ASReml软件讲义ASRemlworkshop.pptVIP

ASReml Workshop,Harry Wu UPSC, Swedish University of Agriculture Science, Sweden CSIRO Plant Industry, Canberra, Australia,Workshop Outline,Linear model Mixed linear model Breeding values ASReml and ConTEXT Primer Example of full-sib mating Example of diallel mating Row-Column design Longitudinal data Spatial analysis,1. What Is a Linear Model?,Y = b1X1 + b 2X2 + b 3X3 + e A linear combination of things (X) multiplied by some coefficients (b) that explain the data (Y), with some error (e) X can be The mean A covariate A factor Want to estimate the coefficients using some data,Put Experiment into a Linear Model,Any experiment can be described by a linear model. How can seed weight (xi) and family (2 families - f1 and f2) affect seedling growth (yi)? The relationship y with x and f can be expressed using a set of simultaneous equations for four seedlings from two families as: y1 = + cx1 + f1 + e1 y2 = + cx2 + f1 + e2 y3 = + cx3 + f2 + e3 y4 = + cx4 + f2 + e4,Put the Linear Model into Matrix,You can get the OLS solution by assuming residuals are iid (independently and identically distributed),Useful Matrix Operations,Transpose Multiplication Trace Determinant Inverse Direct sum ( ) Direct product ( ),2. What Is Mixed Linear Model,A combination of fixed effects and random effects. Fixed: where there are different populations (levels), each with its own mean. We are mostly interested in estimating the means. Random: the levels are random samples from one population. We are interested in the variances (although we might want prediction for the levels). Very powerful at dealing with unbalanced data What are some fixed and random effects?,An Example of Mixed Linear Model,Mixed linear model,A family trial in a replicated experiment: 1. To examine whether there are differences among families 2. Relative importance of variation between-family and between-trees. For the first objective, we can treat family effect either fixed or random, but for the second objective, we have to treat j as random.,yijl = + i + j + ij + eijl,fixed,random,j independently and identically distributed (IID) ij - IID eijl - IID,Mixed Linear Model,Put the scalar model into matrix form,Solution of Mixed Linear Model,Actual solution is through the standard Mixed Model Equation (MME),This Mixed Model can be applied in various genetic trials in forest species.,Traditional Mixed Linear Model in Tree Breeding,In traditional analysis of genetic trial, such as half-sib, full-sib families,Such simple mixed model can be analyzed by most commercial software: SAS GLM,Complex Mixed Linear Model,However, for individual tree model, or multiple-trait, or repeated measure, or spatial model with special variance structure,Such complex mixed model can only be analyzed by specialized software: SAS Mixed, ASReml,Solution of Mixed Linear Model,For solutions need R and G, use and These are the variance of each error and each random effect For simple situations so the variances are needed. They are unknown, but can be estimated Various methods REML is popular ASReml Estimates (co-)variances Solves mixed model equations,REML, Restricted (or Residual) Maximum Likelihood Likelihood of the fixed effects (b) and the data variance (V), given the data (y). A transformation of the data so that fixed effects are excluded Log Likelihood is maximised by iterative methods,ASReml,ASReml is a statistical package that fits linear mixed models using Residual MaximumLikelihood (REML). Uses average information algorithm to climb the likelihood mountain,Likelihood Ratio Test,Fixed effects must be the same in both models Hierarchical models only For single variances 2 * D Log Likelihood where D Log Likelihood is the LL difference with and without the effect (Section 2.5) For multiple variances For correlations against 0 against 1,Other Model Comparators,Non-hierarchical models Akaike Information Criterion Minimise