Estimating Genetic Gain — Why the Right Type of BLUP Matters
Plant breeding is one of many reasons for the huge increase in corn yields from 1920 to now. However, there are many confounding factors, including changes in weather, increased fertilization, better weed control, and growing corn at a higher density (# plants / acre). Don Duvick, of Pioneer Hy-Bred / Corteva, popularized the eRa study design to estimate the contribution due to plant breeding. Seeds from genotypes released in different years are planted in the same year and site, at the same density, and with the same amounts of fertilization and weed control. Any observed differences among the genotypes can then be attributed to genetic gain. An extension of this design is to plant genotypes at both the current density, e.g., 35,000 seeds per acre, and the density when released, e.g., 20,000 seeds per acre or 25,000 seeds per acre.
Duvick used a two-stage analysis: estimate the mean yield (or other trait) for each genotype after accounting for the experimental design, then regress the mean yield on year of release. The slope estimates the genetic gain per year. Recent analyses (numerous published papers) have replaced the genotype means with the genotype BLUP. Duvick modeled genotypes as a fixed effect; recent practice has been to model them as a random effect.
I show that this change, when used in a two-stage analysis, systematically underestimates genetic gain. A one-stage analysis, including the year of release, a random effect for genotypes, and the experimental design, provides unbiased estimates of the genetic gain. The various analyses are illustrated using simulated data and a study of root traits.