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CROP BREEDING & GENETICS

Genetic Gain Equation with Correlated Genotype x Environment Effects

Dep. of Plant Sci., North Dakota State Univ., Fargo, ND 58105

^* Corresponding author (ted.helms{at}ndsu.edu)

The genetic gain formula has been used to determine the best allocation of resources. The assumptions of this formula are that genotypes are selected based on the mean of data averaged across several locations within years. When plant breeders select genotypes after the first year of replicated yield tests, the assumptions of the genetic gain formula are violated. For this reason, information provided by the genetic gain formula is not useful for determining the optimum allocation of replicates and environments. Our objectives were to (i) develop a heritability formula that included covariances between genotype-by-environment (G x E) interaction effects for the same genotype evaluated in different environments; and (ii) show how these G x E covariances influence resource allocation strategies to maximize genetic gain. Our operational genetic gain formula considers genetic gain to be a correlated response between the test and target environments and allows for G x E covariances between the same genotype evaluated at two selection sites. When selection was conducted at two sites that had a small G x E component of variance and also conducted at two sites with a large G x E component of variance, the realized gain was equal in the target environments. Optimal resource allocation cannot be decided, based on the genetic gain formula.

Abbreviations: G x E, genotype-by-environment

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