Variación no-aditiva y selección genómica

Miguel A. Toro y Luis Varona

Dpto. Producción Animal, ETS Ingenieros Agrónomos, Madrid. SpainDpto. Anatomía, Embriología y Genética. Facultad de Veterinaria, Zaragoza. Spain

Jornada de Selección Genómica, Zaragoza, 2009

One locus model

Quantitative genetics models including dominance

Genotype Frequency Genotypic value

Additve value

Dominancdeviation

AA p2 a 2qα -2q2d

Aa 2pq d (q-p) α 2pqd

aa q2 -a -2pα -2p2d

α=a+d(q-p) σ2A =2pqα2 σ2

D=(2pqd)2

Infinitesimal model

Quantitative genetics models including dominance

Animal model

y=Xb+Zu+Wd+e

u~N(0, Aσ2A)

d~N(0, Dσ2D)22

'

222

DAGG

DAG

da

)( ln lmknkmij aaaad

One locus with dominance and inbreeding

Finite number of loci model

- Instaed of using coancestry coefficients the model uses artificially created loci to model resemblance among relatives

-The objective is to estimate variance components and to predict breeding values

-Gibbs sampling

True Infinitesimal Finite number of loci (biallelic)

20 10 20 50

Ve 80 78.7 70.7 74.3 80.8

Va 20 18.6 18.5 19.8 21.4

Vd 10 14.4 21.1 15.8 7.2

D -14.1 -14.1 -11.1 -13.8 -14.7

It depends on the number of loci used in the analysis(Pong-Wong et al., 1997)

Estimation of non-additive effects is important-Ignore non-additive effects :

-will produce biased estimates of breeding values-It should have an effect on ranking breeding values

-Include non-additive effects :-It will produce more correct statistical-It will produce more genetic response

Varona & Misztalabout 10%

low h2

high d2

low ihigh % full-sibs (>20%)

-It is associate to inbreeding depression

Dominance effect have been rarely included in genetic evaluation

-computational complexity (?)

-inaccurate estimation of variance components (?)20-100 more data>20% full-sibs

-little evidence of non-additive variance (?)

Estimates of additive and dominance variance respect to the phenotypic variance (Misztal et al., 1998)

Species (breed) Trait Additive Dominance d2/h2

Dairy cattle (Holstein) Milk yield 43.5 5.7 0,13

Fat yield 42.6 7.0 0,16

Protein yield 40.6 4.9 0,12

Stature 45.3 6.9 0,15

Strength 27.8 8.0 0,28

Body depth 34.5 9.8 0,28

Dairy form 23.4 5.3 0,22

Fore udder attachment 24.3 4.7 0,19

Swine (Yorkshire) Number of born alive 8.8 2.2 0.25

21-day litter weight 8.1 6.3 0,78

Days to 104.5 kg 33.1 10.3 0.31

Backfat at 104.5 kg 43.6 4.8 0,11

Beef cattle (Limousin) Postweaning gain 21.0 9.9 0,47

Salmon Body weight 7.8 4.6 0,59

Chicken Egg production 2.3 -

Body weigth 4.6 -

Age at 1st egg 7.4 -

Estimates of additive and dominance variance respect to the phenotypic variance (Crokrak & Roff, 1995)

Wild (Vd / Va)1.17 life-history traits1.06 physiological traits0.19 morphological traits

Domestic (Vd / Va)0.80

How to profit from dominance

Any methodology that pretends to use non-additive effects:

- it must contemplate TWO types of matings:

- matings from which the population will be propagated

- matings to obtain commercial animals

This can be carried out in a single population: there is not need of having separated lines

- selection should be applied not to individuals but to matings (mate selection)

Mating plans (Mating allocation) are used in Animal Breeding

-To control inbreeding

-When economic merit is not linear

-When there is an intermediate optimum (or restricted traits)

-To increase connection among herds

-To profit from dominance genetic effects

How to profit from dominance

CROSSBREEDING

A B

A BAB

ABA B

How to profit from dominanceRECIPROCAL

RECURRENT

SELECTION

A B

A BAB

ABA B

How to profit from dominanceProgeny test with inbreeding

♂ ♀

N

FullsibMating

ProgenyTest

M

♀ Random

Selection

How to profit from dominanceProgeny test scheme

M♂ M♀

N♂ N♀M x n

M♂ M♀

Generation t

Generation t + 1

M x n

Minimum Coancestry

Maximum Coancestry

How to profit from dominance

MATING ALLOCATION

A

A C

CA

Genomic Selection

• Availability of very dense panels of SNPs.

