PBG 650 Advanced Plant Breeding
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Transcript of PBG 650 Advanced Plant Breeding
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
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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
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6
7
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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
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2
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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