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Genetics and
Genetic Prediction
in Plant Breeding
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Qualitative Genetics
Segregation, linkage, epistasis,
tetraploid, 2
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Quantitative Genetics
Continuous variation, genetic
models, model testing
QTL’s
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0
500
1000
1500
2000
2500
3000
3500
25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105
Fre
qu
ency
Plant height (cm)
Height of 4,000 F2 wheat plants
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0
500
1000
1500
2000
2500
25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105
Fre
qu
ency
Plant height (cm)
Height of 4,000 F2 wheat plants
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0
100
200
300
400
500
600
0.4 0.7 1 1.3 1.6 1.9 2.2 2.7 3 3.3 3.6 3.9 4.2 4.5 4.8 5.1 5.4
Fre
qu
ency
Plant Yield (kg)
Tuber yield of 4,000 genotypes
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P = G + E + GE + 2e
Phenotype
Genotype
Environment
Geno x Environ
Error
Additive v other
Quantitative Genetics
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0
100
200
300
400
500
600
0.4 0.7 1 1.3 1.6 1.9 2.2 2.7 3 3.3 3.6 3.9 4.2 4.5 4.8 5.1 5.4
Fre
qu
ency
Plant Yield (kg)
Tuber yield of 4,000 genotypes
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400
600
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500 510 520 530 540 550 560 570 580 590 600 610 620
Histogram
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0
200
400
600
800
1000
500 510 520 530 540 550 560 570 580 590 600 610 620
Normal Distribution
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Normal Distribution Function
Relationship to plant genetics
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Consider two homozygous parents of
canola (Brassica napus).
Parent 1 has yield of 620 lbs/acre.
Parent 2 has yield of 500 lb/acre.
The F1 has 560 lb/acre yield.
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Parent 2 x Parent 1
aa AA
500+0+0=500 500+60+60=620
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Parent 2 x Parent 1
aa AA
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Parent 2 x Parent 1
aa AA
aA
Aa aa AA
500 560 620
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Parent 2 x Parent 1
aabb AABB
500+0+0+0+0=500 500+30+30+30+30=620
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Parent 2 x Parent 1
aabb AABB
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Parent 2 x Parent 1
aabb AABB
Aabb
AaBb
aABb
AabB
aAbB
aaBB
aabB
aaBb
aAbb
Aabb
AABb
AAbB
aABB
AaBB aabb AABB
500 530 560 590 620
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Parent 2 x Parent 1
aabbcc AABBCC
500+0+0+0+0+0+0=500 500+20+20+20+20+20+20=620
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aaBbCC
aAbBcC
aAbBCc
aAbbCC
aAbbCC
AabBcC
AabBcC
AaBbcC
AaBbCc
AaBBcc
aabBCC
aaBBcC
aaBBCc
aABbcC
aABbCc
aABBcc
AAbbCc
AAbbcC
AAbBcc
AABbcc
aabbCC
aabBcC
aabBCc
aaBbcC
aaBbCc
aaBBcc
AabbcC
aAbbCc
aAbBcc
aABbcc
AabbcC
aAbbCc
AabBcc
AaBbcc
AAbbcc
AABBcc
AABbCc
AABbcC
AAbBCc
AAbBcC
AAbbCC
AaBBCc
AaBBcC
AaBbCC
AabBCC
aABBCc
aABBcC
aABbCC
aAbBCC
aaBBCC
aabbcC
aabbCc
aabBcc
aaBbcc
aAbbcc
Aabbcc
AABBcC
AABBCc
AABbCC
AAbBCC
aABBCC
AaBBCC aabbcc AABBCC
500 520 540 560 580 600 620
Relating Genetics to Normal Distribution
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Parent 2 x Parent 1
