PBG 650 Advanced Plant Breeding
Module 12: Selection
– Inbred Lines and Hybrids
Selection for a high mean
• Success is a function of
– the population mean 
– the deviation of the best segregants from 
– ability to identify the best segregants
• Advanced Cycle Breeding = “inbred recycling”
– cross best by best (often related)
– pedigree and backcross selection
– emphasis on high mean at the expense of G2
– need methods for predicting 
Bernardo Chapt. 4
Probability of fixing favorable alleles during inbreeding
Relative fitness
1 21 s
1
1 21 s
(no dominance)
A1A1
A1A2
A2A2
•
Recombinant inbred from an F2
– without selection
1
2
– with selection
1
2
Standardized
effect of a locus
2a
si
σP
(Because p=1/2)
1 21 s
• Three approaches to increase chances of fixing favorable alleles
– selection before inbreeding
– selection during inbreeding
– one or more backcrosses to the better parent before inbreeding
Mean with selfing
Genotypic Value
Frequency
P a
P d
P a
A1A1
A1A2
A2A2
p2+pqF
2pq(1-F)
q2+pqF
F0   p2  pqFP  a   2 pq1 FP  d   q2  pqFP  a 
 P  a p - q   2 pq1 Fd
•
•
Inbreeding decreases the mean if there is dominance
At fixation (with no selection):
RI  P  a p - q 
RI = recombinant inbred lines
does not depend
on dominance
Mean of recombinant inbreds from a single-cross
 A  P  a  pA - q A 
Means of the parents
(for a single locus)
B  P  a  pB - qB 
Mean of recombinant inbreds derived from F2 of a single-cross
RI( AxB )  P  a  21  pA  pB  - 21 q A  qB   21  A  21  B
•
The mean of recombinant inbreds derived from an F2 or
backcross population can be predicted as a simple function of
allele frequencies (the contribution of the parents)
A = 6 t/ha
B = 4 t/ha
RI[(AxB)(A)BC1] = ¾*6 + ¼*4 = 5.5 t/ha
Selfed families from a single-cross
F2=S0 plant
F3=S1 plant
F3=S1 family
represents S0 plant
F4=S2 plant
F4=S2 family
represents S1 plant
F5=S3 plant
F5=S3 family
represents S2 plant
Selfed families from a single-cross
F2
P a
P d
P a
¼A1A1
½A1A2
¼A2A2
 2A  2 pq a  d q - p 2  21 a 2
σD2  4 p2q 2d 2  41 d 2
F3
¼A1A1
Bernardo, Chapt. 9
⅛A1A1
¼A1A2
⅛A2A2
¼A2A2
μ  P  21 d
   
2
G
2
A
2
D
μ  P  41 d
Variance among and within selfed families
F3
2Among 
¼A1A1
1
4
⅛A1A1
¼A1A2
⅛A2A2
¼A2A2
μ  P  41 d
P  a 2  21 P  21 d 2  41 P  a 2  P  41 d 2  21 a 2  161 d 2  2A  41 D2



