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Because in animal breeding we only make use of the prediction of A, and not of G, we should simplify the model of P = G + E to P = A + E. Note that this last E is larger than before because as we cannot estimate them, E also contains the D and I components. It now becomes more obvious why we call σ²_E the error variance: it contains more than only the effect of the environment.

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It is possible to estimate the heritability for a trait in a population if phenotypes and genetic relationships (pedigree) is available. A h² of 0.3 indicates that 30% of the variation you observe in your phenotypes is due to additive genetic differences between the animals. If ALL phenotypic differences are due to genetic differences, then the h² will be 1.0. Larger than 1.0 by definition is not possible. Similarly, if the differences between animals are NOT determined by their genetics, then the h² = 0.0. Smaller than 0.0 by definition is not possible.

Restrictions to estimates of the heritability

 The estimated heritability is always specific for a trait, but also for a particular population in a particular environment. This has two important reasons. First, the influence of the environment will, of course, depend on the environment. Second, as we have seen in the example about genetic variation in human hair colour, genetic variation for a trait may vary between populations.

If phenotypes are recorded in more than one environment, but for the same population, then there may be a third reason for difference in heritability. It could very well be that prerequisites for performance with respect to the trait under consideration may vary between environments. As a consequence, different genotypes may be superior in each of the environments under consideration. For example, if you consider the global Holstein-Friesian cattle population as a single population, then you will compare milk production levels from the Netherlands to those in Bangladesh. It is easy to realise that that may not be fair. It requires different qualities to be a top producer in the Netherlands from those required in Bangladesh. So the genetic variation will be different because partly different genes are required for being a good producer. The environmental variation will also be different because the circumstances are so different. Therefore, you should always estimate the heritability for the trait under selection in your specific population and in a specific environment. However, if somebody else already estimated a heritability for a population very similar to yours that was kept in an environment very similar to yours, then it is fairly safe to assume that the heritabilities will be similar too.

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Table 1. Examples of heritabilities for a number of traits in some populations and species.