## Solutions to Quantitative Genetics Practice Problems

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1. If the slope of a parent-offspring regression is 0.25, what is the heritability h2?

• Slope single parent-offspring regression = h2/2, hence h2/2 = 0.25 or h2 = 0.5

2. If the slope of a midparent-offspring regression is 0.75, what is the heritability h2?

• Slope mid parent-offspring regression = h2, hence h2 = 0.75

3. If h2 = 0.3, the population mean is 10, and the value of a parent is 15, what is the expected mean of an offspring from this parent?

• Offspring mean = 10 + (0.3/2)*(15-10) = 10.75

4. If h2 = 0.4, the population mean is 16, and the value of both parents are mother = 12, father = 17.

What is the midparental value?

• (12+17)/2 = 14.5

What is the expected mean of an offspring from these parents?

• Offspring mean = 16 + (0.4)*(14.5-16) = 15.4

5. If the mean of a group of selected parents is 10 units above the population mean, while the mean value of their offspring is 3 units above the original population mean, what is the heritability h2?

• Since R = h2 S, h2 = R/S = 3/10 =0.3

6. Suppose 5 locus underlie a character of interest and that each capital letter allele at each locus adds value one to the character (so that genotype aabbccddee has value 0 while AABBCCDDEE has value 10). Suppose Freq(A) = Freq(B) = ... = Freq(E) and we assume H-W.

If Freq(A) = 0.7, what is the probability of an individual with genotype aabbccddee ?

• freq(aa) = 0.32= 0.09. Hence freq(aabbccddee) = (0.32)5 = 0.00000059

Suppose now that selection changes the allele frequencies to Freq(A) = 0.1, now what is the probability of an individual with genotype aabbccddee ?

• freq(aa) = 0.92= 0.81. Hence freq(aabbccddee) = (0.92)5 = 0.35

7. If the correlation between dizygotic twins for weight is 0.5, while the correlation between monozygotic twins is 0.75, what is the heritability of weight?

• h2 = 2 [ corr(DZ twins) - corr(MZ twins) ] = 2[ 0.75-0.5 ] = 0.5