1/9/97 1

PHENOTYPIC SELECTIONTHEORY AND APPLICATIONPHENOTYPIC SELECTION

THEORY AND APPLICATION

Kendall R. LamkeyUSDA-ARS

Department of AgronomyIowa State University

Ames, IA 50011

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OUTLINE

• Mendelian vs. Quantitative Traits

• Genotypic Value

• Average Effect

• Breeding Value

• Heritability

• Genetic Gain

• Empirical Results

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REFERENCES

Falconer, D. S. 1981. Introduction to quantitative genetics. 2nd ed. Longman, New York.

Lush, J. L. 1994. The genetics of populations. Iowa Agriculture and Home Economics Experiment Station, College of Agriculture, Iowa State University, Ames.

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QUANTITATIVE GENETICS

ContinuousVariationMendelism

Fisher, R. A. 1918. The correlation between relatives on the supposition of Mendelian Inheritance. Trans. Roy. Soc. Edinburgh 52:399-433.

Haldane, J. B. S. 1932. The causes of evolution. Longmans, Green, London

Wright, S. 1921. Systems of Mating. Genetics 6:111-178

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QUANTITATIVE GENETICS

Phenotype

Environment Genotype

Genes

TemperaturePrecipitation

Etc.

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QUANTITATIVE GENETICS

SELECTION

• Selection Must Be on Phenotype or Some Function of Phenotype

• Breeders Only Rarely Know Genotypes for More Than a Few of the Loci an Individual Possesses

• Individuals Chosen As Parents Transmit Only a Sample of Half of the Genes It Has

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QUANTITATIVE GENETICS

SELECTION

• Show Us How to Choose Individuals With the Best Merit (Breeding Value)

• Predict the Outcome of Selection to Compare Different Breeding Schemes

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QUANTITATIVE GENETICS

P = G + E

PHENOTYPIC VALUE (P) = Value observed when the character is measured on an individual

GENOTYPIC VALUE (G) = Value attributable to the particular assemblage of genes possessed by an individual

ENVIRONMENTAL DEVIATION (E) = Value attributable to all nongenetic circumstances that influence phenotype

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QUANTITATIVE GENETICS

Assumptions

• Random Mating Equilibrium

• No Linkage

• No Epistasis

• Diploid Inheritance

f(A) = pf(a) = qp + q = 1

p2AA + 2pqAa + q2aa

Random Mating Population

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GENOTYPIC VALUE

aa Aa AA

-a-4

0 d2

a4

aa Aa AA

6 12 14Yield

MP = (14 + 6)/2 = 10 a = 14 - 10 = 4d = 12 - 10 = 2 d/a = 2/4 = 0.5

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GENOTYPIC VALUE

Genotype Frequency Value Freq x Value

AA p2 a p2a

Aa 2pq d 2pqd

aa q2 -a -q2a

Mean = a(p-q) + 2pqd

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GENOTYPIC VALUE

• With selection we are concerned with the transmission of value from parent to offspring.

• This cannot be determined based on genotypic value alone.

• Parents pass on their genes and not their genotypes to the next generation.

• Genotypes are created anew in each generation.

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GENOTYPIC VALUE

• Individuals transmit genes (alleles) to their progeny.

• One result of this is that some aspects of the value of a particular genotype are unpredictable.

• Selection theory can work only with the predictable aspects of the union of two gametes.

• Therefore, we need to introduce the average effect of a gene.

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AVERAGE EFFECT

P = ijij + E

i = Average (or additive) effect of allele i

ij = Dominance deviation

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AVERAGE EFFECT

Average effect of a gene - the mean deviation from the population mean, of individuals that received the gene from one parent, the gene received from the other parent having come at random from the population.

Average effect of a gene - let a number of gametes carrying A unite at random with gametes from the population; then the mean of the genotypes so produced deviates from the population mean by an amount that is the average effect of the A gene.

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AVERAGE EFFECT

p2AA + 2pqAa + q2aa

pA + qa

pA + qaA

pAA + qaa

Mean = a(p-q) + 2pqd

Mean = pa + qd

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AVERAGE EFFECT

= q[a + d(q - p)]

a= -p[a + d(q - p)]

= a

Average effect of a gene substitution - The mean change in value produced by changing (a) genes at random into (A) genes.

