Advanced Plant Breeding PBG 650
Midterm 2, Fall 2015
Name
KEY
Please show your work.
1) A plant breeder is evaluating a random-mating population of Russian dandelion as a
potential source of natural rubber. She conducts progeny trials and estimates the breeding
values of genotypes segregating at a single locus that affects rubber production.
Frequency
A 1A 1
A 1A 2
A 2A 2
8 pts
0.36
0.48
0.16
Genotypic Breeding
Value
Value
25
5.28
20
-1.32
11
-7.92
a) What is the additive genetic variance for this trait at this locus in this population?
There are many ways to solve this problem with the information provided.
Method 1: Use the formula VA=2pq2
p=0.36 + 0.5*0.48 = 0.36 + 0.24 = 0.60 q = 1 – 0.6 = 0.4
To calculate  you could work with known formulas for the individual genotypes, or use
a, d, and –a and the formula  = a + d(q - p).
For example, the breeding value of A1A1 is 2q = 5.28, so =5.28/(2*0.4)=6.6
Alternatively, with MP = 18, a=7, and d=2,  = a + d(q - p)=7 + 2(0.4-0.6)=7-0.4=6.6
VA=2pq2=2*0.6*0.4*6.62 = 20.9088
Method 2: Calculate the variance among breeding values
V (Y)   f i Yi2  μY2
 0.36 *5.282  0.48* ( 1.32) 2  0.16 * ( 7.92) 2  0 2
 10.036  0.836  10.036  20.9088
8 pts
b) She decides to cross an A1A1 genotype with an A1A2 genotype. What is the expected
breeding value of the offspring from this cross?
The expected breeding value of the progeny will be the average breeding value of the
parents. In this case the average of 5.28 and -1.32 is 3.96/2 = 1.98
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 (r=4) and evaluated in two years (y=2).
Source
6 pts
df
MS
Expected Mean Square
Years
y-1
Blocks(Years)
r-1
Families
f-1
381
2
 e2  r FY
 ry F2
Families x Years
(f-1)(y-1)
183
2
 e2  r FY
Error
y(r-1)(f-1)
55
 e2
a) Calculate the genetic variance among families.
 F2  (MS  MS ) / ry  (381  183) / 8  24.75
F
FY
b) Calculate additive genetic variance for the reference population.
6 pts
6 pts
2A  42F  4 * 24.75  99
c) What is the heritability for this trait, assuming that selection would be based on half-sib
family means averaged across blocks and years? (Hint: 𝜎𝑃2 = 𝑀𝑆(𝑓𝑎𝑚𝑖𝑙𝑖𝑒𝑠)/𝑟𝑦)
 F2
 F2
 F2
24.75
24.75
24.75
h  2  2 




 0.5197
381
183
 P  F  ry  y  F2   X2
24.75

47.625
8
8
2
2
e
2
FY
2
10 pts
3) In the equation below, fill in the appropriate coefficients for the covariance of full-sibs when
two-locus epistasis is present.
CovFS 
8 pts
1
2
2
2
 A2  14  D2  14  AA
 81  AD

1
16
2
 DD
4) The mixed model equation that is used to estimate Best Linear Unbiased Predictors is
Y = X + Z + 
Briefly explain what X, ,
Z and  in the model represent.
X is the design matrix for fixed effects
Beta is the matrix of fixed effects that we wish to estimate
Z is the design matrix for random effects
Mu is the matrix of random effect
8 pts
5) The benefits of using BLUP values for selection rather than the average performance of an
individual or family would be greatest when….(circle the best answer for each of the four
criteria)
Criteria
Heritability
Low
High
Parents
Related
Unrelated
Data
Balanced (genotypes are evaluated to
the same extent)
Unbalanced
Lifespan of the species
Short
Long
3
6) Heritability can be estimated from parent-offspring regression. Which statement about
parent-offspring regression is true?
6 pts
a) Heritability is expected to be higher when it is estimated from regression on midparent
values than it is for regression on a single parent.
b) Heritability is expected to be higher when we evaluate more offspring from each parent.
c) The slope for regression of offspring on midparent is expected to be twice as large as
the slope for regression on one parent.
d) The standard error of the heritability will be the same for regression on midparent
values as it is for regression on a single parent.
6 pts
7) A breeder selfs individual plants from a noninbred meadowfoam population in the
greenhouse. She harvests the seed from each plant and grows a row of 10 plants from each
parent plant in an outdoor nursery. She hires some honeybees to intermate all of the plants
in the nursery. Each row of 10 plants that came from a common parent is harvested in bulk
to create a half-sib family for progeny tests in the next cropping season. Can she assume
1
that the covariance for half-sib families is 4 𝜎𝐴2 , or will she need to make an adjustment for
inbreeding of the parents? Explain your answer.
1
Yes, the covariance should be 4 𝜎𝐴2 and no adjustment for inbreeding is needed. Each S1
family represents the genotype of a noninbred parent plant.
6)
6 pts
10 pts
A plant breeder has been hired to initiate a quinoa breeding program in Montana. He has
obtained some germplasm and plans to make diallel crosses using Griffing’s Method 4. He is
not sure how he should interpret his results.
a) List at least three questions that you would ask him to help him decide how to interpret
his data.
 How were the parents chosen and what is their breeding history?
 How many parents are there?
 Is his main interest in this particular set of parents and how they perform in crosses,
or does he want to understand more about the inheritance of specific traits in
quinoa?
b) Describe (in general) how his answers would determine the inferences that can be made
from his experiment.
The main issue is to determine if genotypes are fixed or random and if the assumption that
the parents are a representative sample from of a random-mating reference population can
be met. If he is using a random model and the necessary assumptions can be met, then he
can estimate additive genetic variance and dominance variance (Model II). If the genotypes
4
are fixed and/or the assumptions are not met, then he can only estimate GCA and SCA
(Model I).
7)
Using 10 barley plants (A, B, C, D, E, F, G, H, I, and J), describe how you would make
1) Design I crosses (Nested)
12 pts
2) Design II crosses (Factorial)
For each mating design, indicate how the crosses would form
1) A half-sib family
Give an example for each mating design:
You don’t have to designate all possible
half-sib and full-sib families.
2) A full-sib family
Nested Design
Cross A as a male to females B, C, D, and E
Cross F as a male to females G, H, I, and J
An example of one half-sib family would include AxB, AxC, AxD, and AxE (all have A as a
common parent).
AxB represents a full-sib family
Design II
A
B
C
D
E
F
X
X
X
X
X
G
X
X
X
X
X
H
X
X
X
X
X
I
X
X
X
X
X
J
X
X
X
X
X
An example of one half-sib family would include AxF, AxG, AxH, AxI, and AxJ (all have A as a
common parent).
AxF represents a full-sib family
5