PBG 650 Advanced Plant Breeding Module 11: Multiple Traits –Genetic Correlations – Index...
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Transcript of PBG 650 Advanced Plant Breeding Module 11: Multiple Traits –Genetic Correlations – Index...
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 traits 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
2
Y
2
X
hh2
Ar
hh2
r1 2Y
2X
A
Estimates of the genetic correlation - alternatives
• Genetic correlations can be estimated from parent-offspring regression
• Can also estimate genetic correlations from double selection experiments
– observe direct response (R) and correlated response (CR) to selection for each trait
Y
Y
X
X2
A R
CR
R
CRr
Falconer and Mackay, Chapt. 19
XYA
XX YY
Covr
Cov Cov
Parent-offspring covariance for traits X and Y
Parent-offspring covariance for trait X
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