Regional Statistics Course – module 1

Generation, analysis and interpretation of experimental and genetic designs applied to plant breeding

General objectives of the course

Through lectures, practicals and discussion, you will learn:

• Basic experimental designs theory
• Randomized complete blocks, incomplete blocks, augmented and partially-replicated designs
• Analysis of variance, fi xed and mixed models
• Design and analysis of multi-environment trials, including modeling genotype-by-environment interaction
• Spatial analysis of individual and combined experiments
• Genetic designs, selection indices and genomic breeding values (GEBVs)
• Use of statistical software including SAS, GenStat, R, and ASReml

Primary lecturers

Dr. Mateo Vargas, Genetic Resources Program, CIMMYT;
E-mail: vargas_mateo@hotmail.com
Dr. Gregorio Alvarado, Genetic Resources Program, CIMMYT;
E-mail: G.Alvarado@cgiar.org

Program

I. Randomized complete blocks designs (RCBD) and multiple comparison procedures

Objectives:

1. Identify the basic components of variation in a randomized complete blocks design.
2. Analyze information generated from fi eld experiments using RCBD and interpret the results of analysis

Contents:

1. Advantages and disadvantages, fixed effect models
2. Generation of designs using SAS
3. Statistical model and Analysis of Variance
4. Example of analysis and interpretation using SAS, GENSTAT, R
5. Multiple Comparison Tests: Least Signifi cant Diff erence(LSD), Honest Signifi cant Diff erence (Tukey), Scheffé

II. Incomplete blocks designs or lattices

Objectives:

• Identify the basic components of variation in an incomplete blocks design (IBD), recovery of intrablock and interblock information
• Increase the precision of experiments using covariance structures with the purpose of extract correlation sources between experimental plots
• Analyze information generated from experiments in agree with the former designs and interpret the results

Contents:

1. Incomplete Block Designs (BIBDs) or Lattices
2. Advantages of Linear Mixed Models
3. Alpha Lattice Designs: Generation using AlphaWin, DiGGer
4. Statistical modeling with and without covariate(s)
5. Example of analysis and interpretation using SAS, GENSTAT, R
6. Best Linear Unbiased Estimators (BLUEs), LSD, Grand Mean and Coeffi cient of Variation using the Standard Errors of Diff erences (SED)
7. Best Linear Unbiased Predictors (BLUPs), Heritability in Broad Sense (H2) and Genetic Correlations

III. Augmented designs and spatial analysis

Objectives:

1. Identify the basic characteristics and evaluate the advantages of the Augmented Designs and the Spatial Analysis
2. Analyze information generated from experiments based on Augmented Designs and Spatial Analysis, interpretation of the results

Contents:

1. Basic concepts and properties of augmented designs
2. Basic concepts and properties of spatial analysis
3. Generation of augmented designs using DiGGer, GENSTAT and ASREML
4. Analysis and Interpretation of augmented designs and spatial analysis using SAS, GENSTAT and ASREML
5. Analysis and Interpretation of augmented designs and spatial analysis using SAS, GENSTAT and ASREML

IV. Multi Environment trials

Objectives:

1. Increase validation space of conclusions by mean of evaluating trials among various locations, years or combinations between them and make a best selection of genotypes
2. Estimate and interpret the genetic parameters of evaluated populations at multi-environment trials
3. Model and interpret the Genotype by Environment interaction using diff erent strategies
4. Introduce external information of environmental and/ or genotypic covariates for assist in the interpretation of genotype by environment interaction
5. Analyze information generated from multienvironment trials using diff erent software and make the interpetation of analysis outputs

Contents:

1. Combined analysis across multi trials:
   • Statistical models
   • Estimation of BLUEs and BLUPs with and without covariate(s)
   • LSD, Grand Mean and Coeffi cient of Variation using the Standard Errors of diff erences (SED)
   • Heritability in Broad Sense (H² ) and Genetic Correlations among locations
   • Dendrogram and PCA Biplot of genetic correlations matrix among locations
2. Demo of the META: Suite of SAS programs which performs everyone of the all before trials under diff erent conditions: Randomized Complete Blocks Designs, Incomplete Block Designs with and without covariate(s), Individual and Combined Analyses
3. Statistical models for the interpretation of the genotype by environment interaction: AMMI, SREG, GREG, SHMM
4. Statistical models incorporating environmental and/ or genotypic covariates
   • Partial least Squares regression (PLS)
   • Factorial regression (FR)
   • Modelling with structural equations
5. Practical using SAS, GENSTAT, R

V. Genetic designs, selection indices and genomic breeding values (GEBVs)

A. Genetic designs

Objectives:

1. Increase the knowledge of basic issues of genetic plant breeding using statistical software
2. Strategies for comprehension of genetic plant breeding using genetic designs

Contents:

1. Importance of genetic plant breeding
2. A genetic plant breeding defi nition
3. Challenges and needs of the plant breeders
4. Genetic designs
5. How to design a genetic mating scheme, commonly mating designs
   • Single-Pair mating
   • North Carolina I
   • North Carolina II
   • Line by Tester
   • Diallel designs
   • Use of statistical software for analysis of genetic designs
   • Recent advances in genetic designs

B. Phenotypic selection indices: Smith, ESIM, Kempthorne and Nordskog, RESIM

C. Genomic selection indices: Lande and Thompson, Lange and Whitaker

D. Genomic breeding values (GEBVs)