Advanced Plant Breeding PBG 650
Midterm 2, Fall 2013
Name
KEY
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.
Value
28
Value
A1A1
Frequency
0.49
A1A2
0.42
26
d=3
A2A2
0.09
18
-a = -5
a=5
MP = 23
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.
p = 0.49+0.42/2 = 0.7 q = 1-0.7 = 0.3
M = a(p-q)+2pqd = 5(0.7-0.3) + 2(0.7)(0.3)*3 = 2.0 + 1.26 = 3.26
 = MP + 3.26 = 26.26
 = a+d(q-p) = 5+3(0.3-0.7) = 5-1.2 = 3.8
Breeding value = (q-p)
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.
The breeding value indicates the expected performance of progeny of an A1A2 individual
when mated at random in this population. Breeding values are expressed as deviations from
the population mean, and are a function of gene frequencies in the population. In this case,
progeny that have an A1A2 individual as a parent are expected to perform 0.5*(-1.52) units
below the mean, on the average. In this case, that would be 26.26 – 0.5*(1.52) = 25.5 units.
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.
 F2  (MSF  MS ) / r
= (269-73)/(4) = 49
E
b) Calculate additive genetic variance for the reference population.
6 pts
8 pts
 2A  4F2
= 4*49 = 196
c) What is the heritability for this trait, assuming that selection would be based on progeny
means evaluated at comparable levels of precision?
 F2
 F2
 F2
49
49
h  2  2   2


 0.7286
2
269
73
P F  r F   X
49  4
4
2
2
e
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
The sets of environments are considered to be fixed and the cultivars are considered to be
random.
b) For the example above, fill in the missing elements of the X and Z matrices:
1
0
b1
1
0
b2
4.
0
3.
0
3.
8 pts
3.
=
1
0
0
u1
0
1
0
u2
1
1
0
0
u3
1
0
0
1
+
3
e11
+
e12
e21
e23
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?
AA = 1 (pureline) ; CovAA = 2
AB = (1+F) Half-sibs = (1+1)⅛ = ¼ (F refers to inbreeding of common parent)
CovAB = 2*¼*A2 = ½*A2
A=
2
½
0
½
2
0
0
0
2
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
b1 (for set 1)
b2 (for set 2)
1 (for cultivar A)
2 (for cultivar B)
3 (for cultivar C)
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
Cultivar B has the highest BLUP value (0.1983673) and would be the best bet for use in
crosses to D. BLUP values indicate the expected performance of progeny and are measured
as a deviation from zero.
4
12 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
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?
This is a diallel experiment, and he will be using Griffing’s Method 4 if parents and
reciprocal crosses are not included. Genotypes are probably fixed in this case, because he is
interested in this particular set of parents. He can estimate GCA to determine the best parents
to use in his pureline breeding program. Crosses that show favorable SCA should be
maintained in distinct heterotic groups for future inbred-hybrid development. If he includes
the parents in the trial, then specific tests could be made for heterosis (Gardner-Eberhart
analysis). He cannot get good estimates of additive genetic variance or dominance variance
from this study. The assumption of linkage equilibrium would not be met because the lines
come from diverse genetic backgrounds. The sample size (6) is also too small to accurately
estimate VA and VD. Also, because he is interested in the parents per se, the assumption that
they are a random representation of a reference population does not seem appropriate.
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).
Any vegetatively propagated crop could be used as an example, because favorable
dominance interactions and epistasis can be immediately fixed by selection of good plants.
Examples mentioned in class include hops and hazelnuts. Hybrid cultivars can also exploit
nonadditive genetic variance. Corn would be a good example.
Crops that can be easily crossed and that produce large quantities of seed for testing would
also be favored, because they can be readily evaluated for gca and sca.
Crops that are generally grown as pureline cultivars such as barley, wheat and beans, would
not be good examples, unless there are systems available for development of hybrids.
Meadowfoam also does not qualify because there is no practical way to produce hybrid seed
in large enough quantities, so we are presently limited to use of open-pollinated varieties.
Some amount of dominance could be exploited through development of synthetics, because
selfing can be readily accomplished.
Experimentally, G X E interactions are part of environmental variance. Although it is
possible to breed for specific adaptation to environments, the question does not really address
that issue.
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