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

• 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

Predicting hybrid performance

Three-way crosses

AxCAxB21

BxCAx YY

Double-crosses

BxDBxCAxDAxC41

CxDxAxB YYYY

Synthetics ii ' iSynthetic ii '

Y YY

n

= avg yield of all F1 hybrids n = number of parents

= avg yield of parents

ii '

i

Y

Y

Wright’sFormula