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AVERAGE EFFECT

• Dependent on genotypic value.

• Dependent on gene frequencies.

• Property of the population as well as the genes concerned.

• Average effect of a gene cannot be measured.

• So, we introduce the concept of breeding value.

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BREEDING VALUE

Breeding value is the value of an individual judged by the mean value of its progeny.

The Breeding Value of an individual is equal to the sum of the average effects of the genes it carries. The summation is over pairs of alleles at a locus and over all loci.

Genotype Breeding ValueAA 2

Aa A + a

aa 2a

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0 1 2aa Aa AA

-a

0

d+a

-2p

(q - p)

0

2q

BREEDING VALUE

p =3

4

q =1

4

d =3

4a

q2 2pq p2

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p s

Z

c

P

PHENOTYPIC SELECTION

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Parents

Offs

prin

g

S

R

R = ResponseS = Selection Differential

R = bopS

PHENOTYPIC SELECTION

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BaseBasePopulationPopulation

DevelopDevelopProgenieProgenie

ss

EvaluateEvaluateProgeniesProgenies

IntermateIntermateSelectionsSelections

C1C2..

Cn

C1C2..

Cn

PHENOTYPIC SELECTION

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PHENOTYPIC SELECTION

OBJECTIVES OF SELECTION

• Increase the Frequency of Favorable Alleles, Which Is to Increase the Mean of the Population in the Favorable Direction

• Maintain Genetic Variability for Continued Selection by Intermating Superior Progenies for Each Cycle of Selection.

• Therefore, Enhancing the Probability of Obtaining Superior Genotypes (Lines or Hybrids) From the Population.

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-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

PHENOTYPIC SELECTION

OriginalPopulation

ImprovedPopulation

Best Hybrid FromOriginal Population

Best Hybrid FromImproved Population

XC0 XCn

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• Plant Breeders Determine Merit Based on Phenotypes.

• The Goal of Plant Breeding Is to Separate the Environment From the Breeding Value.

• From a Quantitative Genetic Point of View This Is Equivalent to Maximizing the Heritability.

• From a Statistics/Regression Point of View This Is Equivalent to Maximizing the Correlation Between Phenotype and Breeding Value.

PHENOTYPIC SELECTION

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HERITABILITY

V(P) = V(G) + V(E)

V(P) = V(i)V(j)V(ij) + V(E)

V(P) = V(A) + V(D) + V(E)

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HERITABILITY

V(P) = Variance among phenotypes Phenotypic variance

V(A) = Variance among breeding values Additive variance

V(D) = Variance among dominance deviations Dominance Variance

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HERITABILITY

Heritability = The extent to which phenotypes are determined by genes transmitted from the parents.

h2 = V(A)/V(P)

The goal of an artificial selection program is to maximize heritability

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GENETIC GAIN

( )b

op=

covop

12

V P

R = b Sop S = X XS P-

( )cov =1

2V A

op

( )( )

b =V A

V P= h

op2 R = h S2

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GENETIC GAIN

R = h S2

Z

p

Xp Xs

R = ih2p i =

X XS P

p

-

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GENETIC GAIN

G =ic

yre e

G2

e2

GE2

G2

where,

i = Standardized selection differentialc = parental controly = years per cycler = number of replications per environmente = number of environments

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INCREASING GENETIC GAIN

• Increase Selection Intensity

• Increase Genetic Variance

• Decrease Years per Cycle

• Decrease Phenotypic Variance

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INCREASING GENETIC GAIN

Increase Selection Intensity

G =ic

yre e

G2

e2

GE2

G2

Proportion Selected I

30 of 100 1.149

20 of 100 1.386

10 of 100 1.730

5 of 100 2.018

1 of 100 2.508

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INCREASING GENETIC GAIN

Increase Genetic Variance

G =ic

yre e

G2

e2

GE2

G2

TC-I HS TC-B FS FR S1 S2 Method

0

10

20

30

40

50

60

70

80

Her

itabi

lity

(%)

