PBG 650 Advanced Plant Breeding

Module 11: Multiple Traits– Genetic Correlations– Index Selection

Genetic correlations

• Correlations in phenotype may be due to genetic or environmental causes

• May be positive or negative

• Genetic causes may be due to

– pleiotropy

– linkage

– gametic phase disequilibrium

• The additive genetic correlation (correlation of breeding values) is of greatest interest to plant breeders

– “genetic correlation” usually refers to the additive genetic correlation (rG is usually rA )

• We measure phenotypic correlations

Falconer and Mackay, Chapt. 19; Bernardo, Chapt. 13

Components of the phenotypic correlation

YX PP

PP

Covr

YX PPPP rCov

EAP CovCovCov Includes covariance among residuals and non-additive genetic covariances

YX AA

AA

Covr

YX AAAA rCov

PA h

YXYXYX EEEAAAPPP rrr

P

2

E h1

Components of the phenotypic correlation

YXYXYX P

2

YP

2

XEPYPXAPPP h1h1rhhrr

2

Y

2

XEYXAP h1h1rhhrr

divide by YX PP

• When heritabilities are high, most of the observed phenotypic correlation is due to genetics

• When heritabilities are low, most of the observed rP is due to the environment

• If rA and rE are opposite in sign, rP may be close to zero

– example: stalk strength and ear number in corn

Extimating the genetic correlation

• Genetic correlations can be estimated from the same mating designs used to estimate genetic variances

• Perform analysis of covariance rather than ANOVA

• Mixed model approaches can also be used (ref. below)

Example: half-sib families

2

HS

2

A

HSxEnvHS

2

HS

4

re/)MSMS(

r = #reps, e = #environments

XYXY

XY

HSA

HSxEnvHSHS

Cov4Cov

re/)MCPMCP(Cov

MCP is the Mean Cross Products between trait X and Y

YX

XY

YX

XY

HSHS

HS

AA

A

A

CovCovr

Piepho, H-P and J. Mӧhring. 2011. Crop Sci. 51: 1-6.

Estimates of the genetic correlation

• Genetic correlations vary greatly with gene frequency

– estimates are unique for each population

• Standard errors of estimates of rA are extremely large

• Can also estimate genetic correlations from double selection experiments

– observe direct response (R) and correlated response (CR) to selection for each trait

2

Y

2

X

hh2

Ar

hh2

r1 2Y

2X

A

Y

Y

X

X2

A R

CR

R

CRr

Correlated response to selection

• Consequence of genetic correlation– selection for one trait will cause a correlated response in

the other

• May be unfavorable– example: selection for high yield in corn increases

maturity, plant height, lodging, and grain moisture at harvest

• May be helpful– a correlated trait may have a higher heritability or be

easier and/or less costly to measure than the trait of interest; indirect selection may be more effective than direct selection

Correlated response to selection

• Change in breeding value of Y per unit change in breeding value of X

X

Y

X

YX

A

A

A2

A

AA r

Covb

XX P

2

XAXX hhR ii Direct response to selection for X

XAY RbCRYX

YYX

X

Y

PAYXAAXAX

A

A

AY rhhrhhrCR

iii

coheritability:analagous to h2 in response to direct selection

Indirect selection

• Can we make greater progress from indirect selection than from direct selection?

• In theory, molecular markers should be useful tools for indirect selection because they have an h2=1

• Need to consider other factors (time, cost)

• Is there a benefit to practicing both direct and indirect selection at the same time?

XX

AYY

AXX

AAYY

X

X

h

rh

h

rh

R

CR

X

X

i

i

i

i

is hYrA > hX?

Strategies for multiple trait selection

• So far, we have only considered the case where one trait has economic value, and the secondary (correlated) trait either has no value or should be held at a constant level

• We usually wish to improve more than one trait in a breeding program. They may be correlated or independent from each other.

• Options:– independent culling

– tandem selection

– index selection

Independent culling

• Minimum levels of performance are set for each trait

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10

Trait X

Tra

it Y

Tandem selection

• Conduct one or more cycles of selection for one trait, and then select for another trait

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10

Trait X

Tra

it Y

Select for trait Xin the next cycle

Selection indices

• Values for multiple traits are incorporated into a single index value for selection

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9 10

Trait X

Tra

it Y

Effects of multiple trait selection

• Selection for n traits reduces selection intensity for any one trait

• Reduction in selection intensity per trait is greatest for tandem selection, and least for index selection

• Expected response to selection:

index selection ≥ independent culling ≥ tandem selection

Smith-Hazel Index

• Also called the “optimum index”

• Incorporates information about

– heritability of the traits

– economic importance (weights)

– genetic and phenotypic correlations between traits

Smith-Hazel Index

• We want to improve the aggregate breeding value

• Calculate an index value for each individual

I = b1X1 + b2X2 + …. bnXn = ΣbiXi

ai’s are the economic weights and Ai’s are the breeding values for each trait

b = P-1Ga

H = a1A1 + a2A2 + …. anAn = ΣaiAi

bi’s are the index weights and Xi’s are the phenotypic values for each trait

Ga = Pb

solve for the index weights

G is a matrix of genetic variances and covariancesP is a matrix of phenotypic variances and covariances

Expected gain due to index selection

I 2I

b G b GR

b Pb

i i

P

2

ARi

Selection index example

Traits are oil (1), protein (2), and yield (3) in soybeans on a per plot basis

Brim et al., 1959

b = P-1Ga

b1 σP12 CovP1P2 CovP1P3 -1 σA1

2 CovA1A2 CovA1A3 a1

b2 = CovP1P2 σP22 CovP2P3 CovA1A2 σA2

2 CovA2A3 a2

b3 CovP1P3 CovP2P3 σP32 CovA1A3 CovA2A3 σA3

2 a3

1.74 287.5 477.4 1266 -1 128.7 160.6 492.5 1-1.66 = 477.4 935 2303 160.6 254.6 707.7 0.60.60 1266 2303 5951 492.5 707.7 2103 0.5

I = 1.74Xoil – 1.66Xprotein + 0.60Xyield

Selection indices to improve single traits

• Family index

– selection for a single trait using information from relatives

– related to BLUP

• Covariate index

– selection is practiced on a correlated trait that has no economic value

– aim is to maximize response (direct + indirect) for the trait of interest

Other selection indices for multiple traits

• Desired gains index

• Restricted index– holds certain traits constant while improving other traits

• Multiplicative index– does not require economic weights

– cutoff values established for each trait (similar to independent culling)

• Retrospective index– measures weights that have been used by breeders

b = G-1d d is a matrix of desired gains for each trait

b = P-1s s is a matrix of selection differentials

Base index

• Proposed by Williams, 1962

• Economic weights are used directly as weights in the index

• May be better than the Smith-Hazel index when estimates of variances and covariances are poor.

• It’s quick and easy – can be done on a spreadsheet

I = a1X1 + a2X2 + …. anXn = ΣaiXi

Base index

Suggestions (more of an art than a science)

•Use results from ANOVA and estimates of h2 and rg when prioritizing traits for selection and setting weights

– For traits of greatest importance, use blups or adjust weights to account for differences in h2

– For secondary traits, emphasize traits with high quality data for the particular site or season

– Consider applying some selection pressure to correlated traits

•Standardize genotype means or blups

•Monitor selection differentials for all traits

– Verify desired gains

– Avoid undesirable changes in correlated traits (these will be based on phenotypic correlations, but that’s better than nothing)

I = a1X1 + a2X2 + …. anXn = ΣaiXi

i

P

Y Y