Package {JM4QTN}

Joint Mapping for QTN

Description

The "JM4QTN" package is based on composite interval mapping and regression analysis to do association analysis and linkage analysis for multiple-line cross population and multiple traits. The package can also identify pleiotropic or linked QTL.

Details

Author(s)

JunhuLi,GuoliangLi,HeliChen,KunCheng,WenxinLiu

Maintainer: JunhuiLi<junhuili@cau.edu.cn>

References

Junhui Li, Haixiao Hu, Yujie Meng, Kun Cheng, Guoliang Li, Wenxin Liu, and Shaojiang Chen.(2016)Pleiotropic QTL detection for stalk traits in maize and related R package programming. Journal of China Agricultural University. DOI 10.11841/j.issn.1007-4333.2016.06.00(in chinese)

Data about genetic map

Description

A data frame with 1722 observations on the following 3 variables, where the first column is marker name, the second column is chromosome numeric ID and the last column is marker genetic distance position

Usage

data("GeneticMap")

Format

A data frame with 1722 observations on the following 3 variables.

marker

a vector for marker name

chr

a numeric vector for chromosome id

pos

a numeric vector for marker genetic distance position

Details

The name of marker must be the same with marker's name of data in GenoData, and the chromosome ID and genetic distance position are numeric, otherwise an error will occur.

References

Hu, H., Meng, Y., Wang, H., Liu, H., and Chen, S. (2012). Identifying quantitative trait loci and determining closely related, stalk traits for rind penetrometer resistance in a high-oil maize, population. Theoretical and Applied Genetics, 124(8), 1439-1447.

Hu, H., Liu, W., Fu, Z., Homann, L., Technow, F., and Wang, H., et al. (2013). Qtl mapping of stalk bending strength in a recombinant inbred line maize population. Theoretical and Applied Genetics, 126(9), 2257-66.

Examples

data(GeneticMap)

Data about molecular markers genotype

Description

A data frame with 647 individual observations on the following 1722 variables, where 2, 1 and 0 stands for different markers genotype AA AB and BB, NA for missing marker genotype

Usage

data("GenoData")

Format

A data frame with 647 individual observations on the following 1722 marker genotype variables

Details

Missing markers are subsitituted only by NA, otherwise an error will occur.

References

Hu, H., Meng, Y., Wang, H., Liu, H., and Chen, S. (2012). Identifying quantitative trait loci and determining closely related, stalk traits for rind penetrometer resistance in a high-oil maize, population. Theoretical and Applied Genetics, 124(8), 1439-1447.

Hu, H., Liu, W., Fu, Z., Homann, L., Technow, F., and Wang, H., et al. (2013). Qtl mapping of stalk bending strength in a recombinant inbred line maize population. Theoretical and Applied Genetics, 126(9), 2257-66.

Examples

data(GenoData)

Data about information of molecular markers chromosome id, genetic distance position and genotype with estimated missing markers

Description

A data frame with 647 individual observations, chromosome id and genetic distance position on the following 1722 molecular maker variables

Usage

data("GenoData_EST")

Format

A data frame with 649 observations on the following 1722 variables

A data frame with 649 observations on the following 1722 maker variables, the rows 'chr' and 'pos' is the chromosome id and genetic distance position of markers, other rows are the marker genotype on 647 individuals, where 0 and 2 stands for genotype AA and BB respectivly, decimal is missing marker conditional probability genotype.

Details

This data frame is combined from geneticMap and genotype data with estimated missing markers, which can be calculated by function calGenoProb(GeneticMap, GenoData, steps=0, croType, Gn)

References

Hu, H., Meng, Y., Wang, H., Liu, H., and Chen, S. (2012). Identifying quantitative trait loci and determining closely related, stalk traits for rind penetrometer resistance in a high-oil maize, population. Theoretical and Applied Genetics, 124(8), 1439-1447.

Hu, H., Liu, W., Fu, Z., Homann, L., Technow, F., and Wang, H., et al. (2013). Qtl mapping of stalk bending strength in a recombinant inbred line maize population. Theoretical and Applied Genetics, 126(9), 2257-66.

Examples

data(GenoData_EST)

Data about information of molecular markers chromosome id, genetic distance position and estimated missing markers genotype with steps = 2

Description

A data frame with 647 individual observations, chromosome id and genetic distance position on the following 2431 molecular maker variables

Usage

data("GenoData_S2")

Format

A data frame with 649 observations on the following 2431 variables

A data frame with 649 observations on the following 2431 variables, the rows 'chr' and 'pos' is the chromosome id and genetic distance position of markers, other rows are the marker genotype on 647 individuals, where 0 and 2 stands for genotype AA and BB respectivly, decimal is marker conditional probability genotype with steps = 2.

