Multi-environment GWAS and genomic prediction: penalized regression and mixed model approaches

Transcription

1 Multi-environment GWAS and genomic prediction: penalized regression and mixed model approaches Montpellier, 9 June 2015 Fred van Eeuwijk & Willem Kruijer Daniela Bustos Korts, Marcos Malosetti, & Martin Boer WUR-Biometris, Wageningen, The Netherlands

2 WU contribution to EU-DROPS Development of multi-environment GWAS and genomic prediction pipeline with facilities for modelling GxE/QTLxE Incorporation of genetic (phenotyping platforms) and environmental characterizations (envirotyping) in multienvironment models; Predictions for new genotypes in new environments Generalizations to multi-trait multi-environment models Additional constraints on genetic correlations between traits and environments Network models / Crop growth models

3 Two-way fixed genotype x environment interaction ANOVA y ij = μ + g i + e j + ge ij + ε ij μ ij = μ + g i + e j + ge ij ; ε ij ~N(0, σ 2 ) FW ge ij = β i E j + δ ij A AMMI ge ij = a=1 r ai c ai + δ ij P PCA/ GGE/ SREG g ij = p=1 r pi c pi + δ ij F F Factorial regression ge ij = f=1 β fi z fj + δ ij ; ge ij = f=1 x fi α fj + δ ij Grouping ge ij = rc kl + δ i(k)j(l)

4 Multi-environment QTL mapping (linkage & LD) & genomic prediction y ij = μ j + Q q=1 x iq α jq + G ij + ε ij Phenotype = Environmental mean + Environment specific QTLs + Environment specific polygenic genetic effect + Environment specific error {G ij }~MVN(0, Σ); {ε ij }~MVN(0, R) Σ = Σ G Σ E ; Σ G = A for assocation mapping and Σ G = I for QTL mapping Σ E = ΓΓ + Ψ kinship, pedigree, markers (A = WW ) group unstructured, smoothed, diagonalised factor analytic group unstructured, environmental kinship (Jarquin et al., 2014) Environment specific QTLs linear function of environmental covariates y ij = μ j + Q x iq q=1 γ q + δ q z j + G ij + ε ij

5 So m e r elevant p ap er s 4th Annual meeting 25th 29th March 2014, Aachen, Germany

6 Cit at io ns t o Gx E m et ho d o logy p ap er s: Daniela Bu st o s 4th Annual meeting 25th 29th March 2014, Aachen, Germany

7 Ignacio Romagosa Steptoe X Morex: QTLxE for grain yield QTL effects Ppd-H1 C3P51 C6P65 QTL effects ID91 ID91 MAN92 MAN92 MTd91 ID92 MTd91 MTd92 MTd92 MTi91 MTi92 MTi91 SC03 MTi92 SC05 SC03 SKs92 SC05 WA91 SKs92 WA92 WA91 WA Cross-over interaction: 1 Depending 2 3on the site 4 the contribution 5 of 6 the Morex 7 allele can be either positive or negative. Chromosomes Chromosomes There is a clear genetic control of heading, but depending on the meteorological conditions through grain filling it could be either positive or negative to have early heading.

8 L effects QTL effects L effects ID91 QTL effects ID91 ID91 ID91 MAN92 ID92 MAN92 ID92 MAN92 MTd91 MAN92 MTd91 MTd91 MTd92 MTd91 MTd92 MTd92 MTi91 MTd92 MTi91 MTi91 MTi92 MTi91 MTi92 MTi92 SC03 MTi92 SC03 SC03 SC05 SC03 SC05 SKs92 SC05 SKs92 SC05 SKs92 WA91 SKs92 WA91 WA91 WA92 WA91 WA92 WA92 WA ,80 0,60 0,40 0,20 0,00-0,20-0,40-0,60 Steptoe x Morex: Factorial Regression Yield QTL effect (t/ha): Ppd-H1-0,80 8,0 10,0 12,0 14,0 16,0 18,0 Tdif_H Ppd-H1 Morex allele (yellow-red) non-responsive at long photoperiod better adapted to intermediate Tdif_H Sco05 Sco Chromosomes Chromosomes 5 5 SK92 WA MAN MTi92 WA92 MTd92 MTi91 MTd ID91 ID92 R 2 = 0.784; p=0.0002

9 QTL-effect QTLxE 0.20 NP WN94 NP AD94 SV94 GC95 MR CI95 YK YA PR SV average min. temperature period 4

10 Smart tools for Prediction and Improvement of Crop Yield RIL population (n=149) Parents: Yolo Wonder, CM 334 Greenhouse experiments, two locations x two seasons Netherlands (Wageningen) & Spain (Almeria) Crop measurements Plant weight (stem, leaves, fruit; initial and final) Number of internodes Leaf area (initial and final) Fruit harvest (number, weight) Environment Temperature Radiation

