1. PBG 650 Advanced Plant Breeding
Module 12: Selection
Inbred Lines and Hybrids

2. 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

3. Probability of fixing favorable alleles during inbreeding
Standardized effect of a locus
Relative fitness
(no dominance)
A1A A1A A2A2
Recombinant inbred from an F2
without selection
with selection
(Because p=1/2)
For most quantitative traits, probability of fixing the favorable allele is closer to ½ than to one.
Bernardo calls s the selection coefficient – related to “fitness” concepts
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

4. Mean with selfing Genotypic Value A1A1 A1A2 A2A2 Frequency p2+pqF
q2+pqF
Inbreeding decreases the mean if there is dominance
At fixation (with no selection):
does not depend on dominance
RI = recombinant inbred lines

5. Mean of recombinant inbreds from a single-cross
Means of the parents
(for a single locus)
Mean of recombinant inbreds derived from F2 of a single-cross
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

6. Selfed families from a single-cross
F2=S0 plant
F3=S1 plant
F4=S2 plant
F5=S3 plant
F3=S1 family
F4=S2 family
F5=S3 family
represents S0 plant
represents S1 plant
represents S2 plant

7. Selfed families from a single-cross
¼A1A1 ½A1A2 ¼A2A2 F3
¼A1A1 ⅛A1A1 ¼A2A2
¼A1A2
⅛A2A2
Bernardo, Chapt. 9

8. Variance among and within selfed families
¼A1A1 ⅛A1A1 ¼A2A2
¼A1A2
⅛A2A2

9. Genetic variance with selfing

10. Inbreeding as a Selection Tool for OPVs
More genetic variation among lines
Increased uniformity within lines
Visual selection can be done for some traits
Permits repeated evaluation of fixed genotypes in diverse environments, for many traits
Sets of inbred lines can be used to identify marker-phenotype associations for important traits
Best lines can be intermated to produce synthetic varieties with defined characteristics

11. Genotypic value of testcross
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)
A2A2
- a
Bernardo, Section 4.5

12. Effect of alleles in testcrosses
Tester is an inbred line or population in HWE
Genotypic Value
A1A A1A A2A2
Frequency
ppT
pqT + pTq
qqT

13. Testcross mean of recombinant inbreds
Testcross means of parental inbreds
Testcross mean of recombinant inbreds derived from F2 of a single-cross
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
TA = 8 t/ha
TB = 6 t/ha
For RI derived from the F2 of AxB
TRI(AxB) = ½*8 + ½*6 = 7 t/ha

14. Testcross means p2+pqF T+qT 2pq(1-F) T+½(q - p)T q2+pqF T - pT
Genotype
Frequency
Testcross Mean
A1A1
p2+pqF
T+qT
A1A2
2pq(1-F)
T+½(q - p)T
A2A2
q2+pqF
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

15. 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
definition of a modified single-cross
advantages and disadvantages of double-crosses
Bernardo, Chapt. 12

16. Amount of heterosis due to a single locus = d
A1A1 x A2A2
A1A2 F1 F2
¼A1A1 ½A1A2 ¼A2A2
Amount of heterosis due to a single locus = d
50% is lost with random-mating

17. 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
-1 +2 +1
tight, repulsion phase linkages
partial to complete dominance
A1 B2
A2 B1
A1 B2 X
A1 B2
A2 B1
A2 B1 +2

18. 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
Extremely divergent populations or lines may not be adapted to the same environments

19. 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: [q-bio.PE]

20. 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

21. Identifying heterotic patterns
Diallel crosses among populations
Crosses to testers representing known heterotic groups
Use molecular markers to establish genetic relationships, and make diallel crosses among dissimilar groups
initial studies were disappointing
markers must be linked to important QTL

22. Exploiting heterosis
Recycle inbreds within heterotic groups
Evaluate testcrosses between heterotic groups
elite inbreds often used as testers
BLUP can predict performance of new single-crosses using data from single-crosses that have already been tested
fairly good correlations between observed and predicted values

23. What is a synthetic? Lonnquist, 1961: Poehlman and Sleper:
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 open- pollination
Must be periodically reconstituted from parents
Parents selected based on combining ability or progeny tests

24. Predicting hybrid performance
Three-way crosses
Double-crosses
Wright’s
Formula
Synthetics
= avg yield of all F1 hybrids n = number of parents
= avg yield of parents