Alternative single-step type genomic prediction equations

Transcription

1 63rd Annal Meeting of the EAAP Bratislava, Slovakia, Agst 7-3, Alternative single-step tpe genomic prediction eqations N. engler,. Niewhof,3, K. Konstantinov,3, M. oddard 3,4 ULg - emblox Agro-Bio ech, B-53 emblox, Belgim ADHIS, Bndoora, Astralia 3 DPI, Victoria, Bndoora, Astralia 4 Universit of Melborne, Melborne, Astralia

2 Partitioning enetic (Co)variances eneral Model for enomic Prediction wo sorces of genetic (co)variances. Explained b genomic differences between animals Crrentl SNP based Bt can also be known Ls, major gene effects or cop-nmber variant (CNV) based effects. Explained b pedigree polgenic residal Logical choice andom mixed inheritance model Jointl modelling and estimating: SNP (or similar) effects and residal polgenic effects

3 Expectation and variances emarks:, and D can have whatever strctre needed alwas fnction of A (pedigree based relationship) and polgenic (co)variances, where indicates linked to polgenic AND SNP effects strictl genomic (co)variance strctre,. D with D D D e g Var and e g E e g e eneral Model A e.g.,

4 ' g D ' ' ' ' ' ' () () e g e raditional MME for

5 ' g D ' ' ' ' ' ' () () Simpler MME? e g e raditional MME for

6 ' g D ' ' ' ' ' ' () () Simpler MME? Similarit to enetic rops! e g e raditional MME for

7 Alternative MME based on aas-pollack ransformation Please note three advantages:. Inverted here based on inverted A, no genomic relationships! Major advantage, sal method to set-p. Explicit eqations for estimation of SNP effects (g) Major advantage of mlti-step genomic prediction (MS-P) 3. Direct estimation of Major advantage of single-step genomic prediction (SS-P) ' g D ' ' û - A (3)

8 eneral MME based on aas-pollack ransformation ' g D ' '

9 Identification Of wo Blocks in ransformed MME st Block ' g D ' ' g ' ' '

10 Identification Of wo Blocks in ransformed MME nd Block ' g D ' ' g D ' '

11 Practical Considerations In practice not all animals genotped Non-genotped animals = enotped animals = Definition of direct SNP contribtion to EBV (dv) or genotped animals: or non-genotped animals predicted from dv of genotped animals sing selection index theor: d d - d g - - g

12 Not All Animals Are enotped (Sstem II: SNP Sstem) - D g I I - D g - ' ' NB: = non-genotped, = genotped animals

13 Not All Animals Are enotped (Sstem I: BLUP Sstem) irst assme onl genotped animals have records ' ' ' - - g ecovering genetic (co)variance not explained b strictl polgenic effect b assming proportionalit between polgenic and total (co)variance: then - Predicting animals withot genotpes

14 rther Modification BLUP Sstem Introdcing - ' ' ' - g Predicting animals withot genotpes inside MME (Henderson, 976) Lifting restriction on records onl for animals ' ' - - ' - g

15 rther Modification BLUP Sstem Using again, following MME are derived Please note similarit to Baesian procedres to integrate external information into genetic evalations (Vandenplas and engler, ) g ' ' ' - -

16 eassembling Sstems I and II ' g D ' ' ' '

17 eassembling Sstems I and II Alternative MME sing strictl genomic (co)variances ' g D ' ' ' ' ' d ' '

18 Eqivalence with Single-Step MME ' d ' ' ' ' ' ' - - Eqivalence derived from:. Absorb eqations for d into those for. Appl rles inverse of sm of matrices: (3) (4)

19 ' d ' ' ' ' ' ' - - Polgenic and enomic (Co)Variances

20 ' d ' ' ' ' ' ' - - Polgenic and enomic (Co)Variances Often called genomic (co)variance matrix (infact combined one with implicit weights)

21 ' d ' ' ' ' ' ' - - Polgenic and enomic (Co)Variances Definition of polgenic residal as part of total genetic (co)variance

22 ' d ' ' ' ' ' ' - - Polgenic and enomic (Co)Variances represents strictl genomic (co)variance matrix

23 ' d ' ' ' ' ' ' - - Polgenic and enomic (Co)Variances Weight here defined as constant across all traits, however eqations can be modified to allow different weights across traits

24 Most Usefl MME No - Needed ' g D ' ' ' ' Alternative Single Step enomic Prediction (SS-P) Allows combining advantages of SS-P and MS-P Different implementations, other advantages Setting-p as one sstems (cf. above) direct solving Setting-p two sstems as seen before, some advantages: Solving throgh parallel sstems b pdating HS periodicall Alternative SNP Sstems possible alternative models, solvers Exclding some (e.g., preferentiall treated cows), adding other (e.g., external ()EBV for external animals)

25 Conclsions Developed alternative genomic prediction eqations have man advantages: Explicit weighting of genomic (SNP) and polgenic effects Direct estimation of SNP effects Better se of High-Densit SNP panels Other genetic effects (e.g. CNV) can be accommodated Direct estimation of EBV effects enomic relationship matrix never explicitl formed, stored or inversed Implementation straight-forward Based on se of existing software Sstem I and Sstem II can rn in parallel (pdating of HS) Bt additional research reqired: Especiall to test and validate proposed method for large data sets

26 inal emarks eneral consenss Single-step methods combine all sorces of information into accrate rankings for animals with and withot genotpes Especiall adapted for novel traits (e.g., milk fat composition) and more complex models (e.g., mltitrait, random regression model) With increasing nmber of genotped animals eqivalent models not reqiring inverting genomic relationship matrix herefore crrentl different research efforts o get these eqivalent models his development complementar approach becase Not based on (matrix of) relationship differences Bt on partitioning of genetic (co)variances However still inverse of A needed New methods (ax et al. )

27 Acknowledgments ADHIS and DPI - Victoria ( Visiting ellows Project ) Spport for sta of Nicolas engler in Astralia in National nd for Scientific esearch (Belgim) Spport for Nicolas engler as former Senior esearch Associate (ntil end of ) and as recipient of several research and travel grants Eropean Commission, Directorate-eneral for Agricltre and ral Development, nder rant Agreement 78 his std has been carried ot with financial spport from the Commission of the Eropean Commnities, P7, KBBE-7-. It does not necessaril reflect its view and in no wa anticipates the Commission's ftre polic in this area And man colleages, in particlar Jérémie Vandenplas

28 hank o ver mch for or attention