Statistical software for crop improvement

Experimental design: generating randomised layouts such as alpha-lattice or augmented designs that fit many entries into limited land while controlling field variation. R packages such as agricolae and FielDHub support this.

Single-site analysis: fitting mixed models with genotypes and spatial or block effects to estimate adjusted means (BLUEs) or predictions (BLUPs).

Multi-environment analysis: modelling genotype-by-environment interaction across sites and years to identify stable and locally adapted lines.

Heritability: estimating the share of variation due to genetics, which indicates how much selection will gain.

Genomic prediction: using marker-based relationship matrices to predict breeding values (GBLUP), handled by sommer, rrBLUP and ASReml.

R is free, extensible and the default in academic breeding research, but requires coding. ASReml is widely used in commercial and public breeding for its speed and flexibility with complex variance structures, and is available both standalone and as an R package. SAS remains common in some institutions. META-R provides a menu interface over R for breeders who prefer not to code.

Spatial analysis has become standard: models such as SpATS in R fit smooth surfaces to field trends, often improving precision compared with block-only models.

Treating genotypes as fixed when the goal is selection, ignoring spatial trends, pooling sites without testing interaction, and reporting heritability without the design that produced it. Document model choices so results can be reproduced.

A variety that performs best in one region may not be best in another. Genotype-by-environment interaction, often shortened to G×E, describes this. Statistical software models G×E using approaches such as factor-analytic mixed models, which summarise how genotypes respond across environments, and AMMI or GGE biplots, which visualise which lines win where. Understanding G×E guides decisions about whether to release a broadly adapted variety or several regionally targeted ones. It also informs trial network design: if interaction is large, more test environments are needed to rank lines reliably.

Breeding decisions are made every season and revisited for years, so analyses should be reproducible. Write analyses as scripts rather than clicking through menus, keep scripts under version control, record software and package versions, and store the exact data snapshot used. R Markdown or Quarto documents combine code, results and explanation in one report. These habits make it possible to rerun an analysis when an error is found, to hand work to a new team member, and to defend decisions to reviewers or partners.

Package documentation and vignettes on CRAN are the primary references for lme4, sommer and SpATS. VSN International publishes ASReml user guides. CIMMYT provides documentation for META-R alongside its data repository. Many breeding programmes also share training materials through international research networks, which are useful for learning applied mixed-model analysis on realistic trial data.

Genomic prediction with dense marker data can require substantial memory. Test on a subset first, and consider dedicated servers or cloud instances for large training populations.

Mixed model: a model with both fixed and random effects. BLUE: best linear unbiased estimate of a fixed effect. BLUP: best linear unbiased prediction of a random effect. Heritability: the proportion of variation due to genetics. GBLUP: genomic BLUP using a marker-based relationship matrix. Alpha-lattice: an incomplete block design for many entries. Spatial analysis: modelling field trends by plot position.

Consider a breeder testing 300 wheat lines at four sites in an alpha-lattice design. Data from tablets is exported from the breeding database with plot, block, row, column and genotype identifiers. In R, the breeder first plots yield by field position at each site to check for spatial trends and errors, then fits a single-site spatial model at each location to obtain adjusted values and site-level heritability. Sites with very low heritability are reviewed for problems such as drought damage. A multi-environment mixed model across the remaining sites then estimates genotype effects and their interaction with environment. Lines are ranked on predicted value, compared against check varieties, and the top selections are written back to the database with notes explaining the decision.

The same workflow can add genomic data at the multi-environment step: a marker relationship matrix lets the model borrow information between related lines, improving predictions for lines tested at only a few sites.

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