Details

This data frame is combined from geneticMap and genotype data with estimated missing markers, which can be calculated by function calGenoProb(GeneticMap, GenoData, steps=2, croType, Gn)

References

Hu, H., Meng, Y., Wang, H., Liu, H., and Chen, S. (2012). Identifying quantitative trait loci and determining closely related, stalk traits for rind penetrometer resistance in a high-oil maize, population. Theoretical and Applied Genetics, 124(8), 1439-1447.

Hu, H., Liu, W., Fu, Z., Homann, L., Technow, F., and Wang, H., et al. (2013). Qtl mapping of stalk bending strength in a recombinant inbred line maize population. Theoretical and Applied Genetics, 126(9), 2257-66.

Examples

data(GenoData_S2)

Data about all phenotype

Description

A data frame with 647 observations on the following 10 variables, the phenotype value is calculated by best linear unbias estimates.

Usage

data("PhenoData")

Format

A data frame with 647 observations on the following 13 variables.

Indi

The ID of individuals, which is a factor with levels of Pop1 with 131 individuals, Pop2 with 120 individuals, Pop3 with 200 individuals and Pop4 with 200 individuals

Popu

a factor with levels Pop1 Pop2 Pop3 Pop4 for multiple-line cross population

Ma

a factor with levels A D for parent 1

Pa

a factor with levels B C E F for parent 2

newEC1

a numeric vector for trait newEC1

newEC2

a numeric vector for trait newEC2

newEC3

a numeric vector for trait newEC3

BM1

a numeric vector for trait BM1

BM2

a numeric vector for trait BM2

BM3

a numeric vector for trait BM3

predPH1

a numeric vector for trait predPH1

predPH2

a numeric vector for trait predPH2

predPH3

a numeric vector for trait predPH3

Details

Popu is the levels of multiple cross populations with different parent crosses, if it is filled with several levels, then linkage mapping or association mapping analysis is done for multiple cross populations, otherwise just for only one population

References

Hu, H., Meng, Y., Wang, H., Liu, H., and Chen, S. (2012). Identifying quantitative trait loci and determining closely related, stalk traits for rind penetrometer resistance in a high-oil maize, population. Theoretical and Applied Genetics, 124(8), 1439-1447.

Hu, H., Liu, W., Fu, Z., Homann, L., Technow, F., and Wang, H., et al. (2013). Qtl mapping of stalk bending strength in a recombinant inbred line maize population. Theoretical and Applied Genetics, 126(9), 2257-66.

Examples

data(PhenoData)

Expected Allele Genotype Distribution Calculator

Description

Calculates expected allele genotype distribution probabilities for different marker types and cross types in genetic mapping studies. This function implements sophisticated algorithms to compute genotype probabilities based on flanking marker information and population structure.

Usage

expected_genotype_dist(marType, croType, Gn = 2, x, y = 0)

Arguments

Details

This function calculates expected genotype probabilities using different approaches:

Marker Type Classification:

• Double flanking markers ("22", "21", "20", etc.): Both left and right flanking markers are observed, providing maximum information

• Single right flanking marker ("N2", "N1", "N0"): Only the right flanking marker is observed

• Single left flanking marker ("2N", "1N", "0N"): Only the left flanking marker is observed

Calculation Methods by Cross Type:

• Fn populations: Uses genotype_freq for complex calculations involving multiple genotype classes

• F2, DH, RIL: Uses analytical formulas based on classical genetics

• BCP1, BCP2: Uses genotype_freq with specific genotype indices

Mathematical Framework: The function uses different probability calculations depending on the available information:

• When both flanking markers are observed, it uses conditional probabilities

• When only one flanking marker is observed, it uses marginal probabilities

• The calculations incorporate recombination fractions and population-specific parameters

Genotype Coding: The marker types use a coding system where:

• 2: Homozygous for alternative allele

• 1: Heterozygous

• 0: Homozygous for reference allele

• N: Missing or unknown genotype

Value

A numeric value representing the expected probability of the specified genotype. The result is typically between -1 and 1, where positive values indicate higher probability of the target genotype.

References

Haldane, J.B.S. (1919). The combination of linkage values and the calculation of distances between the loci of linked factors. Journal of Genetics, 8(3), 299-309.