• Methods to use dominance variation should be revisited.

• Mating allocation could the easier option.

Simulation

- Population of Ne=100 during 1000 generations

- Then population was increased up to 500 males and 500 females during 3 generations

- These 3000 (generation 1001,1002 and 1003) individuals were genotyped and phenotyped and used as training population to estimate additive and dominance effects of SNPs

- Generation 1004 was formed from 25 sires and 250 dams of generation 1003

Simulation

Generation 1004 was formed from 25 sires and 250 dams selected from generation 1003

Three strategies of selection compared:

Mass selection using phenotypes with Random Mating

Genomic selection based on additive effects with Random Mating (GS)

Genomic selection based on additive effects and Optimal mating allocation based on dominance effects (GS+OP)

Simulation

Genetic assumptions

-10 chromosomes of 100 cM-10000 loci (9000 SNP and 1000 QTLs)

- Both SNPs and QTLs have two alleles

- Mutation rates were 0.0025 following Meuwissen et al. (2001) for SNPs and 0.00005 for QTLs (about 8000 SNP and 80 QTLs were segregating in generation 1000)

Simulation

Genetic effects

- Additive effects sampled from N(0,1)

- Dominance effects sampled from - N(0,1)

Residual effects

- Residuals were samples from a N(0,1) and rescaled according the desired heritability

Evaluation

BLUP: Animal Model solved with Gibbs sampling

Genomic selection: Estimation of additive and dominance effects with method Bayes A

Genomic selection (method Bayes A) and Optimal mating based on dominance effects with simulated annealing

SNP estimation

Bayes A

jj edgy i

p

iiji

p

iij wx

),0(~g 2gii N ),0(~e 2

eN

)0,2(~ 22 e),(~ 22 Svgi

002.0012.4 Sv

),0(~d 2dii N

),(~ 22 Svdi

Bayes B., 2003

),0(~g 2gN ),0(~e 2

eN

)0,2(~ 22 e

)0,2(~ 22 g

),0(~d 2dN

)0,2(~ 22 d

jj edgy i

p

iiji

p

iij wx

Optimal Mate Allocation

From the 6250 (25 x 250) possible matings, we choose the best 250 based on the dominance prediction of the mating, and we obtain 4 new individuals for each mate.

The algorithm of searching was a simulated annealing.

First generation 11.89%

First generation 22.34%

First generation 5.71%

First generation 16.05%

First generation 5.31%

First generation 14.38%

First generation 2.76%

First generation 8.36%

h2 d2 Bayes A Bayes AMate Sel

Bayes B Bayes BMate Sel

0.20 0.05 0.471 0.527 0.433 0.456

0.20 0.10 0.470 0.575 0.445 0.509

0.40 0,05 0.815 0.815 0.724 0.744

0.40 0.10 0.754 0.875 0.730 0.791

Bayes A vs Bayes B

h2 d2 Additive + Dominance model

Additive model

Advantage (%)

0.20 0.05 0.471 0.431 9.29

0.20 0.10 0.470 0.412 14.08

0.40 0,05 0.815 0.750 2.80

0.40 0.10 0.754 0.733 2.86

Genomic selection including or not dominance in the model (Bayes B)

REMARKS

-Including dominance effects in the model of genomic evaluation increases the accuracy of additive genomic evaluation

up to 15% for h2=0.20 and d2=0.10

-Dominance can be used to improve phenotypic performaces through mating allocation

The increase of response of GSOM (Genomic Selection and Optimal Mating) vs. GS (Genomic Selection) is about 6-22%

BUT

-Selection suffers a fast and deep decay of response after the first generation

-Decay of linkage disequilibrium between markers and causal genes

-Increase of linkage disequilibrium among causal genes due to selection

- Advantage of mating allocation disappear after one generation of response

Gracias