AIC = -2*LogL+2p (p=no. vcs) Bayes Information Criterion Minimise BIC = -2*LogL+p*log(dfe),3. Basic Concept of Breeding Value,Considering a simplest case with individual trees without any replication, with linear model as yi = + i + ei where i is the additive genetic value of individual.,A is the additive genetic relationship matrix with Aij = 2 * and the is the coefficient of coancestry between tree i and j.,The variance and covariance of u is,Basic Concept of Breeding Value,where = E2/A2 = (1-h2)/h2, and since R-1= E-2 I, and G-1= A-2 A-1,Substitute X, Z, this reduces to,If we assume residual errors are unrelated between individuals, R= E2 I, the MME reduced to,Basic Concept of Breeding Value,A numerical example of five individuals in two generations,1. Build A matrix assuming tree 1, 2 and 3 are non-inbred and unrelated 2. Use previous equation to calculate breeding value for tree 1 to 5 assuming h2=0.5 and 0.2 (see BV calculation.xls),Basic Concept of Breeding Value,A numerical example of five individuals in two generations,Basic Concept of Breeding Value,A numerical example of five individuals in two generations,= E2/A2 = (1-h2)/h2,4. ASReml primer,Prepare the data (using a spreadsheet or data base program) Export that data as a .csv file from Excel Prepare a job file with filename extension .as Run the job file with ASReml Review the various output files Revise the job and re-run it, or Extract results for your report Examples:,ConTEXT Primer,1. Install ConText using ContextSetup.exe 2. Copy ASREML.chl to the c:/program files/context/highlighters folder 3. Restart ConText 4. Set up Context to run ASReml a. From the menu select “Options” “Environment Options” b. Go to the tab “Execute Keys” c. Under the “User exec keys” box select “Add” d. For the file extensions, enter “as, asc” e. In the “User exec keys” box, under “as,asc”, select “F9” f. Fill in the other information as below: i. Execute: C:Program FilesASReml2binASRemlV3.exe ii. Parameters: %f iii. Hint: Run ASReml iv. Capture console output: yes v. Scroll console to last line: yes,Case Analysis,Full-sib (2-way treatment in a RCB) Diallel mating structure Row-column design Longitudinal data structure Spatial data analysis,5. Full-sib (2-way treatment in RCB),The phenotypic value can be derived from:,Non-additive SCAMD (i.e. dominance and epistasis) effects can be calculated as:,Full-sib (2-way treatment in RCB),Parental model for full-sib families:,Individual-tree model for full-sib families:,Full-sib (2-way treatment in RCB),Heritability and dominance proportion for a parental model:,and for an individual tree model :,Full-sib (Factorial treatment in RCB),Single-pair matings,Full-sib (Factorial treatment in RCB),Full-factorial matings,Full-sib (Factorial treatment in RCB),Tester (male) design:,Full-sib (Factorial treatment in RCB),Example 2: RAD200p full-factorial design analyses:,Full-sib (Factorial treatment in RCB),6. Diallel Mating Structure,Same parent can be male and female Four types of diallel mating method Method 1 - full diallel including self and reciprocal Method 2 - half diallel with self Method 3 full diallel without self Method 4 half diallel,Diallel Mating Structure,Uniqueness of diallel same individual used for male and female In the Z sub-matrix for additive effect, not a diagonal sub-matrix,The model without design structure is y= + gi + gj + sij + eijk where gi and gj are the ith and jth general combining ability (GCA), and sij is the ijkth SCA effect.,Diallel Mating Structure,Uniqueness of diallel same individual used for male and female In the Z sub-matrix for non-additive effect, a diagonal sub-matrix,The model without design structure is y= + gi + gj + sij + eijk where gi and gj are the ith and jth general combining ability (GCA), and sij is the ijkth SCA effect.,Diallel Mating Structure,Example using SAS Mixed and ASReml Without missing crosses, Diallel-SAS and Diallel-SAS05 