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INCREASING GENETIC GAIN

G =ic

yre e

G2

e2

GE2

G2

Decrease Years per Cycle

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INCREASING GENETIC GAIN

Decrease Phenotypic Variance

G =ic

yre e

G2

e2

GE2

G2

1 2 3 4 5 6 7 8 9 10Number of Environmnets

0.3

0.4

0.5

0.6

0.7

0.8

Her

itabi

lity

One Rep per EnvironmentTwo Reps per EnvironmentFour Reps per Environment

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PHENOTYPIC SELECTION

APPLICATIONEMPIRICAL RESULTS

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RECIPROCAL RECURRENT SELECTION

BSSSC0 BSCB1C0

HS Families

HS Families

BSSS(R)C1 BSCB1(R)C1

BSSS(R)C9 BSCB1(R)C9

BSSS(R)C12 BSCB1(R)C12

BSSS(R)C1 X BSCB1(R)C1

FS Families

BSSS(R)C12 X BSCB1(R)C12

S1

S1

S1

S1

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RECIPROCAL RECURRENT SELECTION

BSSS - Iowa Stiff Stalk Synthetic

- 16 Inbred Line Synthetic

- Synthesized in Early 1930s

BSCB1 - Iowa Corn Borer Synthetic #1

- 12 Inbred Line Synthetic

- Synthesized in 1940s

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IOWA STIFF STALK SYNTHETIC

Os WD Ind Ill CI CI Ill Oh Ind TR A3G- CI LeI159 I224 420 456 461-3 12E 617 540 HY 3167B AH83 9116 F1B1 313 187-2 23

SingleCrosses

DoubleCrosses

Double-Double Crosses

Bulk Equal Quantities Seed

BSSSC0

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0 2 4 6 8 10 12Cycle

3

4

5

6

7

8

Gra

in Y

ield

(M

g/h

a)

BSSS(R)Cn b = 0.06 Mg/haBSCB1(R)Cn b = 0.06 Mg/haCn x Cn b = 0.28 Mg/ha

IOWA STIFF STALK SYNTHETIC

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C0 C11Cycle

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Gra

in Y

ield

(M

g/h

a)

Total Genetic VarianceAdditive Genetic VarianceDominance Genetic Variance

IOWA STIFF STALK SYNTHETIC

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1.44 2.88 4.32 5.76 7.20 8.64

0

5

10

15

20

25

30

35

Fre

qu

ency

1.44 2.88 4.32 5.76 7.20 8.64

0

5

10

15

20

25

30

35

Fre

qu

ency

1.44 2.88 4.32 5.76 7.20 8.64

0

5

10

15

20

25

30

35

Fre

qu

ency

Grain Yield Mg ha-1

BSSS(R)C0X

BSCB1(R)C0

BSSS(R)C5X

BSCB1(R)C5

BSSS(R)C11X

BSCB1(R)C11

X = 3.87

= 0.72ph

X = 5.01

= 0.73ph

X = 6.64

= 0.63ph

IOWA STIFF STALK SYNTHETIC

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-4

-3

-2

-1

0

1

2

3

4

PC

A2

-4 -3 -2 -1 0 1 2 3 4PCA1

C0

C4

C7C9

C11

BSSS(R) BSCB1(R)

C0 C4

C7

C9

C11

IOWA STIFF STALK SYNTHETIC

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0

10

20

30

40

50

60

70

80

90

Fre

qu

en

cy

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Heterozygosity

Observed HeterozygosityExpected Heterozygosity

BSSS(R)C0

0

10

20

30

40

50

60

70

80

90

Fre

qu

en

cy

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Heterozygosity

Observed HeterozygosityExpected Heterozygosity

BSSS Progenitors

0

10

20

30

40

50

60

70

80

90

Fre

qu

en

cy

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Heterozygosity

Observed HeterozygosityExpected Heterozygosity

BSSS(R)C12

IOWA STIFF STALK SYNTHETIC

Heterozygosity

Population Observed Expected

Progenitors 0.01 0.59

C0 0.44 0.49

C12 0.31 0.34

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IOWA CORN BORER SYNTHETIC #1