aa AA
aA
Aa aa AA
500 560 620
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Parent 2 x Parent 1
aabb AABB
Aabb
AaBb
aABb
AabB
aAbB
aaBB
aabB
aaBb
aAbb
Aabb
AABb
AAbB
aABB
AaBB aabb AABB
500 530 560 590 620
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aaBbCC
aAbBcC
aAbBCc
aAbbCC
aAbbCC
AabBcC
AabBcC
AaBbcC
AaBbCc
AaBBcc
aabBCC
aaBBcC
aaBBCc
aABbcC
aABbCc
aABBcc
AAbbCc
AAbbcC
AAbBcc
AABbcc
aabbCC
aabBcC
aabBCc
aaBbcC
aaBbCc
aaBBcc
AabbcC
aAbbCc
aAbBcc
aABbcc
AabbcC
aAbbCc
AabBcc
AaBbcc
AAbbcc
AABBcc
AABbCc
AABbcC
AAbBCc
AAbBcC
AAbbCC
AaBBCc
AaBBcC
AaBbCC
AabBCC
aABBCc
aABBcC
aABbCC
aAbBCC
aaBBCC
aabbcC
aabbCc
aabBcc
aaBbcc
aAbbcc
Aabbcc
AABBcC
AABBCc
AABbCC
AAbBCC
aABBCC
AaBBCC aabbcc AABBCC
500 520 540 560 580 600 620
Relating Genetics to Normal Distribution
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0
200
400
600
800
1000
1200
Yield
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Yield
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0
100
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Yield
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0
100
200
300
400
500
600
700
800
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1000
Yield
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0
200
400
600
800
1000
500 510 520 530 540 550 560 570 580 590 600 610 620
Normal Distribution
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= x = (x1 + x2 + x3 + …. + xn)
n
= x = in (xi)/n
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0
200
400
600
800
1000
500 510 520 530 540 550 560 570 580 590 600 610 620
Normal Distribution
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= [in (xi - )2/n]
^ S = [i
n (xi - x)2/(n-1)]
= {[in xi
2 – [(in xi)
2/n]}/n
^ S = {[i
n xi2 – [(i
n xi)2/n-1]}/(n-1)
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P = G + E + GE + 2e
Quantitative Genetics
P = G + E + GE + e
2P =
2G +
2E +
2GE +
2e
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2 = in (xi - )2/n
^ S2 = i
n (xi - x)2/(n-1)
2 = {in xi
2 – (in xi)
2/n}/n
^ S2 = {i
n xi2 – (i
n xi)2/n}/(n-1)
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200
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600
800
1000
500 510 520 530 540 550 560 570 580 590 600 610 620
Variance Partition
2P
2G
2GE
2e
.
.
.
.
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Quantitative Genetics
Models
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Consider two homozygous parents of
canola (Brassica napus).
Parent 1 has yield of 620 lbs/acre.
Parent 2 has yield of 500 lb/acre.
The F1 has 560 lb/acre yield.
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P2 F1 P1
500 560 620 m
[a] [a]
[a] = (P1 - P2)/2
m = P1 – [a] or P2 + [a]
P1 = m + [a] : P2 = m – [a]
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P2 F1 P1
500 560 620 m
[a] [a]
[a] = (620-500)/2 = 60
m = 620–60 or 500+60 = 560
P1 = 560 + 60 : P2 = 560 – 60
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Parent 2 x Parent 1
aa AA
500+0=500 500+120=620
F1
Aa
500+120 = 620
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Parent 2 x Parent 1
aa AA
500 620
aA
Aa
AA aa
F2 = 590
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Parent 2 x Parent 1
aabb AABB
500+0+0+0=500 500+60+30+30=620
F1
AaBb
500+60+30+0 = 590
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AABb
AAbB
aAbB
AabB
aABb
AaBb
AAbb
Aabb
aAbb
aaBB
AABB
aABB
