Advanced Plant Breeding PBG 650
Midterm 2, Fall 2013
Name
1) A random-mating population of pearl millet is segregating at the ‘A’ locus, which determines
stalk strength. The table below shows the frequency of genotypes and their genotypic values.
A1A1
Frequency
0.49
Value
28
A1A2
0.42
26
A2A2
0.09
18
6 pts
a) Add the coded genotypic values (expressed as deviations from the midparent value) to
the table above.
6 pts
b) Calculate the breeding value for the A1A2 genotype.
10 pts
c) Explain what is meant by a breeding value and use your answer to question 1b above to
illustrate what it tells you about the A1A2 genotype.
1
2) An experiment is conducted to estimate additive genetic variance from 200 half-sib families,
obtained from noninbred parents. Each plot represents a family, and the families are
replicated in four randomized blocks at one location.
Source
Replications
df
r-1
MS
Expected Mean Square
Families
f-1
269
(r-1)(f-1)
73
 e2  r F2
 e2
Error
6 pts
a) Calculate the genetic variance among families.
b) Calculate additive genetic variance for the reference population.
6 pts
8 pts
c) What is the heritability for this trait, assuming that selection would be based on progeny
means evaluated at comparable levels of precision?
3) When conducting genetic analyses we often assume that epistasis is absent. If this
assumption is not valid, what proportion of the additive by additive epistasis is expected to
contribute to the covariance of half-sib families? (choose one answer)
6 pts
1
4
1
b) 8
1
c) 16
1
d) 64
a)
2
4) Cultivar A, B and C are pureline varieties (inbred lines) that have been evaluated for yield in
multilocational trials. Cultivar A and B were tested in a common set of 10 locations, and
Cultivar A and C were tested in another set of 6 locations. Average yields are shown in the
table below:
Environments
Cultivar
Yield t/ha
Set 1
10
A
3.4
Set 1
10
B
3.7
Set 2
6
A
4.2
Set 2
6
C
3.9
You wish to estimate the Best Linear Unbiased Predictors for the three cultivars. The linear
model in matrix notations is Y = X+Z+, where  represents the location effects and 
represents the BLUPs for the cultivars.
a) Which factors are considered to be fixed and which are random in this model?
6 pts
b) For the example above, fill in the missing elements of the X and Z matrices:
b1
3.4
8 pts
3.7
=
b2
u1
+
u2
u3
4.2
e11
+
e12
e21
e23
3.9
3
Question 4, continued.
The solution to the normal equations would have the following format:
β̂
û
10 pts
=
-1
X’R-1X
X’R-1Z
Z’R-1X
Z’R-1Z + A-1(σε2/σA2)
X’R-1Y
Z’R-1Y
c) If Cultivar A and Cultivar B had one common pureline parent, and Cultivar C is unrelated
to A and B, what would the covariance matrix (A) be for the three cultivars in this
example?
d) SAS IML was used to solve the normal equations, which produced the following result:
B
3.4489796
4.1289796
0.0036735
0.1983673
-0.161633
You wish to make crosses to another cultivar ‘D’ that is unrelated to A, B, and C. Which of
the three cultivars would you be most inclined to use as a parent if your goal is to breed a
new high yielding cultivar? Use the solution above to justify your answer.
6 pts
5) A plant breeder has been hired to initiate a quinoa breeding program in Montana. He obtains
six unrelated pureline accessions from various sources. He intends to make all 15 possible
12 pts
4
crosses among the lines and to evaluate the F1 hybrids in replicated trials. His immediate
objective is to identify the best parents to use in crosses to develop pureline cultivars. He
would also like to know which crosses exhibit heterosis, because there may be an opportunity
to initiate an inbred-hybrid breeding program in the future.
Describe in a general way how you think he should analyze and interpret his results i.e., what
type of mating design is he using and what inferences can be made from his experiment?
10 pts
6) A breeder of ______________________ (name a plant species) can readily exploit both
additive and nonadditive genetic variances for crop improvement because…
(Briefly explain your answer).
5
5 pts
Extra Credit
Select the answer below that best describes your understanding of lattice designs (you can
choose more than one answer):
a. A type of incomplete block design that only includes incomplete blocks.
b. Complete block designs because all blocks include all of the treatments.
c. A type of incomplete block design that has both incomplete blocks and resolvable,
complete blocks (also called replications).
d. A type of fencing that is sturdier than chicken wire.
e. A type of upper crust that is only used on pumpkin pie and not on apple pie.
f. This is an unfair question because I do not eat pie!!
g. Personally, I like σ more than π.
6