.linear.gpmap' print(x, ...)
x |
An object of class |
... |
No effect for the moment. |
The print method being actually very similar for the linear and
multilinear regressions, both call the common method print.noia.common.
Arnaud Le Rouzic, Arne B. Gjuvsland
Le Rouzic A, Alvarez-Castro JM. (2008). Estimation of genetic effects and genotype-phenotype maps. Evolutionary Bioinformatics, 4.
The simulatePop function takes a Genotype-to-Phenotype map (i.e. a vector
defining the genotypic value of all possible genotypes) and
returns a data frame containing the simulated population.
simulatePop(gmap, N = 100, sigmaE = 1, type = "F2", freqmat=NULL)simulatePop(gmap, N = 100, sigmaE = 1, type = "F2", freqmat=NULL)
gmap |
The Genotype-to-phenotype map: a vector of size |
N |
Number of individuals. |
sigmaE |
Standard deviation of the environmental noise (normally distributed). |
type |
Type of population. |
freqmat |
For For |
The type of population refers to the expected allelic and genotypic frequences:
"F1"First generation of an intercross between two parental populations fixed for alleles A and B respectively; expected genotypic frequencies are: AA: 0, AB: 1, BB: 0.
"F2"Second generation of an intercross between two parental populations fixed for alleles A and B respectively; expected genotypic frequencies are AA: 0.25, AB: 0.5, BB: 0.25.
"Finf"Theoretical population from an infinite number of generations after an intercross between two parental populations fixed for alleles A and B respectively; expected genotypic frequencies are AA: 0.5, AB: 0, BB: 0.5.
"UWR"Theoretical population corresponding to ideal (but experimentally unrealistic) equal genotypic frequencies; expected genotypic frequencies are AA: 0.333, AB: 0.333, BB: 0.333. In such a population, the "UnWeighted Regression model" (UWR) by Cheverud and Routman 1995 provides orthogonal estimates.
"G2A"Population at Hardy-Weinberg frequencies; expected genotypic frequencies are: AA: p*p, AB: 2p(1-p), BB: (1-p)(1-p), the frequency of allele A (p) at locus i being provided by the i-th element of vector freqmat. "G2A" is the name of the statistical model by Zeng et al. (2005) in which genetic effects estimated from such a population are orthogonal.
"noia"Population in which genotypic frequencies are arbitrary; expected genotypic frequencies are: AA: pAA, AB: pAB, BB: pBB, frequences pAA, pAB, and pBB at locus i being provided by the i-th line of matrix freqmat. "noia" is the name of the statistical model by Alvarez-Castro and Carlborg (2007) in which genetic effects estimated from such a population are orthogonal. In all populations, loci are considered as independent and are at linkage equilibrium.
Returns a data frame, in which the first column ($phen) contains the
phenotypes, and the following ones ($Loc1, $loc2, etc) the
genotypes of all individuals.
Arnaud Le Rouzic, Arne B. Gjuvsland
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.
Cheverud JM, Routman, EJ. (1995). Epistasis and its contribution to genetic variance components. Genetics 139:1455-1461.
Le Rouzic A, Alvarez-Castro JM. (2008). Estimation of genetic effects and genotype-phenotype maps. Evolutionary Bioinformatics, 4.
Zeng ZB, Wang T, Zou W. (2005). Modelling quantitative trait loci and interpretation of models. Genetics 169: 1711-1725.
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") str(pop) ## Create a "noia" population with genotype frequencies 1/3,1/3,1/3 for locus 1 ## and 0.2,0.6,0.2 for locus 2 pop = simulatePop(map, N=1000, sigma=1, type='noia', freqmat=matrix(c(1/3,1/3,1/3,0.2,0.6,0.2),nrow=2, byrow=TRUE))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") str(pop) ## Create a "noia" population with genotype frequencies 1/3,1/3,1/3 for locus 1 ## and 0.2,0.6,0.2 for locus 2 pop = simulatePop(map, N=1000, sigma=1, type='noia', freqmat=matrix(c(1/3,1/3,1/3,0.2,0.6,0.2),nrow=2, byrow=TRUE))
Variance decomposition in a classical operation in quantitative genetics (e.g. Fisher 1918, Lynch and Walsh 1998). The genetic variance, i.e. the part of phenotypic variance that can be identify as due to genetic factors, can be decomposed into several orthogonal components (generally, the part due to additive factors Var(A), to dominance factors Var(D), and to genetic interactions Var(I)).
varianceDecomposition(obj) ## S3 method for class 'noia.vardec' print(x, ...)varianceDecomposition(obj) ## S3 method for class 'noia.vardec' print(x, ...)
obj |
An object of class |
x |
An object of class |
... |
No effect for the moment. |
The details of the variance decomposition are provided for all levels of interaction: Var(A) and Var(D) for marginal effects, Var(AA), Var(AD) and Var(DD) for 2nd order interactions, etc.
varianceDecomposition returns a list of vectors. Each element of the list corresponds
to an order of interactions, and the vectors detail the variance
decomposition within each level.
print.noia.vardec prints the previous list in a nice way, and computed the percentage of
genetic variance explained by each variance component.
Arnaud Le Rouzic
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.
Fisher RA. (1918). The correlation between relatives on the supposition of Mendelian inheritance. Thans. Roy. Soc. Edinburgh 52:339-433.
Le Rouzic A, Alvarez-Castro JM. (2008). Estimation of genetic effects and genotype-phenotype maps. Evolutionary Bioinformatics, 4.
Lynch M, Walsh B (1998) Genetics and Analysis of Quantitative Traits. Sunderland, MA; Sinauer Associates.
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") # Regression linear <- linearRegression(phen=pop$phen, gen=cbind(pop$Loc1, pop$Loc2)) # Variance decomposition varianceDecomposition(linear)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") # Regression linear <- linearRegression(phen=pop$phen, gen=cbind(pop$Loc1, pop$Loc2)) # Variance decomposition varianceDecomposition(linear)