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).
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
)Return:
List with one data.frame per QTL that contains the following
elements:
QTL parent allele main effect expressed as deviation with respect to the reference parent
QTL parent allele effect in environment j expressed as deviation with respect to the reference parent
Significance of the parent main effect expressed as the -log10(p-val)
Significance of the parent QTLxE effect expressed as the -log10(p-val)
An object of class mppData.
Character vector specifying which traits (environments) should be used.
Character vector specifying the environment names.
By default, E1, ... En
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.
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 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'
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.
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.
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.
results from QTL_effect_main_QEI
maximum number of iterations for the lme optimization algorithm. Default = 100.
maximum number of iterations for the optimization step inside the lme optimization. Default = 100.
Vincent Garin
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.
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>.
QTL_effect_main_QEI
if (FALSE) {
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
}
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