2Avg.Within  41 0  21 2A  D2  41 0  21 2A  D2

2

F23plants  38 P  a  41 P  d

2  38 P  a 2  P  41 d 2  34 a 2  163 d 2  32 2A  34 D2
Genetic variance with selfing
Among families
Within
families
Total
σ 2A
σ D2
1/2
3/2
3/4
3/16
1/4
7/4
7/16
7/4
7/64
1/8
15/8
15/64
15/16
15/8
15/256
1/16
31/16 31/236
1
2
0
0
Generation
F(g)
σ 2A
σ D2
F3=S1
1/2
1
1/4
F4=S2
3/4
3/2
F5=S3
7/8
F6=S4
F∞=S∞
σ2A , σD2
2
0
Inbreeding as a Selection Tool for OPVs
•
•
•
•
More genetic variation among lines
•
Sets of inbred lines can be used to identify markerphenotype associations for important traits
•
Best lines can be intermated to produce synthetic
varieties with defined characteristics
Increased uniformity within lines
Visual selection can be done for some traits
Permits repeated evaluation of fixed genotypes in
diverse environments, for many traits
Testcrosses
• The choice of tester will determine if an allele
is favorable or not
Testcross genotypic values with complete dominance
Genotypic value of testcross
Parent of cross
A2A2 tester
A1A1 tester
A1A1
d
a=d
A1A2
½(d - a)
a=d
-a
a=d
A2A2
Bernardo, Section 4.5
Effect of alleles in testcrosses
Tester is an inbred line or population in HWE
Genotypic Value
Frequency
P a
P d
P a
A1A1
A1A2
A2A2
ppT
pqT + pTq
qqT
T  P  a ppT  qqT   d  pqT  pT q 
  qa  d qT  pT 
T
1
T2  -pa  d qT  pT 
   -   a  d qT  pT 
T
T
1
T
2
Testcross mean of recombinant inbreds
Testcross means of parental inbreds
T  P  a  p A pT - q AqT   d  p AqT  q A pT 
A
T  P  a  pB pT - qB qT   d  pB qT  qB pT 
B
Testcross mean of recombinant inbreds derived from F2 of a single-cross
T
RI(AxB)
•
 21 T  21 T
A
B
The testcross mean of recombinant inbreds derived from an
F2 or backcross population can be predicted as a simple
function of allele frequencies (the contribution of the parents)
T=AxC and BxC
For RI derived from the F2 of AxB
TA = 8 t/ha
TRI(AxB) = ½*8 + ½*6 = 7 t/ha
TB = 6 t/ha
Testcross means
Genotype
A1A1
A1A2
A2A2
•
Frequency
Testcross Mean
p2+pqF
2pq(1-F)
q2+pqF
T+qT
T+½(q - p)T
T - pT
Testcross mean of the heterozygote is half-way between the
two homozygotes
• Cross “good” by “good”
• But, the correlation between the performance of inbred lines
per se and their performance in testcrosses is very poor for
yield and some other agronomic traits
Heterosis or Hybrid Vigor
•
Quantitative genetics:
– superiority over mean of parents
•
Applied definition
– superiority over both parents
– economic comparisons need to be made to nonhybrid
cultivars
•
Various types
– population cross
– single-, three-way, and double-crosses
– topcrosses
– modified single-cross
Bernardo, Chapt. 12
Heterosis
P a
P a
A1A1 x A2A2
A1A2 P  d
F1
F2
¼A1A1
½A1A2
¼A2A2
μ  P  21 d
• Amount of heterosis due to a single locus = d
• 50% is lost with random-mating
Theories for Heterosis
•
Dominance theory: many loci with d  a
– Should be possible to obtain inbred  single-cross
– Expect skewed distribution in F2 (may not be the case if
many loci control the trait)
•
•
Overdominance theory: d > a
Pseudo-overdominance - decays over time
+1 -2
A1 B2
A1 B2
X
-1 +2
A2 B1
+1
A1 B2
A2 B1
A2 B1
+2
• tight, repulsion
phase linkages
• partial to complete
dominance
Heterosis – some observations
• Experimental evidence suggests that heterosis is largely
due to partial or complete dominance
• Yields of inbred lines per se are poor predictors of hybrid
performance
– due to dominance
– hybrids from vigorous lines may be too tall, etc.
– due to heritability <1
• Heterosis generally increases with level of genetic
divergence between populations, however….
– There is a limit beyond which heterosis tends to decrease
– A high level of divergence does not guarantee that there
will be a high level of heterosis
Heterosis – more observations
•
Epistasis can also contribute to heterosis
– does not require d>0
•
Selection can influence heterosis
– Iowa Stiff Stalk Synthetic
(BSSS)
– Iowa Corn Borer Synthetic
(BSCB1)
– High density SNP array
shows increasing
divergence over time in
response to reciprocal
recurrent selection
Gerke, J.P. et al., 2013 arXiv:1307.7313 [q-bio.PE]
Heterotic groups
•
Parents of single-crosses generally come from
different heterotic groups
•
Two complementary heterotic groups are often
referred to as a “heterotic pattern”
•
Temperate maize
– ‘Reid Yellow Dent’ x ‘Lancaster Sure Crop’
– Iowa Stiff Stalk x Non Stiff Stalk
•
Tropical maize
– Tuxpeño x Caribbean Flint
Identifying heterotic patterns
•
•
Diallel crosses among populations
•
Use molecular markers to establish genetic
relationships, and make diallel crosses among
dissimilar groups
Crosses to testers representing known heterotic
groups
– initial studies were disappointing
– markers must be linked to important QTL
Exploiting heterosis
•
•
Recycle inbreds within heterotic groups
Evaluate testcrosses between heterotic groups
– elite inbreds often used as testers
•
BLUP can predict performance of new singlecrosses using data from single-crosses that have
already been tested
– fairly good correlations between observed and
predicted values
What is a synthetic?
•
Lonnquist, 1961:
– Open-pollinated populations derived from the intercrossing of
–
•
selfed plants or lines
Subsequently maintained by routine mass selection procedures
from isolated plantings
Poehlman and Sleper:
– Advanced generation of a seed mixture of strains, clones,
–
–
–
inbreds, or hybrids
Propagated for a limited number of generations by openpollination
Must be periodically reconstituted from parents
Parents selected based on combining ability or progeny tests
Predicting hybrid performance
Three-way crosses

 AxBxC   21 YAxB  YAxC 
Double-crosses

 AxB x CxD   41 YAxC  YAxD  YBxC  YBxD 
Synthetics
Synthetic
 Yii'  Yi 
 Yii'  

 n 
Yii '
= avg yield of all F1 hybrids
Yi
= avg yield of parents
Wright’s
Formula
n = number of parents