See Also

genotype_freq for genotype frequency calculations, genotype_prob for missing genotype imputation

Examples

# Calculate probability for RIL population
prob_ril <- expected_genotype_dist("00", "RIL", Gn = 2, x = 0.1, y = 0.2)

# Example with different recombination fractions
prob_low_rec <- expected_genotype_dist("22", "F2", Gn = 2, x = 0.05, y = 0.05)
prob_high_rec <- expected_genotype_dist("22", "F2", Gn = 2, x = 0.3, y = 0.4)

Genotype Frequency Calculator for Genetic Populations

Description

Calculates genotype frequencies for different cross types and generations in genetic mapping studies. This function implements complex recurrence relations to compute genotype frequencies in various genetic populations including Fn, backcross, and advanced generation populations.

Usage

genotype_freq(
  cross_type,
  generation = 2,
  genotype_index,
  recomb_aq,
  recomb_qb = 0
)

Arguments

Details

This function calculates genotype frequencies using sophisticated mathematical models:

For Fn Populations (y > 0):

• Handles 20 different genotype classes with complex recurrence relations

• Accounts for recombination between three loci (A, Q, B)

• Uses the relationship z = x + y - 2xy for flanking marker recombination

• Implements generation-by-generation frequency calculations

For BCP1 Populations:

• Handles 8 genotype classes

• Backcross to the first parent (AAQQBB)

• Specific recurrence relations for each genotype class

For BCP2 Populations:

• Handles 8 genotype classes

• Backcross to the second parent (aaqqbb)

• Different initial conditions and recurrence relations

For F2 Populations (y = 0):

• Handles 9 genotype classes

• Simplified two-locus model

• Standard F2 generation frequencies

Mathematical Foundation: The function uses recurrence relations to calculate genotype frequencies across generations. For each generation, the frequency of each genotype class is computed based on the frequencies in the previous generation and the recombination fractions between loci.

Value

A numeric value representing the frequency of the specified genotype in the given generation. The result is always between 0 and 1.

References

Haldane, J.B.S. (1919). The combination of linkage values and the calculation of distances between the loci of linked factors. Journal of Genetics, 8(3), 299-309.

See Also

expected_genotype_dist for expected allele genotype distribution calculations

Examples

# Calculate frequency for F2 generation, genotype 1, with recombination fraction 0.1
freq_f2 <- genotype_freq("Fn", generation = 2, genotype_index = 1, recomb_aq = 0.1, recomb_qb = 0)

# Calculate frequency for BCP1 generation, genotype 5, with recombination fractions
freq_bcp1 <- genotype_freq(
  "BCP1", generation = 3, genotype_index = 5, recomb_aq = 0.15, recomb_qb = 0.25
)

# Calculate frequency for Fn generation, genotype 10, with recombination fractions
freq_fn <- genotype_freq(
  "Fn", generation = 4, genotype_index = 10, recomb_aq = 0.2, recomb_qb = 0.3
)

# Calculate frequency for BCP2 generation, genotype 3
freq_bcp2 <- genotype_freq(
  "BCP2", generation = 2, genotype_index = 3, recomb_aq = 0.1, recomb_qb = 0.2
)

# Example with different generation numbers
freq_gen3 <- genotype_freq("Fn", generation = 3, genotype_index = 1, recomb_aq = 0.1, recomb_qb = 0)
freq_gen5 <- genotype_freq("Fn", generation = 5, genotype_index = 1, recomb_aq = 0.1, recomb_qb = 0)

Calculate Genotype Probabilities and Impute Missing Data

Description

Calculates genotype probabilities and imputes missing genotype data for genetic mapping studies. Supports both Association Mapping (AM) and Linkage Mapping (LM) methods with comprehensive missing data handling and virtual marker creation capabilities.

Usage

genotype_prob(GeneticMap, GenoData, method, croType = NULL, steps = 0, Gn = 2)

Arguments

Details

This function provides comprehensive genotype data processing for genetic mapping:

Association Mapping (AM):

• Simply combines genetic map with genotype data

• Converts missing values to code 9

• No imputation performed

Linkage Mapping (LM):

• Validates genotype codes based on cross type expectations

• Imputes missing genotypes using flanking marker information

• Creates virtual markers at specified intervals when steps > 0

• Uses Haldane mapping function for recombination calculations

• Applies cross-type specific genotype probability calculations

Cross Type Genotype Expectations:

• RIL/DH: Only codes 0 and 2 allowed

• F2: Codes 0, 1, and 2 allowed

• BCP1/BCP2: Codes 0, 1, and 2 with specific constraints

• Fn: Codes 0, 1, and 2 for advanced generations

Virtual Marker Creation: When steps > 0, virtual markers are created at regular intervals between existing markers to improve mapping resolution and handle large gaps in the genetic map.