With missing crosses, DIAFIXED and DIARAND (Wu and Matheson) ASReml Example: DiallelHaymanM4.as,Diallel analyses - Hayman diallel Methed4 data (1954) rep 2 mother !I father !AS mother y S5E_DiallelHaymanM4.txt !skip 1 y mu rep !r mother and(father) mother.father,Diallel Mating Structure,y mu rep !r mother and(father) mother.father,Diallel Mating Structure,BLUP for GCA and first 8 SCA listed,Diallel Mating Structure,Also can be analysed by individual tree model Diallel analyses - Hayman diallel Methed4 data (1954) genotype !P rep 2 mother 7 father 8 y S5E_DiallelHaymanM4p.txt !skip 1 S5E_DiallelHaymanM4.txt !skip 1 !AISING # Diallel individual tree model y mu rep !r genotype,Diallel Mating Structure,BLUP for GCA compared using diallel model and individual tree model,7. Row-column Design,Half-sib Factorial full-sib Diallel mating Prov/family,RCB Split-plot Incomplete block Lattice design Latin square Row-column,Overall Aim: reducing residual error,Row-column Design,We use a row-column design to demonstrate incomplete block design. The example is based on a CSIRO Casuarina trial. The design (see following figure for layout) There were 60 seedlots, A latinized row-column design for 4 replicates generated, each with six rows and 10 columns. Only 59 seedlots were planted. Each plot consisted of 5 x 5 trees.,5 Row-column Design,Row-column Design,Linear model for RCB yijm = + i + j + eijm Linear model for row and column yijklm = + i + j + ck+ cik + ril + eijklm Analyses were done by RCB, and row-column to demonstrate the extra efficiency using incomplete blocks.,ASReml Example: RCCasuarina.as,Row-column Design,Casuarina Row-Column Design Model Repl 4 Row 6 Column 10 Inoc 2 Prov 59 !I Country 18 DBH Casuarina.csv !SKIP 1 !DOPART 3 !PART 1 # RCB analysis DBH mu Repl Prov !PART 2 # Row-Column fixed DBH mu Repl Column Repl.Row Repl.Column Prov !PART 3 # Row-Column random DBH mu Repl Column Prov !r Repl.Row Repl.Column,Row-column Design,The best provenance changed,Row-column Design,The prediction error reduced,8. Longitudinal Data Structure,Repeated measures on time and space on the same subjects,Longitudinal Data Structure,Longitudinal Data Structure,The mixed linear model is:,Longitudinal Data Structure,Unstructured (US) co-variance matrix between n measurements n(n + 1)/2 parameters to estimate.,i.e. for n = 10 measurements there are 55 parameters to estimate,Longitudinal Data Structure,Parameters can be reduced with a structured variance and covariances: AR1 correlation structure has only one correlation parameter ,Longitudinal Data Structure,Examples using 36 radiata families: 1. Modelling AR1 correlation structure 2. Random regression model,Longitudinal Data Structure,!PART 2 D80 D85 D90 D95 Trait !r Trait.Blk Trait.Family !f mv 1 2 2 0 !S2=1 Trait 0 DIAG 93 188 283 421 Trait.Blk 2 Trait 0 DIAG 1 5 10 17 !GP Blk Trait.Family 2 Trait 0 DIAG 5 20 30 50 !GP Family,First, regard each measurement as independent trait and estimate variance for residual, block and family,Longitudinal Data Structure,!PART 2 D80 D85 D90 D95 Trait !r Trait.Blk Trait.Family !f mv 1 2 2 0 !S2=1 Trait 0 DIAG 93 188 283 421 Trait.Blk 2 Trait 0 DIAG 1 5 10 17 !GP Blk Trait.Family 2 Trait 0 DIAG 5 20 30 50 !GP Family,First, regard each measurement as independent trait and estimate variance for residual, block and family,Longitudinal Data Structure,Source Model terms Gamma Component Comp/SE % C Residual DIAGonal 1 108.362 108.362 16.32 0 U Residual DIAGonal 2 194.844 194.844 16.30 0 U Residual DIAGonal 3 289.454 289.454 16.27 0 U Residual DIAGonal 4 428.241 428.241 16.17 0 U Trait.Blk DIAGonal 1 0.703281 0.703281 0.45 0 P Trait.Blk DIAGonal 2 4.14438 4.14438 1.04 0 P Trait.Blk DIAGonal 3 9.32464 9.32464 1.31 0 P Trait.Blk DIAGonal 4 15.6495 15.6495 1.39 0 P Trait.Family DIAGonal 1 4.64890 4.64890 1.67 0 P Trait.Family DIAGonal 2 17.5049 17.5049 2.40 0 P Trait.Family DIAGonal 3 33.1926 33.1926 2.63 0 P Trait.Family DIAGonal 4 55.7703 55.7703 2.74 0 P,Most Blk effects are not significant,Longitudinal Data Structure,So we focused on correlated residual and family effect,!PART 5 D80 D85 D90 D95 Trait Rep !r Trait.Family !f mv # 1 2 1 0 !S2=1 Trait 0 US !