Genomic Prediction and Selection forMulti-Environments with Big Data using the BGLR

statistical package

Biometrics and Statistics Unit, Global Maize and Wheat programs

June, 2015.

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Contents

1 BGLR

2 Prediction in multi-environments

3 Models

4 Cross validation

5 Application examples

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BGLR

BGLR

A novel software for whole genomic regression an prediction forcontinuous, discrete traits, censored and uncensored.Suitable for big p and small n problems.Many non-parametric and parametric models implemented in aconsistent manner.Large collection of Bayesian models included:

Bayesian ridge regression.Bayesian LASSO.BayesA, BayesB, BayesC-π.Reproducing Kernel Hilbert Spaces.Reproducing Kernel Hilbert Spaces with Kernel-Averaging.

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BGLR

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BGLR

BGLR in a nutshell

Data equation: y = η + ε where η = 1µ+∑

X jβj + ul .Piors: Different priors can be assigned to regression coefficients andrandom effects ul , which leads to different models.Model fitting using MCMC algorithms (Gibbs sampler andMetropolis-Hastings) implemented efficiently.

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Prediction in multi-environments

Prediction in multi-environments

In most agronomic traits, the effects of genes are modulated byenvironmental conditions, generating G×E.Researchers working in plant breeding have developed multiple methodsfor accounting for, and exploiting G×E in multi-environment trials.Genomic selection is gaining ground in plant breeding.Most applications so far are based on single-environment/single-traitmodels.Preliminary evidence (e.g., Burgueño et al., 2012) suggests that there isgreat scope for improving prediction accuracy using multi-environmentmodels.The ideas can be taken one step further by incorporating information onenvironmental covariates.

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Prediction in multi-environments

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Prediction in multi-environments

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Models

Models

Model 1 (EL, Environment + Line, no pedigree)

yij = µ+ Ei + Li + eij

Model 2 (EA, Environment + Line, with markers)

yij = µ+ Ei + gj + eij

Model 3 (Environments, Line and interactions markes and environment)

yij = µ+ Ei + gj + Egij + eij

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Models

Assumptions

It is assumed that Ei ∼ N(0, σ2E), g ∼ N(0,σ2

gG) with G being the genomicrelationship matrix and Egij the interaction term between genotypes andenvironment. Eg ∼ N(0, (Z gGZ T

g ) · Z EZ TE), Z g connects genotypes with

phenotypes, Z E connects phenotypes with environments, and · stands forHadamart product between two matrices.

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Cross validation

Cross validation

1 CV1: Prediction of performance of newly developed lines (i.e., lines thathave not been evaluated in any field trials).

2 CV2: Prediction in incomplete field trials; here the aim was to predictperformance of lines that have been evaluated in some environments butnot in others.

See Figure in next slide.

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Cross validation

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Figure 1: Two hypothetical cross-validation schemes (CV1 and CV2) for five lines(Lines 1-5) and five environments (E1-E5), source: Jarquín et al. (2014).

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Application examples

Example 1 Wheat dataset (Ravi, Jessica et al.)

The phenotypic information consists in grain yield for wheat in 5 megaenvironments.

Table 1. Number of lines evaluated in each environment

The problem is to predict 9, 000 unobserved individuals in all theenvironments.

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Application examples

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Table 2. Phenotypic correlations between environments.

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In order to do model fitting we used COP and markers (GBS).1 COP: We computed a relationship matrix (A). The matrix has about

50k × 50k = 2500,000,000 entries.We used BROWSE, the program took several days to finish.We used a ‘ad-hoc’ version of the R program pedigreemm and we got thematrix in about 3 hours.

2 Markers: Information for about 21,000 individuals and 14,000 individualswas available.

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Application examples

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Application examples

Benchmark: Predicting 2014 using previous records

Figure 2: Predictions in testing

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Application examples

The real problem

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Application examples

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Application examples

Example 2: Biparental Tropical maize populations(Xuecai et al.)

Genotypic and phenotypic information for about 20 biparentalpopulations.Low (about 200) and Hight density markers (about 60,000).Individuals evaluated in several environments.

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Figure 3: Results from CV1

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Figure 4: Results from CV2

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Application examples

Collaborators in this work

J. CrossaJuan BurgueñoG. de los CamposJessica RutoskiRavi SinghEnrique AutriqueJesee PolandJuan Carlos Alarcón

Susan DreisigakerPaulino PérezX. ZhangK. SemagnY. BeyeneR. BabuF. San VicenteM. OlsenNewman Samayoua

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Application examples

References

Burgueño, J., G. de-los-Campos, K. Weigel, and J. Crossa. (2012).Genomic prediction of breeding values when modeling genotype ×environment interaction using pedigree and dense molecular markers.Crop Science, 43: 311-320.

Jarquín, D., J. Crossa, X. Lacaze, P. Cheyron, J. Daucourt, J. Lorgeou, F.Piraux, et al . (2014).A reaction norm model for genomic selection using high-dimensionalgenomic and environmental data.Theoretical and Applied Genetics, 127 (3): 595-607.

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