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
• 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
A1A1 A1A2 A2A2
Relative fitness s211 s2
111
s21
21 121
• Recombinant inbred from an F2
– without selection
– with selection
P
2a
s i σ
(Because p=1/2)
Standardized effect of a locus
(no dominance)
Mean with selfing
• Inbreeding decreases the mean if there is dominance
• At fixation (with no selection):
A1A1 A1A2 A2A2
aP aP dP Genotypic Value
Frequency p2+pqF q2+pqF2pq(1-F)
apqqdpqapqp PFPF12PF 220F
dpqq-pa F12P
q-pa PRI
RI = recombinant inbred lines
does not depend on dominance
Mean of recombinant inbreds from a single-cross
Mean of recombinant inbreds derived from F2 of a single-cross
BB
AA
q-pa
q-pa
P
P
B
AMeans of the parents (for a single locus)
BABABA qq-ppa 21
21
21
21
AxBRI P)(
• 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/haB = 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 F4=S2 plant F5=S3 plant
F3=S1 family F4=S2 family F5=S3 familyrepresents S0 plant represents S1 plant represents S2 plant
Selfed families from a single-cross
¼A1A1½A1A2¼A2A2F2
aP aP dP dPμ 21
22122
A 2 ap-qdapq
24122
Dσ ddqp 224
¼A1A1⅛A1A1¼A2A2
¼A1A2
⅛A2A2
dPμ 41F3
2D
2A
2G
Bernardo, Chapt. 9
Variance among and within selfed families
¼A1A1⅛A1A1¼A2A2
¼A1A2
⅛A2A2
dPμ 41
2D4
12A
21612
212
412
412
21
212
412
Among PPPP dadada
2D
2A2
1412
D2A2
1412
WithinAvg 00 .
F3
2D4
32A2
321632
432
412
832
412
832
plantsF PPPP3
dadada
Genetic variance with selfing
Among families Within families
Total
Generation F(g)
F3=S1 1/2 1 1/4 1/2 3/2 3/4
F4=S2 3/4 3/2 3/16 1/4 7/4 7/16
F5=S3 7/8 7/4 7/64 1/8 15/8 15/64
F6=S4 15/16 15/8 15/256 1/16 31/16 31/236
F∞=S∞ 1 2 0 0 2 0
2Aσ 2
Dσ 2D
2A σσ , 2
Aσ 2Dσ
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
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
A2A2 - a a = d
Bernardo, Section 4.5
Effect of alleles in testcrosses
A1A1 A1A2 A2A2
aP aP dP Genotypic Value
Frequency ppT pqT + pTq
qppqdqqppa TTTTT P
Tester is an inbred line or population in HWE
qqT
TTT pqdaq 1
TTT pqda-p 2
TTTTT pqda- 21
Testcross mean of recombinant inbreds
Testcross mean of recombinant inbreds derived from F2 of a single-cross
TBTBTBTBT
TATATATAT
pqqpdqq-ppa
pqqpdqq-ppa
P
P
B
A
Testcross means of parental inbreds
BA TTT 21
21
RI(AxB)
• 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 BxCTA = 8 t/haTB = 6 t/ha
For RI derived from the F2 of AxBTRI(AxB) = ½*8 + ½*6 = 7 t/ha
Testcross means
• 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
Genotype Frequency Testcross Mean
A1A1 p2+pqF T+qT
A1A2 2pq(1-F) T+½(q - p)T
A2A2 q2+pqF T - pT
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
• Amount of heterosis due to a single locus = d
• 50% is lost with random-mating
A1A1 x A2A2
A1A2
aP aP
dP
¼A1A1½A1A2¼A2A2dPμ 2
1
F1
F2
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
A1 B2
A1 B2
XA2 B1
A2 B1
A1 B2
A2 B1
• tight, repulsion phase linkages
•partial to complete dominance
+1 -2 -1 +2 +1
+2
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
• 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
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
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 open-pollination
– Must be periodically reconstituted from parents
– Parents selected based on combining ability or progeny tests