Breeder-facing statistical software and automated analysis
I developed an R package that takes multi-environment field-trial data from raw observations to breeder-ready reports. It runs data diagnostics, derives traits, specifies design-aware mixed models, and evaluates and selects among candidate models automatically, reporting BLUPs and, where the data support it, G×E results. The aim is reproducible analysis that reduces the statistical complexity breeders need to manage.
How does accounting for field variation change which genotypes we select?
Each square is one plot of a simulated field trial. A mixed model splits what was measured in each plot into three parts: what the field contributed, what the genotype contributed, and what remains unexplained.
Simulated data. The models are fitted in your browser as you read.
Methods and assumptions
- Simulated trial
- 36 genotypes in three complete replicates, on a field of 9 rows and 12 columns (108 plots). Each replicate is a band of three rows, and genotypes are randomised within replicates. A measurement is 10 + replicate + row + column + genotype + residual, with genotype effects drawn with a standard deviation of 0.8 and residuals with 1. The four example fields differ in what the field adds: a trend across columns, nothing, differences between replicates, or trends along both rows and columns.
- Candidate models
- y = μ + genotype + ey = μ + genotype + replicate + ey = μ + genotype + replicate + row + column + e
- The overall mean μ is the only fixed effect. Genotype, replicate, row and column effects are random and independent, each with its own variance, and e is an independent residual.
- Estimation
- Variance components are estimated by REML. The fit uses Henderson’s mixed model equations, with the residual variance profiled out of the restricted likelihood and the remaining variance ratios found by a Nelder–Mead search. It runs in the browser when the figure comes into view.
- Model comparison
- AIC = −2 log L + 2k, where L is the restricted likelihood and k the number of variance parameters. Restricted likelihoods can be compared only between models with the same fixed effects, which is the case here. Models that differ in their fixed effects would have to be compared by maximum likelihood. A variance estimated at zero still counts as a parameter.
- Predicted genetic values
- BLUPs of the genotype effects, solved from the mixed model equations at the estimated variance components. The whiskers are one standard error of prediction on either side. They do not include the uncertainty in the variance components themselves.
- The split of each plot
- For every plot, measured − μ = field + genotype + unexplained, exactly. The field part is the sum of the predicted replicate, row and column effects of that plot, the genotype part is the BLUP of its genotype, and the rest is the residual. The percentages under the maps are shares of the estimated variance components, not of the variance of the values drawn.
- Accuracy
- The correlation between predicted and true genetic values over the 36 genotypes, which can be shown only because the data are simulated. With complete replicates, the first two models rank genotypes exactly as their plain averages do. Only row and column terms can change the order.
- Choice of examples
- For each kind of field, the seed shown is one whose outcome is close to the average over 160 seeds, so the examples are typical rather than flattering.
- Limitations
- One trait, one trial, no missing plots, and no correlation between neighbouring plots beyond rows and columns. Real trials are rarely this tidy.
