Interpretation of the breeding value and behaviour of herita

Dear All,

Using the function –reml-pred, I extracted the breeding value (bv) and its environmental (e) counterpart of a phenotype y. When I compute the ratio: bv/(bv+e) for each participant, the resulting average is very close to the heritability estimate in GCTA (around 20% for this phenotype). However, I also obtained not plausible values (like 200% or negative values). I plotted this ratio bv/(bv+e) against the phenotypic score (see figure). And it seems that this is due to phenotype values around 0 (the phenotype being centered). It seems logical as bv and e are a decomposition of y so that, when y is near 0, values very close to 0 are used at the numerator and denominator in the ratio, producing instability.
So my questions are:
Is there anyway to avoid that?
What does it means in terms of the usability of the breeding value outside GCTA?
Finally, I’m unsure of the interpretation of the breeding value. Can it be interpreted at the individual level? I ask that because, except around 0, the ratio is pretty constant around 20% so that it does not seem to be individualized. So it is rather a global “breeding value” of the phenotype? If it is the case, it would be great to know examples of when the individual predicted breeding values can be useful.


Figure below, Y axis is bv/(bv+e) for each person, with overall mean close to 20% heritability. The X axis is the centered phenotype. There is a stable straight line around 0.20. However, important instability around 0

Many Thanks!

JB