IM.search {QTLEMM}

QTL search by IM

Description

Expectation-maximization algorithm for QTL interval mapping to search for possible position of QTL in all chromosomes.

Usage

IM.search(
  marker,
  geno,
  y,
  method = "EM",
  type = "RI",
  D.matrix = NULL,
  ng = 2,
  cM = TRUE,
  speed = 1,
  crit = 10^-5,
  d.eff = FALSE,
  LRT.thre = TRUE,
  simu = 1000,
  alpha = 0.05,
  detect = TRUE,
  QTLdist = 15,
  plot.all = TRUE,
  plot.chr = TRUE,
  console = TRUE
)

Arguments

marker

matrix. A k*2 matrix contains the marker information, where the row dimension 'k' represents the number of markers in the chromosomes. The first column labels the chromosomes where the markers are located, and the second column labels the positions of markers (in morgan (M) or centimorgan (cM)). It's important to note that chromosomes and positions must be sorted in order.

geno

matrix. A n*k matrix contains the genotypes of k markers for n individuals. The marker genotypes of P1 homozygote (MM), heterozygote (Mm), and P2 homozygote (mm) are coded as 2, 1, and 0, respectively, with NA indicating missing values.

y

vector. A vector with n elements contains the phenotype values of individuals.

method

character. When method="EM", it indicates that the interval mapping method by Lander and Botstein (1989) is used in the analysis. Conversely, when method="REG", it indicates that the approximate regression interval mapping method by Haley and Knott (1992) is used in the analysis.

type

character. The population type of the dataset. Includes backcross (type="BC"), advanced intercross population (type="AI"), and recombinant inbred population (type="RI"). The default value is "RI".

D.matrix

matrix. The design matrix of the IM model. If D.matrix=NULL, the design matrix will be constructed using Cockerham’s model: In BC population, it is a 2*1 matrix with values 0.5 and -0.5 for the additive effect; In RI or AI population, it is a 3*2 matrix. The first column consists of 1, 0, and -1 for the additive effect, and the second column consists of 0.5, -0.5, and 0.5 for the dominant effect.

ng

integer. The generation number of the population type. For instance, in a BC1 population where type="BC", ng=1; in an AI F3 population where type="AI", ng=3.

cM

logical. Specify the unit of marker position. If cM=TRUE, it denotes centimorgan; if cM=FALSE, it denotes morgan.

speed

numeric. The walking speed of the QTL search (in cM).

crit

numeric. The convergence criterion of EM algorithm. The E and M steps will iterate until a convergence criterion is met. It must be a value between 0 and 1.

d.eff

logical. Specifies whether the dominant effect will be considered in the parameter estimation for AI or RI population.

LRT.thre

logical or numeric. If set to TRUE, the LRT threshold will be computed based on the Gaussian stochastic process (Kao and Ho 2012). Alternatively, users can input a numerical value as the LRT threshold to evaluate the significance of QTL detection.

simu

integer. Determines the number of simulation samples that will be used to compute the LRT threshold using the Gaussian process. It must be a value between 50 and 10^8.

alpha

numeric. The type I error rate for the LRT threshold.

detect

logical. Determines whether the significant QTL, whose LRT statistic is larger than the LRT threshold, will be displayed in the output dataset or not.

QTLdist

numeric. The minimum distance (in cM) among different linked significant QTL.

plot.all

logical. When set to TRUE, it directs the function to output the profile of LRT statistics for the genome in one figure.

plot.chr

logical. When set to TRUE, it instructs the function to output the profile of LRT statistics for the chromosomes.

console

logical. Determines whether the process of the algorithm will be displayed in the R console or not.

Value

effect

The estimated effects and LRT statistics of all positions.

LRT.threshold

The LRT threshold value is computed for the data using the Gaussian stochastic process (Kuo 2011; Kao and Ho 2012).

detect.QTL

The positions, effects, and LRT statistics of the detected QTL are significant using the obtained LRT threshold value.

Graphical outputs including LOD value and effect of each position.

References

KAO, C.-H. and Z.-B. ZENG 1997 General formulas for obtaining the maximum likelihood estimates and the asymptotic variance-covariance matrix in QTL mapping when using the EM algorithm. Biometrics 53, 653-665. <doi: 10.2307/2533965.>

KAO, C.-H., Z.-B. ZENG and R. D. TEASDALE 1999 Multiple interval mapping for Quantitative Trait Loci. Genetics 152: 1203-1216. <doi: 10.1093/genetics/152.3.1203>

KAO, C.-H. and H.-A. Ho 2012 A score-statistic approach for determining threshold values in QTL mapping. Frontiers in Bioscience. E4, 2670-2682. <doi: 10.2741/e582>

See Also

EM.MIM IM.search2 LRTthre

Examples

# load the example data
load(system.file("extdata", "exampledata.RDATA", package = "QTLEMM"))

# run and result
result <- IM.search(marker, geno, y, type = "RI", ng = 2, speed = 7, crit = 10^-3, LRT.thre = 10)
result$detect.QTL