Quantitative Genetics, Homework #2, Question #3

Professor Z. Wu, BCB 504

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This is an attmept to answer Dr Wu's homework # 2 question.

N = 30  # Size of each line
lineN = 100  # Number of lines
Genes0 = array(NA, dim = c(lineN, 2 * N))
# Matrix to store alleles and genotypes (two adjacent alleles form a
# genotype).  Each row represent a line.

# Initialize Genes for population 0
for (i in 1:lineN) {
    Genes0[i, ] = sample(x = c(0:1), size = 10, replace = T, prob = c(0.3, 0.7))
    # Randomly form genotypes by sample function with Pr=(0.3,0.7)
}
generationN = 300
ParentGenes = Genes0
AlleleFreq = array(NA, dim = c(generationN, 2))
GeneFreq = array(NA, dim = c(generationN, 3))
for (g in 1:generationN) {
    ChildGenes = array(NA, dim = c(lineN, 2 * N))
    for (i in 1:lineN) {
        ChildGenes[i, ] = sample(ParentGenes[i, ], replace = T)  # Randam sampling with replacement <=> simple inbreeding 
    }
    ParentGenes = ChildGenes
    AlleleFreq[g, ] = table(ChildGenes)/(lineN * 2 * N)
    # Convert allele to genotypes: AA <=> 2 Aa / aA <=> 1 aa <=> 0.
    Genotypes = array(NA, dim = c(lineN, N))
    for (j in 1:N) {
        Genotypes[, j] = ChildGenes[, 2 * j - 1] + ChildGenes[, 2 * j]
    }
    GeneFreq[g, ] = table(Genotypes)/(lineN * N)  # Genotype frequencies.
}

## Error: number of items to replace is not a multiple of replacement length

par(mfrow = c(2, 1))

names = c("AA", "Aa", "aa")
colors <- rainbow(3)
linetype <- c(1:3)
plot(c(1, generationN), 0:1, type = "n", xlab = "Generations", ylab = "Genome Frequency")
title("Genotype frequencies of 100 inbreeding populations")

for (i in 1:3) {
    lines(GeneFreq[, i], type = "l", lwd = 2, col = colors[i])
}
legend(c(0, 50), c(0.55, 1), names, cex = 0.8, col = colors, title = "Genotype", 
    lty = 1)

names = c("A", "a")
colors <- rainbow(2)
linetype <- c(1:2)
plot(c(1, generationN), 0:1, type = "n", xlab = "Generations", ylab = "Allele Frequency")
title("Allele frequencies of 100 inbreeding populations")

for (i in 1:2) {
    lines(AlleleFreq[, i], type = "l", lwd = 2, col = colors[i])
}
legend(c(0, 50), c(0.6, 1), names, cex = 0.8, col = colors, title = "Genotype", 
    lty = 1, )