The Correlation Coefficient cannot be greater then the absolute value of 1 because it is a measure of fit between two variables that are not affected by units of measurement.

A correlation coefficient is a measure of how well the data points of a given set of data fall on a straight line. It tells you if there is a linear relationship between the two variables involved (It is possible for two variables that are related but not linearly to have a correlation coefficient of zero).

A correlation coefficient of -1 says that there is a perfect negative linear relationship, and a correlation coefficient of +1 says there is a perfect positive relationship. A correlation coefficient of 0 shows there is no linear relationship present. But correlation coefficients can take values between -1 and +1.

Are you calculating FST? If so then what method are you using? If you could generate a minimal working example that exhibits this effect that would be useful.

Let P1 denote phenotype 1 and P2 phenotype 2 and H their respective heritability:

a GENETIC correlation is given by corr(P1;P2)/sqrt(HP1*HP2)

Therefore it only takes the product of the heritabilities to be very small to get the absolute value of the correlation greater than one :)

However, a more biologically realistic view on the matter would be to say that at least one trait is not heritable and therefore the traits are not genetically correlated since there are no genetic basis to one of them.

Baye: could you please give us some detail of your experimental design, whether you use same trait measured on different environment, different traits measured in the same environment or different traits in different environment? Do you calculate genetic variance and co-variance from replicated trial?

I think Alexandre is referring to the equation used for the same trait measured in different environments. In that case environment and error variances are not accounted, and the estimate easily exceeds the -1 to 1 range. If your analysis falls in this category and you are using the output just for relative comparison, you can standardize your genetic corr matrix to -1 and 1. Or you can use the  formula that dissects the environment and error variance in the first place: rG  = geneticcovP1P2/[sqrt(genetvarp1*geneticvarp2)]. 

I would first estimate the genetic correlation of the trait with itself and the rG should be exactly 1. When it exceeds 1, check the error variance in the analysis of co-variance. It occurs when the the genetic co-variance is either over or under estimated in your ANOVA. 

A correlation value greater than 1 would be an absurdity, theoretically, but I have seen r=1.01 reported. I expect that the objective correlation is 1.00 and the excess would follow from rounding error. 

Probability is there that if any character is less heritable then its genotypic correlation could surpass the value of 1.00. So it would be better to remove that particular character from the analysis and try to analyse the correlation

Hi Baye, did you fix the problem? How did you fix it? I also had the same problem - genetic correlation value being greater than 1.