+10 113.5 142.4 215.6 158.6 259.3 330.3 173.1 299.9 397.6 499.4 Trait.Family 2 Trait 0 AR1H 0.9 5 18 33 55 Family,Longitudinal Data Structure,So we focused on correlated residual and family effect,=0.999 12=5.04, 22=21.06, 32=40.25, 42=65.72,Covariance/Variance/Correlation Matrix UnStructured Residual 1 2 3 4 1 97.56 0.9221 0.8347 0.7419 2 128.7 199.6 0.9705 0.9103 3 142.6 237.2 299.3 0.9775 4 155.3 272.5 358.3 449.0,Longitudinal Data Structure,!PART 2 Diam mu Rep Meas !r pol(Meas,2).Family predict Meas Family,Fitting random regression for a two-degree polynomial,Longitudinal Data Structure,Fitting random regression for a two-degree polynomial,3 parameters for each family? pol(Meas,2).Family 1.311 -0.1357 1.904 pol(Meas,2).Family 1.511 1.103 1.828 . pol(Meas,2).Family 2.311 -0.1368 2.261 pol(Meas,2).Family 2.511 1.012 2.163 . pol(Meas,2).Family 3.311 -0.3002 2.338 pol(Meas,2).Family 3.511 0.1568 2.249,9. Spatial Data Analysis,“Things closer together are more likely to be more similar” Saint Ronald A. Fisher,近朱者赤, 近墨者黑,Spatial Data Analysis,Account for macro (trend) or micro-environment variability within site and increase power for detecting differences among genotypes,Spatial Data Analysis,Types of spatial variation Environment of field trials in forestry is usually highly variable Global pattern a gradient or large scale trend (slope, soil depth, old road) Local variation patchy pattern (variation in soil or microclimate) Extraneous variation non-spatial variation (planting procedure, labelling mistakes or measurement errors),Spatial Data Analysis,Methods for spatial analyses Adjustments of data for global and local variation: Nearest neighbour analyses rij=0.5(ri-1,j + ri+1,j) and cij=0.5(ci,j-1 + r i, j+1) Row-column latinised design fitted within replications as random effects permitting different paterns within blocks (i.e. interblock information recovery) Kriging interpolation method smooth surfaces of BLUPs on a spatial grid: 1) variogram - optimal interpolation weights 2) interpolation,Spatial Data Analysis,Semivariance and Variogram The semi-variance (h) was calculated as:,Semivariance increases with distance if there is a spatial association : Variogram,Spatial Data Analysis,The focus of spatial analyses is to model the big R,Spatial Data Analysis,Modelling of the autoregressive process Ordinary least squares errors,AR1 - One-dimensional auto-correlated component in field order,=0.9 =0.6 =0.3,Spatial Data Analysis,Modelling of the autoregressive process,AR1 - One-dimensional auto-correlated component in field order,Spatial Data Analysis,Modelling of the autoregressive process,Two-dimensional separable spatially auto-correlated component,is a first-order autoregressive correlation matrix with an autocorrelation :,Spatial Data Analysis,Two-dimensional separable spatially auto-correlated component,Ending up a very big matrix of nr*nc rows and nr*nc columns,Spatial Data Analysis,Modelling of the autoregressive process,“Nugget” effect unstructured environmental correlation:,Spatial Data Analysis,Modelling of the autoregressive process,RAD195 trial Dothistroma infection data (0-10 scores) surface plot,Spatial Data Analysis,!PART 1 Dothitr_0400 mu !r Rep Plot Genotype_id !f mv 1 2 0 Prow Prow IDEN Ppos Ppos IDEN !PART 2 Dothitr_0400 mu !r Rep Plot Genotype_id !f mv 1 2 0 Prow Prow AR1 0.8 Ppos Ppos AR1 0.8 !PART 3 Dothitr_0400 mu !r Rep Plot Genotype_id units !f mv 1 2 0 Prow Prow AR1 0.8 Ppos Ppos AR1 0.8,Spatial Data Analysis,Spatial Data Analysis,Model 1 gives a variogram that is flat which indicates that the residuals have little spatial structure,Spatial Data Analysis,Making the R matrix have an auto-regressive