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σ2P = σ2G + σ2E + 2covG,E     = σ2G + σ2E

The covariance between G and E is assumed to be 0. In other words: there is no dependency of the genotype on the environment, or vice versa. The genotype does not change if the environment changes. This assumption generally is justified as we usually only consider a single type of environment when estimating variance components. In the chapter about evaluation of the breeding program we will see that this is not always the case. But for now we will just follow the general assumption that there is no mutual dependency between genotype and environment.

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Definition

The σ2E is called the   error variance. This includes the variance caused by environmental influences, but also by some other effects.

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