Value

A data frame containing the processed genotype data with genetic map information and calculated genotype probabilities. The structure depends on the method:

• AM method: Original data combined with genetic map

• LM method: Imputed genotype data with probabilities and optional virtual markers

References

Haldane, J.B.S. (1919). The combination of linkage values and the calculation of distances between the loci of linked factors. Journal of Genetics, 8(3), 299-309.

See Also

haldane_map for recombination fraction calculations, expected_genotype_dist for expected genotype probabilities

Examples

# Example genetic map
genetic_map <- data.frame(
  marker = c("M1", "M2", "M3", "M4", "M5"),
  chr = c(1, 1, 1, 1, 1),
  pos = c(0, 10, 25, 40, 50)
)

# Example genotype data with missing values
geno_data <- matrix(
  c(2, 0, NA, 1, 2,
    1, 0, 2, NA, 0,
    2, 1, 0, 2, 1,
    0, NA, 1, 0, 2),
  nrow = 4, ncol = 5,
  dimnames = list(c("Ind1", "Ind2", "Ind3", "Ind4"), 
                  c("M1", "M2", "M3", "M4", "M5"))
)

# Association mapping (no imputation)
result_am <- genotype_prob(genetic_map, geno_data, method = "AM")
result_am

# Linkage mapping with virtual marker creation
result_lm_vm <- genotype_prob(genetic_map, geno_data, method = "LM", 
                           croType = "F2", steps = 5)
result_lm_vm

Haldane Mapping Function

Description

Converts genetic distance in Morgan units to recombination fraction using the Haldane mapping function. This function implements the Haldane mapping function which assumes no interference between crossovers.

Usage

haldane_map(x)

Arguments

Details

The Haldane mapping function is defined as:

r = \frac{1}{2}(1 - e^{-2x})

where x is the genetic distance in Morgan units and r is the recombination fraction.

This function assumes no interference between crossovers, meaning that the occurrence of one crossover does not affect the probability of other crossovers occurring nearby.

Value

A numeric value representing the recombination fraction (r) between 0 and 0.5.

References

Haldane, J.B.S. (1919). The combination of linkage values and the calculation of distances between the loci of linked factors. Journal of Genetics, 8(3), 299-309.

See Also

genotype_prob for genotype probability calculations

Examples

# Convert 0.1 Morgan (10 cM) to recombination fraction
haldane_map(0.1)

# Convert 0.5 Morgan (50 cM) to recombination fraction  
haldane_map(0.5)

# Convert 1.0 Morgan (100 cM) to recombination fraction
haldane_map(1.0)

Joint Mapping Analysis for Multiple Traits

Description

Performs comprehensive joint mapping analysis for multiple traits using either Association Mapping (AM) or Linkage Mapping (LM) methods to identify QTL affecting multiple traits simultaneously. This function implements sophisticated statistical methods for multivariate QTL analysis with comprehensive cofactor selection and significance testing.

Usage

joint_map(formula, data, skeleton, include, cut_off_list)

Arguments

Value

A list containing pvalue and LOD for each term in the formula:

• pvalue: P-value for each term

• lod: LOD score for each term

References

Jiang, C. and Zeng, Z.B. (1995). Multiple trait analysis of genetic mapping for quantitative trait loci. Genetics, 140(3), 1111-1127.

See Also

permutation_test for permutation thresholds, genotype_prob for genotype probability calculations

Examples

# Example phenotype data
set.seed(1)
pheno_data <- data.frame(
  Trait1 = rnorm(100, mean = 100, sd = 15),
  Trait2 = rnorm(100, mean = 50, sd = 8),
  Popu = rep(c("Pop1", "Pop2"), each = 50)
)

# Example genotype data
geno_data <- matrix(sample(c(0,1,2), 100*50, replace = TRUE),
                    nrow = 100, ncol = 50)
colnames(geno_data) <- paste0("M", 1:50)

data1 <- cbind(pheno_data,geno_data) 

data1$Popu <- as.factor(data1$Popu)

terms <- c("Popu", paste0(colnames(geno_data),":Popu"))
formula1 <- reformulate(terms, response = "Trait1")

cut_off_list <- permutation_test(formula1, data1, n=10, alpha = 0.1, include="Popu")

skeleton <- skeletion_build(
  formula1, data1, strategy = "bidirection", metric = "SBC",
  cut_off_list = cut_off_list, include="Popu"
)

results <- joint_map(formula1, data1, skeleton, include = "Popu", cut_off_list = cut_off_list)

print(results)

Permutation Test for Stepwise Regression

Description

Performs permutation tests for stepwise regression to determine empirical significance thresholds for QTL detection using stepwise regression. This function implements a comprehensive permutation testing framework for stepwise regression.

