## 2009-03-17

### Describing genetic variability

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.

Bob O'Hara said...

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.

Gregor Gorjanc said...

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.