11 Multi-trait multi-environment QTL analysis Environments Environments -log10(p -log10(p) Traits x Environments QT L e ffe c ts Ax l.nl 1 Ax l.nl 2 Ax l.sp1 Ax l.sp2 DW F.NL 1 DW F.NL 2 DW F.SP1 DW F.SP2 DW L.NL 1 DW L.NL 2 DW L.SP1 DW L.SP2 DW S.NL 1 DW S.NL 2 DW S.SP1 DW S.SP2 DW V.NL 1 DW V.NL 2 DW V.SP1 DW V.SP2 INL.NL 1 INL.NL 2 INL.SP1 INL.SP2 L AI.NL 1 L AI.NL 2 L AI.SP1 L AI.SP2 L UE.NL 1 L UE.NL 2 L UE.SP1 L UE.SP2 NF. NL 1 NF. NL 2 NF. SP1 NF. SP2 NI.NL 1 NI.NL 2 NI.S P1 NI.S P2 NL E.NL 1 NL E.NL 2 NL E.SP1 NL E.SP2 p t_ frt.nl 1 p t_ frt.nl 2 p t_ frt.sp 1 p t_ frt.sp 2 p t_ l e a f.nl 1 p t_ l e a f.nl 2 p t_ l e a f.s P1 p t_ l e a f.s P2 SL. NL 1 SL. NL 2 SL. SP1 SL. SP2 SL A.NL 1 SL A.NL 2 SL A.SP2 SL A.SP Test profile and additive effects: MTME QT L e ffe c ts Ax l.nl 1 Ax l.nl 2 Ax l.sp1 Ax l.sp2 DW F.NL 1 DW F.NL 2 DW F.SP1 DW F.SP2 DW L.NL 1 DW L.NL 2 DW L.SP1 DW L.SP2 DW S.NL 1 DW S.NL 2 DW S.SP1 DW S.SP2 DW V.NL 1 DW V.NL 2 DW V.SP1 DW V.SP2 INL.NL 1 INL.NL 2 INL.SP1 INL.SP2 L AI.NL 1 L AI.NL 2 L AI.SP1 L AI.SP2 L UE.NL 1 L UE.NL 2 L UE.SP1 L UE.SP2 NF. NL 1 NF. NL 2 NF. SP1 NF. SP2 NI.NL 1 NI.NL 2 NI.S P1 NI.S P2 NL E.NL 1 NL E.NL 2 NL E.SP1 NL E.SP2 p t_ frt.nl 1 p t_ frt.nl 2 p t_ frt.sp 1 p t_ frt.sp 2 p t_ l e a f.nl 1 p t_ l e a f.nl 2 p t_ l e a f.s P1 p t_ l e a f.s P2 SL. NL 1 SL. NL 2 SL. SP1 SL. SP2 SL A.NL 1 SL A.NL 2 SL A.SP1 SL A.SP Chromosomes Chromosomes How useful is multi-trait GWAS? 11 12

12 Frequency Frequency Frequency Number of QTLs and explained variance when increasing model complexity, without going to genomic prediction Figure 7: Histogram of Explained Variance by individual QTLs as detected by ME, MT and MTME analyses. MTME produced far more QTLs than ME and MT but many of the extra QTLs from MTME are of small effects. 8a: Histogram of Explained Variance8b: Histogram of Explained Variancc: Histogram of Explained Variance ME MT MTME Percentage of Explained Variance Percentage Explained Variance by significant QPercentage Explained Variance by significant Percentage Explained Variance by significant Multi-variate (association) analysis is more powerful, especially in the case when not all traits are associated with the genetic variant being tested. Stephens, PLOS One, 2013

13 EU-DROPS example data 253 genotypes 23 environments = management x location x year 15 environmental characterizations/ indices 333k SNPs (S. Négro, S. Nicolas, A. Charcosset) example trait: grain yield

14 Multi-environment GWAS in DROPS At start DROPS, state of the art multi-trait GWAS (GEMMA): fast GWAS up till 10 traits Improvements for DROPS: GWAS up till 100 traits Advantages multi-trait GWAS: more power, higher resolution Allows testing of contrasts for QTLxE Strategies in GWAS modelling and computation Structured models for correlations between genotypes and between environments Increased speed via diagonalization (Zhou & Stephens, 2014), 12h for 253 genotypes, 23 environments and 333k SNPs Improved convergence by EM algorithms (Dahl et al., 2014)

15 Grain yield y ij = μ j + x i α j + G ij + ε ij for each SNP Test H 0 : α 1 =α 2 = = α 23 =0 When H 0 is rejected regress α 1,... α 23 on environmental characterizations/contrasts/indices

16 Regressions of QTL effects on contrasts/indices/characterizations

17 Multi-environment genomic prediction for DROPS Implemented mixed model approach by Dahl et al. (2014). Fast: O(np 2 +p 3 ) instead of O(n 3 p 2 ) QTLs can be included in fixed part model Predictions for new environments via creation environmental relationship matrix on the basis of environmental characterizations Problems Difficult to find appropriate way of including environmental characterizations in relationship matrix. Jarquin et al (2013) uses equal weights, and include genotypic and environmental main effects, so only modelling GE ij term and not G ij. Genotypic main effect, G i : include explicit genotypic main effect or model with main effect QTLs? In the latter case, how many SNPs to include in fixed part? For random part, should all SNPs have equal variance? See Bayes RC and multi-blup approaches for alternatives For random part, should all SNPs have equal weight?