Usage

permutation_test(
  formula,
  data,
  n = 1000,
  alpha = 0.1,
  include = NULL,
  strategy = "bidirection",
  metric = "SBC",
  type = "linear",
  verbose = FALSE
)

Arguments

Details

This function implements a comprehensive permutation testing framework.

Output Interpretation:

• P-values: Empirical significance thresholds for p-value

• LOD scores: Empirical significance thresholds for LOD score

Value

A list containing the empirical significance thresholds for p-value and LOD score with:

• cut_off: A vector containing the empirical significance thresholds for p-value and LOD score

• pvalue: A vector containing the p-values for each permutation

• lod: A vector containing the LOD scores for each permutation

Examples

# Example phenotype data
set.seed(1)
pheno_data <- data.frame(
  Trait1 = rnorm(100, mean = 100, sd = 15),
  Trait2 = rnorm(100, mean = 50, sd = 8),
  Popu = rep(c("Pop1", "Pop2"), each = 50)
)

# Example genotype data
geno_data <- matrix(sample(c(0,1,2), 100*50, replace = TRUE), 
                    nrow = 100, ncol = 50)
colnames(geno_data) <- paste0("M", 1:50)

data1 <- cbind(pheno_data,geno_data)

data1$Popu <- as.factor(data1$Popu)

terms <- c("Popu", paste0(colnames(geno_data), ":Popu"))
formula1 <- reformulate(terms, response = "Trait1")

cut_off_list <- permutation_test(formula1, data1, n = 10, alpha = 0.1)

formula2 <- reformulate(terms, response = "cbind(Trait1,Trait2)")

cut_off_list <- permutation_test(formula2, data1, n = 10, alpha = 0.1)

Statistical Analysis of Phenotype Data

Description

Performs comprehensive statistical analysis on phenotype data including normality tests, analysis of variance (ANOVA), and least squares means calculations for genetic studies.

Usage

pheno_stats(phenoData, defineForm = NULL, effNotation = "G")

Arguments

Details

This function performs a comprehensive statistical analysis pipeline:

1. Normality Test: Uses Shapiro-Wilk test to assess normality of each trait

2. Model Selection: Automatically generates appropriate statistical models based on data structure

3. ANOVA: Performs analysis of variance to test significance of effects

4. Least Squares Means: Calculates adjusted means for genotypes

Automatic Model Generation: The function automatically generates appropriate formulas based on the experimental design:

• Multiple environments and blocks: trait ~ E + G + E:G + B%in%E

• Multiple environments only: trait ~ E*G

• Custom formulas: User-defined formulas when defineForm is provided

Data Requirements: The phenotype data must have the following structure:

• Column 1: Environment (E) - factor variable

• Column 2: Block (B) - factor variable

• Column 3: Repetition (R) - factor variable

• Column 4: Genotype (G) - factor variable

• Columns 5+: Trait measurements - numeric variables

Value

A list containing comprehensive statistical analysis results for each trait:

References

Shapiro, S.S. and Wilk, M.B. (1965). An analysis of variance test for normality. Biometrika, 52(3-4), 591-611.

See Also

joint_map for joint mapping analysis

Examples

# Example with multiple environments and blocks
pheno_data <- data.frame(
  E = rep(c("Env1", "Env2", "Env3"), each = 60),
  B = rep(c("Block1", "Block2"), each = 30, times = 3),
  R = rep(1:5, 36),
  G = rep(1:12, 15),
  Height = rnorm(180, 175, 8),
  Weight = rnorm(180, 75, 12)
)

# Perform statistical analysis with default formulas
results <- pheno_stats(pheno_data)

# View normality test results
results$Height$normality_test

# View ANOVA results
results$Height$ANOVA

# View least squares means
results$Height$lsmeans

# Example with custom formulas
custom_formulas <- c(
  "Height ~ E + G + E:G + B%in%E",
  "Weight ~ E + G + E:G"
)
results_custom <- pheno_stats(pheno_data, defineForm = custom_formulas)

Fit the stepwise “skeleton” model for joint mapping

Description

Runs StepReg::stepwise() with entry/stay levels set from a permutation p-value threshold, and returns the selected best linear model. The result is typically passed to joint_map() as the skeleton argument.

Usage

skeletion_build(
  formula,
  data,
  type = "linear",
  strategy = "bidirection",
  metric = "SL",
  include = NULL,
  cut_off_list
)

skeleton_build(
  formula,
  data,
  type = "linear",
  strategy = "bidirection",
  metric = "SL",
  include = NULL,
  cut_off_list
)

Arguments

Value

The best model object for the chosen strategy and metric (an element of the StepReg::stepwise() result, typically with a call and call$formula).

See Also

joint_map, permutation_test