5.5 Variance components

The variation in a population can be quantified using statistics related to the Normal Distribution and is expressed as a so-called variance component. In symbols this generally is indicated with a σ². So the phenotypic variance is called σ²_P, the genetic variance is called σ²_G, and the environmental variance is called σ²_E. Our model of P = G + E is also applicable to variance components:

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.

For estimating these variance components, we make use of the fact that if a trait is heritable it would mean that brothers and sisters perform more alike than unrelated individuals. So we combine the phenotypic information on the animals with their genetic relationships (i.e. the pedigree), and then the only component we have no real information about is the environment. Of course we can identify certain components of the environment, like housing and nutrition. But because the influence of the environment already starts at conception, we cannot identify all components of the environment. And some components we are not even aware of, like the potential influence of the weather three weeks ago on the performance today. We can estimate σ²_E by subtracting σ²_G from σ²_P. So E = P – G. Because this is not a very accurate way of estimating the variance due to environmental influences, this variance component is called error variance, rather than environmental variance.