18 Genomic prediction by penalized regression Elastic net: combination of Lasso (L1 penalty) and ridge regression (L2 penalty) Problem 333k SNPs x 15 environmental indices produce more than 5 million interaction terms SNPs are chosen on basis of single environment GWAS scans + to correct for kinship/population structure 10 marker based principal components = about 500 genetic predictors m y ij = X G i,l β G q l=1 l + X E E j,k β k m,q k=1 + l=1,k=1 (X i,l G X j,k E )β lk GE + ε ij Different penalties on β l G, β k E, and β lk GE Accuracies for leave one environment out:

19 Some conclusions for DROPS multi-trait GWAS and genomic prediction Algorithms for fitting multi-trait mixed models developed and implemented Successfully tested for GWAS (power & resolution) Faster than ASReml-R/Genstat, more traits than GEMMA, no convergence problems Environment specific QTL effects regressed on environmental characterizations Further work necessary for defining environmental relations in multi-environment genomic prediction Incorporation of phenotyping platform data

20 Extra slides 1 Fred van Eeuwijk

21 Learning from Nature Genetic architecture underlying resistance to biotic and abiotic stresses in Arabidopsis: A multi-trait genome-wide association mapping approach Fred van Eeuwijk, Marcel Dicke Silvia Coolen, Nelson Davila Olivas, Pingping Huang, Karen Kloth, Manus Thoen Willem Kruijer, Joost van Heerwaarden

22 Learning From Nature Introduction Material Plants exposed to biotic and abiotic stresses, including combined stresses Biotic drought, salt, osmotic, heat Abiotic parasitic plant, phloem feeding aphid, phloem feeding whitefly, cell-content feeding thrips, leaf chewing caterpillar, necrotrophic fungus Combined fungus & caterpillar, drought & fungus, drought & caterpillar, caterpillar and osmotic 350 Arabidopsis accessions phenotyped in multiple experiments 250k SNPs

23 Methods Multi-trait mixed model Genetic correlations Bivariate mixed models for pairs of traits with structuring of random genotype effects by kinship calculated from full set of SNPs = covariance for genomic breeding values QTLs/ candidate genes Multi-trait mixed model GWAS Hypothesis testing within GWAS model context biotic abiotic stresses

24 Genomic (upper right) and phenotypic correlations (lower left) Phenotypic correlations low, genetic correlations show an enriched signal

25 Genomic correlations between traits (bivariate G-BLUP) Structuring of trait/ environmental correlations y it = μ t + G it + ε it ; G it = M m x im a tm

26 Multi-trait GWAS y it = μ t + Q m=1 x im a tm + G it + ε ij

27 Consistent QTLs/ genes y it = μ t + with a tm =a m Q m=1 x im a tm + G it + ε ij

28 Biotic vs abiotic stress y it = μ t + Q m=1 x im a tm with a tm =a t,abiotic or a tm =a t,biotic + G it + ε ij

29 Extra slides 2 Fred van Eeuwijk

30 Crop growth model pepper (integration over time) yield = f(hi, LAI-rate, LUE; Temperature, Light) + error y ij target = f yi components ; z j dt + e ij t f y ij = 1 exp K i LAI i,j,t I j,t t=t 0 LUE i,j FTF i 1 W i FDMC i + ε i,j T j T FTF Genomic prediction for yield from inserting genomic predictions for components into crop growth model not better than genomic prediction for yield from yield itself

31 Accuracy yield predicted from QTLs/ GP for components, within environment (CV) Environment SP1 Strategy QTL_ ST BVS BRR BLA BLV QTL_ MT Direct CGM Direct SP2 CGM

32 Accuracy yield from QTLs/GP for components, across environments (CV) Environment Strategy QTL_ ST BVS BRR BLA BLV QTL_ MT SP1::SP2 CGM SP2::SP1 CGM

33 Causal structure CGM and reconstructions in Spain 1 and 2 Sparse inverse environmental kinship Crop growth model and causal reconstructions of networks for yield and its components define inverse environmental kinship/correlation matrix (compare pedigree for genotypes). The result is a sparse representation of the inverse of the environmental kinship useful for speeding up multi-environment GWAS/ genomic prediction (Willem Kruijer)