It’s not too uncommon to see animal breeding papers citing a paper by Alan Robertson (1959) to support a genetic correlation of 0.8 as a cut-off point for what is a meaningful difference. What is that based on?

The paper is called ”The sampling variance of the genetic correlation coefficient” and, as the name suggests, it is about methods for estimating genetic correlations. It contains a section about the genetic correlation between environments as a way to measure gene-by-environment interaction. There, Robertson discusses experimental designs for detecting gene-by-environment interaction–that is, estimating whether a genetic correlation between different environments is less than one. He finds that you need much larger samples than for estimating heritabilities. It is in this context that the 0.8 number comes up. Here is the whole paragraph:

No interaction means a genetic correlation of unity. How much must the correlation fall before it has biological or agricultural importance? I would suggest that this figure is around 0.8 and that no experiment on genotype-environment interaction would have been worth doing unless it could have detected, as a significant deviation from unity, a genetic correlation of 0.6. In the first instance, I propose to argue from the standpoint of a standard error of 0.2 as an absolute minimum.

That is, in the context of trying to make study design recommendations for detecting genotype-by-environment interactions, Robertson suggests that a genetic correlation of 0.8 might be a meaningful difference from 1. The paper does not deal with designing breeding programs for multiple environments or the definition of traits, and it has no data on any of that. It seems to be a little bit like Fisher’s p < 0.05: Suggest a rule of thumb, and risk it having a life of its own in the future.

In the process of looking up this quote, I also found this little gem, from ”The effect of selection on the estimation of genetic parameters” (Robertson 1977). It talks about the problems that arise with estimating genetic parameters in populations under selection, when many quantitative genetic results, in one way or another, depend on random mating. Here is how it ends:

This perhaps points the moral of this paper. The individuals of one generation are the parents of the next — if they are accurately evaluated and selected in the first generation, the variation between families will be reduced in the next. You cannot have your cake and eat it.

Literature

Robertson, A. ”The sampling variance of the genetic correlation coefficient.” Biometrics 15.3 (1959): 469-485.

Robertson, A. ”The effect of selection on the estimation of genetic parameters.” Zeitschrift für Tierzüchtung und Züchtungsbiologie 94.1‐4 (1977): 131-135.