AaBB
aabB
aaBb aabb 500 530 560 590 620
F2 = 575
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Parent 2 x Parent 1
aabbcc AABBCC
500+0+0+0+0+0=500 500+40+20+20+20+20=620
F1
AaBbCc
500+40+20+20 = 580
![Page 47: Genetics and Genetic Prediction in Plant Breeding...in Plant Breeding Qualitative Genetics Segregation, linkage, epistasis, tetraploid, 2 Quantitative Genetics Continuous variation,](https://reader033.vdocuments.net/reader033/viewer/2022042913/5f4c264adde5984a3905e4fb/html5/thumbnails/47.jpg)
500 520 540 560 580 600 620
F2 = 570
Quantitative Dominance AABBcc
AABbcC
AABbCc
AAbBCc
AAbBcC
AAbbCC
aAbBcC
aAbBCc
aAbbCC
AabbCC
AabBcC
AabBCc
AaBbcC
AaBbCc
AaBBcc
aABbcC
aABbCc
aABBcc
aaBBCC
aaBbCC
aabBCC
aaBBcC
aaBBCc
AaBbCc
AAbbcC
AAbbCc
AAbBcc
AABbcc
aAbbcC
aAbbCc
aAbBcc
aABbcc
AabbcC
AabbCc
AabBcc
AaBbcc
AABBcC
AABBCc
AAbBCC
AABbCC
AaBbCc
AaBbcC
AaBbCC
AabBCC
aABBCc
aABBcC
aABbCC
AabBCC
aabbCC
aaBbcC
aaBbcC
aabBCc
aaBbCc
aaBBcc
Aabbcc
aAbbcc
Aabbcc
aabbcC
aabbCc
aabBcc
aaBbcc
AABBCC
aABBCC
AaBBCC aabbcc
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0
200
400
600
800
1000
500 510 520 530 540 550 560 570 580 590 600 610 620
Fre
quen
cy o
f G
enoty
pes
Yield
All additive
Quantitative Dominance
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0
200
400
600
800
1000
500 510 520 530 540 550 560 570 580 590 600 610 620
Fre
quen
cy o
f G
enoty
pes
Yield
All
additive
1 Dominant,
5 additive
3 Dominant,
3 additive
5 Dominant,
1 additive
Quantitative Dominance
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The performance of the F1 compared to
the mid-parent (m) will be dependant on
the proportion of dominant loci.
There is a relationship between m, the F1
performance, the F2 performance and
dominance (d).
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P2 m F1 P1
500 560 580 620
[d]
m
[a] [a]
P1 = m + [a]
P2 = m – [a]
F1 = m + [d]
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F1
B2 F2 B1
x P2 x self x P1
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F2 = ¼ P1 + ½ F1 + ¼ P2
= ¼ (m+[a]) + ½ (m+[d]) + ¼ (m-[a])
= ¼m + ¼ [a] + ½m + ½[d] + ¼m – ¼ [a]
= m + ½ [d]
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B1 = ½ P1 + ½ F1
= ½ (m+[a]) + ½ (m+[d])
= m + ½ [a] + ½ [d]
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B2 = ½ P2 + ½ F1
= ½ (m-[a]) + ½ (m+[d])
= m - ½ [a] + ½ [d]
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P1 = m + [a]
P2 = m – [a]
F1 = m + [d]
B1 = m + ½ [a] + ½ [d]
B2 = m – ½ [a] + ½ [d]
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P1 = m + [a]
P2 = m – [a]
F1 = m + [d]
B1 = m + ½ [a] + ½ [d]
B2 = m – ½ [a] + ½ [d]
P2 m F1 P1
B2 B1
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P2 = 110; P1 = 170; F1 = 160
[a] = (P1+P2)/n = (110+170)/2 = 30
m = P1 – [a] = 170 – 30 = 140
[d] = F1 – m = 160 – 140 = +20
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P2 = 110; P1 = 170; F1 = 160
[a] = 30; m = 140; [d] = +20
F2 = m + ½ [d] = 140 + 10 = 150
B1 = m + ½[a] + ½[d] = 140+15+10 = 165
B1 = m - ½[a] + ½[d] = 140-15+10 = 135
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P1 = 110; P2 = 170
m = 140; F1 = 160
B1 = 165; B2 = 135
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P1 = 110; P2 = 170
m = 140; F1 = 160
B1 = 165; B2 = 135
P2 m F1 P1
135 165
110 140 160 170
B2 B1
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Testing the
additive/dominance
inheritance model