QTL_effect_main_QxEC {mppR}

Estimation of a model with main and QTL by environmental sensitivity terms

Description

After estimating which parental allelic effects have a significant interaction with the environment (QEI), the function extends the model for the allelic effect with a significant QEI to characterize this interaction in terms of sensitivity to (a) specific environmental covariate(s).

Usage

QTL_effect_main_QxEC(
  mppData,
  trait,
  env_id = NULL,
  ref_env = NULL,
  ref_par = NULL,
  VCOV = "UN",
  QTL = NULL,
  thre_QTL = 2,
  EC,
  Qmain_QEI = NULL,
  maxIter = 100,
  msMaxIter = 100
)

Arguments

mppData

An object of class mppData.

trait

Character vector specifying which traits (environments) should be used.

env_id

Character vector specifying the environment names. By default, E1, ... En

ref_env

Optional Character expression defining the environment that will be used as reference for the parental model. By default, the last environment is set as reference.

ref_par

Optional Character expression defining the parental allele that will be used as reference for the parental model. By default, the parent with the largest MAF is set as reference.

VCOV

VCOV Character expression defining the type of variance covariance structure used. 'CS' for compound symmetry assuming a unique genetic covariance between environments. 'CSE' for cross-specific within environment error term. 'CS_CSE' for both compound symmetry plus cross-specific within environment error term. 'UN' for unstructured environmental variance covariance structure allowing a specific genotypic covariance for each pair of environments. Default = 'UN'

QTL

Object of class QTLlist representing a list of selected marker positions obtained with the function QTL_select() or a vector of character marker positions names. Default = NULL.

thre_QTL

Numerical value specifying the -log10(p-val) threshold for a parental QTL allele to be considered as significant. By default, thre_QTL = 2, which correspond to a p-value of 0.01.

EC

Numeric matrix with environments as row and environmental covariates (EC) as column. The cell i, j of EC specify the value of the jth EC in environment i.

Qmain_QEI

results from QTL_effect_main_QEI

maxIter

maximum number of iterations for the lme optimization algorithm. Default = 100.

msMaxIter

maximum number of iterations for the optimization step inside the lme optimization. Default = 100.

Details

The function first estimate the parental QTL allele main and QTLxE effect using the function QTL_effect_main_QEI. Optionally the output of QTL_effect_main_QEI can be passed through the 'Qmain_QEI' argument. The function consider that a parental QTL allele significantly interacts with the environment if its QTLxE term is significant at the 'thre_QTL' level. Thre_QTL is expressed in terms of -log10(p-val). For example, for p-val = 0.01, thre_QTL = -log10(p-val) = 2. Given this information, the effect of the parental QTL allele with a significant QEI are extended like that \beta_{pj} = EC_j*S_p+l_{p\epsilon} where EC_j represents the EC value in environment j associated with the sensitivity term S_p. The S_{p} determines the rate of change of the parental QTL allelic additive effect given an extra unit of EC. Finally, l_{p\epsilon} is a residual effect. The fitted model becomes:

\underline{y}_{icj} = E_{j} + C_{cj} + \sum_{q=1}^{n_{QTL}} x_{i_{q}p} (\alpha_p + \beta_{pj}) + x_{i_{q}pxE} (\alpha_p + EC_j*S_p+l_{p\epsilon}) + \underline{GE}_{icj} + \underline{e}_{icj}

The estimation is performed using an exact mixed model with function from R package nlme. The significance of S_{p} is assessed using a Wald test.

Value

Return:

List with one data.frame per QTL that contains the following elements:

1. QTL parent allele main effect expressed as deviation with respect to the reference parent

2. QTL parent allele effect in environment j expressed as deviation with respect to the reference parent

3. Significance of the parent main effect expressed as the -log10(p-val)

4. Significance of the parent QTLxE effect expressed as the -log10(p-val)

Author(s)

Vincent Garin

References

Pinheiro J, Bates D, DebRoy S, Sarkar D, R Core Team (2021). nlme: Linear and Nonlinear Mixed Effects Models_. R package version 3.1-152, <URL: https://CRAN.R-project.org/package=nlme>.

See Also

QTL_effect_main_QEI

Examples

## Not run: 

data(mppData_GE)

Qpos <- c("PZE.105068880", "PZE.106098900")

EC <- matrix(c(180, 310, 240, 280), 4, 1)
rownames(EC) <- c('CIAM', 'TUM', 'INRA', 'KWS')
colnames(EC) <- 'cum_rain'

Qeff <- QTL_effect_main_QxEC(mppData = mppData_GE,
                         trait = c('DMY_CIAM', 'DMY_TUM', 'DMY_INRA_P', 'DMY_KWS'),
                         env_id = c('CIAM', 'TUM', 'INRA', 'KWS'),
                         QTL = Qpos, EC = EC)

Qeff


## End(Not run)