0

10

20

30

40

50

60

70

80

90

Fre

qu

en

cy

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Heterozygosity

Observed HeterozygosityExpected Heterozygosity

BSCB1(R)C0

0

10

20

30

40

50

60

70

80

90

Fre

qu

en

cy

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Heterozygosity

Observed HeterozygosityExpected Heterozygosity

BSCB1 Progenitors

0

10

20

30

40

50

60

70

80

90

Fre

qu

en

cy

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Heterozygosity

Observed HeterozygosityExpected Heterozygosity

BSCB1(R)C12Heterozygosity

Population Observed Expected

Progenitors 0.05 0.61

C0 0.52 0.58

C12 0.30 0.32

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BSSS(R)

BSCB1(R)

P

C12

P

C12

0.33

0.26

0.070.66

NEI’S GENETIC DISTANCE

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GENE DIVERSITY

P

C12

C0

0.2

0.3

0.4

0.5

0.6

0.7

Gen

e d

iver

sity Total

Mean within

BSSS(R) and BSCB1(R)

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Full-sib (FS) 5

Half-sib with Inbred Test. (HI) 4

Modified Ear-to-row (MER) 5

Mass selection (MASS) 10

Reciprocal Full-sib (FR) 5

S1 Progeny (S1) 5

S2 Progeny (S2) 4

Last Cycle Method Evaluated

BS11 SELECTION METHODS STUDY

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FSFS BS11BS11 22 100 100 20 20 20 20

MERMER BS11BS11 22 100 100 20 20 20 20

HIHI B79B79 33 100 100 20 20 20 20

S2S2 BS11BS11 33 100 100 20 20 20 20

S1S1 BS11BS11 22 100 100 20 20 20 20

FRFR BS10BS10 22 175 175 20 20 11 11

MASSMASS BS11BS11 1 10000 1001 10000 100 1 1

CycleCycle # Progeny # Progeny Selection Selection Method Tester TimeMethod Tester Time Evaluated Evaluated ** Intermated Intermated Intensity Intensity

*Evaluations based on 2 Reps at 3 Locations

BS11 SELECTION METHODS STUDY

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BS11 SELECTION METHODS STUDY

Grain Yield - Populations Per SeGrain Yield - Populations Per Se

00 11 22 33 44 554.64.6

4.84.8

5.05.0

5.25.2

5.45.4

5.65.6

5.85.8

Mg

ha

Mg

ha-1-1

CycleCycle

S2S2 MER

FR

S1S1

HIHI FS

MASS

ResponseResponse

S2S2 0.21**0.21** 4.54.5MERMER 0.17**0.17** 3.63.6FRFR 0.12**0.12** 2.62.6S1S1 0.09**0.09** 1.91.9HIHI 0.08**0.08** 1.61.6FSFS 0.07**0.07** 1.41.4MASSMASS 0.03**0.03** 0.60.6

Per Cycle %Per Cycle % RR22 = 0.83 = 0.83

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BS11 SELECTION METHODS STUDYStalk Lodging - Populations Per SeStalk Lodging - Populations Per Se

00 11 22 33 44 558.08.0

10.010.0

12.012.0

14.014.0

16.016.0

18.018.0

20.020.0

22.022.0

%%

CycleCycle

ResponsResponsee

S2S2 -2.4** -2.4**MERMER -2.2** -2.2**FSFS -2.2** -2.2** HIHI -2.1** -2.1** S1S1 -2.0**-2.0** FRFR 0.0 0.0 MASSMASS 0.3** 0.3**

Per Cycle Per Cycle

S2S2MER

FR

S1S1

HIHI

FS

MASS24.024.0

RR22 = 0.85 = 0.85

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ACKNOWLEDGEMENTS

Dr. Joanne LabateRoger WeyhrichJode EdwardsPeter GuzmanChris MackKebede MulatuJohn GoldenJim Sears

Dr. Arnel R. HallauerDr. Michael LeeDr. Howie SmithDr. Paul Scott

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1860 1880 1900 1920 1940 1960 1980 2000Year

0102030405060708090

100110120130140150

Gra

in Y

ield

(b

u/a

c)

Open pollinatedOpen pollinatedb = -0.08b = -0.08

Double CrossesDouble Crossesb = 1.10b = 1.10

Single CrossesSingle Crossesb = 2.06b = 2.06

RR22 = 0.96 = 0.96

U.S. CORN YIELD - 1866 to 1996