One of paramount interests of quantitative geneticists is the knowledge about how much visible (phenotypic) variability is due to genetic variability. To describe this we usually compute narrow sense heritability h

^{2}= Var(a) / Var(y), where y is phenotypic and a is additive genetic value (see book by Falconer and MacKay). A usual result from analyses is that fitness related traits have much lower heritability (say 0.1 or similar) than morphological traits (say 0.5 or even more). This eventually leads to the conclusion that selection will not be effective for fitness related traits, since there is not much additive genetic variability. However, this can only be partialy true. The heritability can have a small value due to small additive genetic variance and/or large phenotypic variance. It is clear that if there is a lot of environmental variability that the selection can not be the prime force to change the population. However, this still does not mean that we should neglect the genetic variability. David Houle has dealt with this issue and published a paper in Genetics (1992). I have read that paper several times and I always forget the exact conclusion. Well, there is no exact conclusion. However, Houle suggests that heritability is not a good measure of evolvability (ability of population to respond to selection) or variability (strength of forces that maintain and deplete genetic variation). He suggests that standardizing the additive genetic variance with a mean is better, which in turn leads to the suggestion that additive genetic coefficient of variation (CV_{a}= Var(a) / Mean(y)) is a more informative measure than heritability. There is also some more recent work by Houle (his pub. webpage, this looks very interesting), that I need to digest - sometime.An example: we have two populations A and B (this could also be two different traits!), with means 5 and 10, additive genetic variance 5 and 5, heritabilities 0.2 and 0.2. Based on heritabilities we could conclude that selection will have the same effect in both populations, but this is not true in relative meaning. In population A the additive genetic variance is euqal to the mean, whereas it is only half of the mean in population B. The additive genetic coefficient of variations would be 0.45 and 0.22 for population A and B, respectively. This means that we can achive relatively greater response to selection in population A than in population B.

## 2 comments:

Houle's idea is silly. I was asked to calculate some evolabilities in a project, when the trait was a probability measured on the logit scale. Luckily, the idea of a negative evolvability wasn't appealing.

The idea looks like another attempt to replace thinking and understanding the biology with blind faith in numbers.

Hi Bob,

it is nice to read from you! Did you already find a new position?

You are mentioning a good example where heritability is also not very useful. In general the heritability is not nicely defined if we leave the space of linear models. I agree with you that computing the evolvability as sigma_a / mean(logit) is silly. But there should be a way to do this on the observed scale, i.e., on the probabilities. In any case your conclusion is a very good one!

Another example how heritabilities can be wrongly interpreted is the case when we have some additional "random" effects in the model. Heritability is defined as var(a) / var(p), where var(p) = var(a) + var(...) + var(e). Now if we have few additional "random" effects in the model, the heritability will decrease, but this does not mean that there is less genetic variability.

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