PBG 650 Experimental Design in Agriculture
In-Class Exercise on Genotypic Means, Effects of Alleles
The genotypic means for a locus that affects glucosinolate content (µmol/g) in meadowfoam
seeds are 120 for A1A1, 110 for A1A2 and 90 for A2A2. The population is random-mating with
f(A1) = p = 0.7.
̅ and fill in the table below.
 Calculate the midparent value P
Frequency
Genotypic
value
Genotype
Frequency
A1A1
p2
a
A1A2
2pq
d
A2A2
q2
–a
Genotypic
value
Frequency
x value
For a discrete random variable, the population mean can be calculated as the sum of the
frequencies x values.
E(X) = ΣiXiPr(Xi) =X
(this is a weighted average, where the ΣPr(Xi)=1)
 Calculate the population mean on the coded scale and confirm that M = a(p - q) + 2pqd.
̅ + a(p - q) + 2pqd
 Calculate the population mean on the original scale 𝝁 = 𝑷
(note that you could also calculate this directly from the original values as a weighted
average)
1
 Calculate the average effect of a gene for A1 and A2
A1A1
A1A2
A2A2
Gamete
a
d
-a
A1
p
q
A2
p
q
 (Freq. x
value)
 (Freq. x value)
Average effect
minus M
of a gene
pa + qd
1=q[a+d(q-p)]
pd - qa
2=-p[a+d(q-p)]
 Calculate the average effect of a gene substitution
 = 1 - 2 = a+d(q-p)
 Calculate Breeding Values for the three genotypes A1A1, A1A2 and A2A2
 How would you measure Breeding Value in a breeding program? (It is 2 x GCA)
 Use algebra to convince yourself that the genotypic value of A1A1 adjusted for the mean is
a – [a(p - q) + 2pqd] = 2q(a-pd) = 2q(-qd)
2
 Calculate Genotypic values, Breeding Values, and dominance deviations using the formulas
in the table below.
Genotype
Genotypic Value
(adj. for mean)
A1A1
Breeding Value
(additive effects)
Dominance
Deviation
2q(-qd)
2q
-2q2d
A1A2
(q-p)+2pqd
(q - p)
+2pqd
A2A2
-2p(+pd)
-2p
-2p2d
 Plot your results on a graph showing the regression of breeding values on the frequency of
A1 alleles. Use the coded scale (-a, d, a) on the left axis of the graph and the adjusted values
(in terms of ) on the right axis.
3